On Atkin-Swinnerton-Dyer congruence relations

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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.
25 pages

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Number Theory, 11F33; 14J27

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http://salesiana.dossiersoluciones.com/handle/123456789/69229

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311287
 http://arxiv.org/abs/math/0311287

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arXiv