On Atkin-Swinnerton-Dyer congruence relations
Wen-Ching Winnie Li, Ling Long, Zifeng Yang
Abstract
In this paper we exhibit a noncongruence subgroup whose space of weight 3 cusp forms S3() 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() by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.
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