{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T15:17:53Z","timestamp":1776871073276,"version":"3.51.2"},"reference-count":28,"publisher":"American Mathematical Society (AMS)","issue":"310","license":[{"start":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T00:00:00Z","timestamp":1525132800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We compute Hecke eigenform bases of spaces of level one, degree\u00a0three Siegel modular forms and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2\">\n                        <mml:semantics>\n                          <mml:mn>2<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Euler factors of the eigenforms through weight\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"22\">\n                        <mml:semantics>\n                          <mml:mn>22<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">22<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Our method uses the Fourier coefficients of Siegel Eisenstein series, which are fully known and computationally tractable by the work of H. Katsurada; we also use P.\u00a0Garrett\u2019s decomposition of the pullback of the Eisenstein series through the Witt map. Our results support I.\u00a0Miyawaki\u2019s conjectural lift, and they give examples of eigenforms that are congruence neighbors.\n                  <\/p>","DOI":"10.1090\/mcom\/3218","type":"journal-article","created":{"date-parts":[[2016,10,5]],"date-time":"2016-10-05T11:26:43Z","timestamp":1475666803000},"page":"879-892","source":"Crossref","is-referenced-by-count":4,"title":["Using Katsurada\u2019s determination of the Eisenstein series to compute Siegel eigenforms"],"prefix":"10.1090","volume":"87","author":[{"given":"Oliver","family":"King","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cris","family":"Poor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jerry","family":"Shurman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Yuen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2017,5,1]]},"reference":[{"key":"1","series-title":"Springer Monographs in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-54919-2","volume-title":"Bernoulli numbers and zeta functions","author":"Arakawa, Tsuneo","year":"2014","ISBN":"https:\/\/id.crossref.org\/isbn\/9784431549185"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/PL00005869","article-title":"Siegel modular forms and representations","volume":"104","author":"Asgari, Mahdi","year":"2001","journal-title":"Manuscripta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-2611","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s00029-013-0118-6","article-title":"Siegel modular forms of degree three and the cohomology of local systems","volume":"20","author":"Bergstr\u00f6m, Jonas","year":"2014","journal-title":"Selecta Math. (N.S.)","ISSN":"https:\/\/id.crossref.org\/issn\/1022-1824","issn-type":"print"},{"key":"4","doi-asserted-by":"crossref","unstructured":"S. B\u00f6cherer, \u00dcber die Fourier\u2013Jacobi Entwicklung Siegelscher Eisensteinreihen, Math. Zeitschrift 183 (1983), 21\u201346.","DOI":"10.1007\/BF01187213"},{"issue":"6","key":"5","doi-asserted-by":"publisher","first-page":"1595","DOI":"10.1090\/S0002-9939-00-05586-6","article-title":"On a conjecture of Duke-Imamo\u1e21lu","volume":"128","author":"Breulmann, Stefan","year":"2000","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"6","series-title":"Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6568-7","volume-title":"Sphere packings, lattices and groups","volume":"290","author":"Conway, J. H.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0387985859","edition":"3"},{"key":"7","series-title":"Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68649-8","volume-title":"Siegelsche Modulfunktionen","volume":"254","author":"Freitag, E.","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/3540116613"},{"key":"8","isbn-type":"print","first-page":"114","article-title":"Pullbacks of Eisenstein series; applications","author":"Garrett, Paul B.","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0817631720"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1142\/S1793042113500930","article-title":"On the spinor \ud835\udc3f-function of Miyawaki-Ikeda lifts","volume":"10","author":"Hayashida, Shuichi","year":"2014","journal-title":"Int. J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/1793-0421","issn-type":"print"},{"issue":"1","key":"10","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s12188-009-0028-x","article-title":"On the modularity of the \ud835\udc3a\ud835\udc3f\u2082-twisted spinor \ud835\udc3f-function","volume":"80","author":"Heim, Bernhard","year":"2010","journal-title":"Abh. Math. Semin. Univ. Hambg.