On Atkin–Swinnerton-Dyer congruence relations

Wen-Ching Winnie Li,Ling Long,Zifeng Yang

Journal of Number Theory（2005）

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摘要

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.

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关键词

Modular forms for noncongruence subgroups,Atkin–Swinnerton-Dyer congruence relations,l-adic representations

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