On Atkin-Swinnerton-Dyer congruence relations

Wen Ching Winnie Li, Ling Long, Zifeng Yang

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In this paper, we exhibit a noncongruence subgroup Γ whose space of weight 3 cusp forms S3(Γ) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to S3(Γ) by Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.

Original languageEnglish (US)
Pages (from-to)117-148
Number of pages32
JournalJournal of Number Theory
Issue number1
StatePublished - Jul 2005

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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