{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:53:22Z","timestamp":1776837202699,"version":"3.51.2"},"reference-count":51,"publisher":"American Mathematical Society (AMS)","issue":"344","license":[{"start":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T00:00:00Z","timestamp":1716422400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","award":["2015-04139"],"award-info":[{"award-number":["2015-04139"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","award":["2019-03551"],"award-info":[{"award-number":["2019-03551"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We present and discuss an algorithm and its implementation that is capable of directly determining Fourier expansions of any vector-valued modular form of weight at least\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                    associated with representations whose kernel is a congruence subgroup. It complements two available algorithms that are limited to inductions of Dirichlet characters and to Weil representations, thus covering further applications like Moonshine or Jacobi forms for congruence subgroups. We examine the calculation of invariants in specific representations via techniques from permutation groups, which greatly aids runtime performance. We explain how a generalization of cusp expansions of classical modular forms enters our implementation. After a heuristic consideration of time complexity, we relate the formulation of our algorithm to the two available ones, to highlight the compromises between level of generality and performance that each them makes.\n                  <\/p>","DOI":"10.1090\/mcom\/3847","type":"journal-article","created":{"date-parts":[[2023,5,23]],"date-time":"2023-05-23T10:53:31Z","timestamp":1684839211000},"page":"2861-2891","source":"Crossref","is-referenced-by-count":0,"title":["On the computation of general vector-valued modular forms"],"prefix":"10.1090","volume":"92","author":[{"given":"Tobias","family":"Magnusson","sequence":"first","affiliation":[]},{"given":"Martin","family":"Raum","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,5,23]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1137\/1.9781611976465.32","article-title":"A refined laser method and faster matrix multiplication","author":"Alman, Josh","year":"2021","ISBN":"https:\/\/id.crossref.org\/isbn\/9781611976465"},{"key":"2","isbn-type":"print","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-3-030-80914-0_2","article-title":"Computing classical modular forms for arbitrary congruence subgroups","author":"Assaf, Eran","year":"[2021] \\copyright2021","ISBN":"https:\/\/id.crossref.org\/isbn\/9783030809133"},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/978-3-030-80914-0_4","article-title":"Computing classical modular forms","author":"Best, Alex J.","year":"[2021] \\copyright2021","ISBN":"https:\/\/id.crossref.org\/isbn\/9783030809133"},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"Paper No. 37, 19","DOI":"10.1007\/s40687-018-0155-z","article-title":"Modular forms in Pari\/GP","volume":"5","author":"Belabas, Karim","year":"2018","journal-title":"Res. 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