On Atkin–Swinnerton-Dyer congruence relations
Copyright policy )On Atkin–Swinnerton-Dyer congruence relations
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
- Iowa State University United States
- Pennsylvania State University United States
- Capital Normal University China (People's Republic of)
Algebra and Number Theory, Scholl motive, Mathematics - Number Theory, Atkin--Swinnerton-Dyer congruence relations, 11F33; 14J27, elliptic modular surface, 11F33, Congruences for modular and \(p\)-adic modular forms, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Atkin–Swinnerton-Dyer congruence relations, FOS: Mathematics, 14J27, Number Theory (math.NT), Modular forms for noncongruence subgroups, l-adic representations, Holomorphic modular forms of integral weight, non-congruence subgroup
Algebra and Number Theory, Scholl motive, Mathematics - Number Theory, Atkin--Swinnerton-Dyer congruence relations, 11F33; 14J27, elliptic modular surface, 11F33, Congruences for modular and \(p\)-adic modular forms, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Atkin–Swinnerton-Dyer congruence relations, FOS: Mathematics, 14J27, Number Theory (math.NT), Modular forms for noncongruence subgroups, l-adic representations, Holomorphic modular forms of integral weight, non-congruence subgroup
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