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On Atkin–Swinnerton-Dyer congruence relations

✍ Scribed by Wen-Ching Winnie Li; Ling Long; Zifeng Yang

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
373 KB
Volume
113
Category
Article
ISSN
0022-314X

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✦ Synopsis

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

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