English

On Atkin-Swinnerton-Dyer congruence relations

Number Theory 2007-05-23 v3

Abstract

In this paper we exhibit a noncongruence subgroup \G\G whose space of weight 3 cusp forms S3(\G)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 S3(\G)S_3(\G) by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.

Cite

@article{arxiv.math/0311287,
  title  = {On Atkin-Swinnerton-Dyer congruence relations},
  author = {Wen-Ching Winnie Li and Ling Long and Zifeng Yang},
  journal= {arXiv preprint arXiv:math/0311287},
  year   = {2007}
}

Comments

25 pages

R2 v1 2026-07-22T16:59:45.364Z