On Atkin-Swinnerton-Dyer congruence relations

Wen Ching Winnie Li; Ling Long; Zifeng Yang

doi:10.1016/j.jnt.2004.08.003

On Atkin-Swinnerton-Dyer congruence relations

Wen Ching Winnie Li, Ling Long, Zifeng Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

In this paper, we exhibit a noncongruence subgroup Γ whose space of weight 3 cusp forms S₃(Γ) 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(Γ) by Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.

Original language	English (US)
Pages (from-to)	117-148
Number of pages	32
Journal	Journal of Number Theory
Volume	113
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2004.08.003
State	Published - Jul 2005

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2004.08.003

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title = "On Atkin-Swinnerton-Dyer congruence relations",

abstract = "In this paper, we exhibit a noncongruence subgroup Γ whose space of weight 3 cusp forms S3(Γ) 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(Γ) by Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.",

author = "Li, {Wen Ching Winnie} and Ling Long and Zifeng Yang",

note = "Funding Information: ∗Corresponding author. E-mail addresses: wli@math.psu.edu (W.-C. Winnie Li), linglong@iastate.edu (L. Long), yangzf@mail.cnu.edu.cn (Z. Yang). 1Supported in part by an NSF Grant DMS 99-70651 and an NSA Grant MDA904-03-1-0069. 2Supported in part by an NSF Grant No. DMS 97-29992 and a Liftoff grant from the Clay Mathematical Institute.",

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doi = "10.1016/j.jnt.2004.08.003",

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AU - Li, Wen Ching Winnie

AU - Long, Ling

AU - Yang, Zifeng

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PY - 2005/7

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N2 - In this paper, we exhibit a noncongruence subgroup Γ whose space of weight 3 cusp forms S3(Γ) 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(Γ) by Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.

AB - In this paper, we exhibit a noncongruence subgroup Γ whose space of weight 3 cusp forms S3(Γ) 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(Γ) by Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.

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On Atkin-Swinnerton-Dyer congruence relations

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