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5858","issn-type":"print"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1215\/21562261-1728875","article-title":"Miyawaki\u2019s \ud835\udc39\u2081\u2082 spinor \ud835\udc3f-function conjecture","volume":"52","author":"Heim, Bernhard","year":"2012","journal-title":"Kyoto J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/2156-2261","issn-type":"print"},{"key":"12","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.jnt.2013.07.013","article-title":"Congruences to Ikeda-Miyawaki lifts and triple \ud835\udc3f-values of elliptic modular forms","volume":"134","author":"Ibukiyama, Tomoyoshi","year":"2014","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"3","key":"13","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1215\/S0012-7094-06-13133-2","article-title":"Pullback of the lifting of elliptic cusp forms and Miyawaki\u2019s conjecture","volume":"131","author":"Ikeda, Tamotsu","year":"2006","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1353\/ajm.1999.0013","article-title":"An explicit formula for Siegel series","volume":"121","author":"Katsurada, Hidenori","year":"1999","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"issue":"1","key":"15","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00209-007-0213-5","article-title":"Congruence of Siegel modular forms and special values of their standard zeta functions","volume":"259","author":"Katsurada, Hidenori","year":"2008","journal-title":"Math. Z.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5874","issn-type":"print"},{"issue":"1","key":"16","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1080\/10586458.2010.10129062","article-title":"Exact standard zeta values of Siegel modular forms","volume":"19","author":"Katsurada, Hidenori","year":"2010","journal-title":"Experiment. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1058-6458","issn-type":"print"},{"issue":"2","key":"17","first-page":"109","article-title":"Congruence between Duke-Imamoglu-Ikeda lifts and non-Duke-Imamoglu-Ikeda lifts","volume":"64","author":"Katsurada, Hidenori","year":"2015","journal-title":"Comment. Math. Univ. St. Pauli","ISSN":"https:\/\/id.crossref.org\/issn\/0010-258X","issn-type":"print"},{"issue":"242","key":"18","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1090\/S0025-5718-02-01455-2","article-title":"A mass formula for unimodular lattices with no roots","volume":"72","author":"King, Oliver D.","year":"2003","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"19","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/BF01200463","article-title":"Das Vertauschungsgesetz zwischen Hecke-Operatoren und dem Siegelschen \ud835\udf19-Operator","volume":"46","author":"Krieg, Aloys","year":"1986","journal-title":"Arch. Math. (Basel)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-889X","issn-type":"print"},{"issue":"2","key":"20","doi-asserted-by":"publisher","first-page":"307","DOI":"10.2206\/kyushumfs.46.307","article-title":"Numerical examples of Siegel cusp forms of degree 3 and their zeta-functions","volume":"46","author":"Miyawaki, Isao","year":"1992","journal-title":"Mem. Fac. Sci. Kyushu Univ. Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0373-6385","issn-type":"print"},{"key":"21","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/BF03173489","article-title":"Dimensions of cusp forms for \u0393\u2080(\ud835\udc5d) in degree two and small weights","volume":"77","author":"Poor, C.","year":"2007","journal-title":"Abh. Math. Sem. Univ. Hamburg","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5858","issn-type":"print"},{"issue":"1","key":"22","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1017\/S0004972708001317","article-title":"Lifting puzzles in degree four","volume":"80","author":"Poor, Cris","year":"2009","journal-title":"Bull. Aust. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0004-9727","issn-type":"print"},{"issue":"2","key":"23","first-page":"417","article-title":"On Eisenstein series","volume":"50","author":"Shimura, Goro","year":"1983","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"key":"24","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/BF01597381","article-title":"Einf\u00fchrung in die Theorie der Modulfunktionen \ud835\udc5b-ten Grades","volume":"116","author":"Siegel, Carl Ludwig","year":"1939","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"issue":"4","key":"25","doi-asserted-by":"publisher","first-page":"755","DOI":"10.2307\/2374517","article-title":"On Siegel modular forms of degree three","volume":"108","author":"Tsuyumine, Shigeaki","year":"1986","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"key":"26","series-title":"Lecture Notes in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0072235","volume-title":"Stabile Modulformen und Eisensteinreihen","volume":"1219","author":"Weissauer, Rainer","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/3540171819"},{"key":"27","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/BF02940750","article-title":"Eine Identit\u00e4t zwischen Modulformen zweiten Grades","volume":"14","author":"Witt, Ernst","year":"1941","journal-title":"Abh. Math. Sem. Hansischen Univ.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5858","issn-type":"print"},{"key":"28","unstructured":"D. S. Yuen, \\url{http:\/\/siegelmodularforms.org\/pages\/degree3}"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2018-87-310\/S0025-5718-2017-03218-X\/S0025-5718-2017-03218-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-310\/S0025-5718-2017-03218-X\/S0025-5718-2017-03218-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:33:06Z","timestamp":1776799986000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-310\/S0025-5718-2017-03218-X\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,1]]},"references-count":28,"journal-issue":{"issue":"310","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["S0025-5718-2017-03218-X"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3218","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2017,5,1]]}}}