{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:37:49Z","timestamp":1776847069137,"version":"3.51.2"},"reference-count":6,"publisher":"Wiley","license":[{"start":{"date-parts":[[2010,2,1]],"date-time":"2010-02-01T00:00:00Z","timestamp":1264982400000},"content-version":"unspecified","delay-in-days":3318,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2001]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Modular symbols of weight 2 for a congruence subgroup \u0393 satisfy the identity {\u03b1,\u03b3,(\u03b1)}={\u03b2,\u03b3(\u03b2)} for all \u03b1,\u03b2 in the extended upper half plane and \u03b3 \u220a \u0393. The analogue of this identity is false for modular symbols of weight greater than 2. This paper provides a definition of transportable modular symbols, which are symbols for which an analogue of the above identity holds, and proves that every cuspidal symbol can be written as a transportable symbol. As a corollary, an algorithm is obtained for computing periods of cuspforms.<\/jats:p>","DOI":"10.1112\/s146115700000084x","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T11:42:44Z","timestamp":1375789364000},"page":"170-181","source":"Crossref","is-referenced-by-count":2,"title":["Cuspidal Modular Symbols are Transportable"],"prefix":"10.1112","volume":"4","author":[{"given":"William A.","family":"Stein","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Helena A.","family":"Verrill","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S146115700000084X_ref006","unstructured":"6. Stein W. A. , \u2018Explicit approaches to modular abelian varieties\u2019, Ph.D. thesis, University of California, Berkeley (2000)."},{"key":"S146115700000084X_ref004","first-page":"19","volume":"36","author":"Manin","year":"1972","journal-title":"Parabolic points and zeta functions of modular curves"},{"key":"S146115700000084X_ref001","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"S146115700000084X_ref002","volume-title":"Algorithms for modular elliptic curves","author":"Cremona","year":"1997"},{"key":"S146115700000084X_ref005","first-page":"59","volume-title":"Universal Fourier expansions of modular forms. On Artin's conjecture for odd 2-dimensional representations","author":"Merel","year":"1994"},{"key":"S146115700000084X_ref003","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1997.10504599"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S146115700000084X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T18:28:54Z","timestamp":1559845734000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S146115700000084X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"references-count":6,"alternative-id":["S146115700000084X"],"URL":"https:\/\/doi.org\/10.1112\/s146115700000084x","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001]]}}}