On Atkin-Swinnerton-Dyer congruence relations

Details On Atkin-Swinnerton-Dyer congruence relations On Atkin-Swinnerton-Dyer congruence relations

2003-11-17

arxiv.org/abs/math/0311287v3

Mathematics

Number Theory

25 pages

Scientific paper

In this paper we exhibit a noncongruence subgroup $\G$ whose space of weight 3 cusp forms $S_3(\G)$ 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 $S_3(\G)$ by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.

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