On Atkin-Swinnerton-Dyer congruence relations
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. © 2004 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Journal of Number Theory
Li, W., Long, L., & Yang, Z. (2005). On Atkin-Swinnerton-Dyer congruence relations. Journal of Number Theory, 113 (1), 117-148. https://doi.org/10.1016/j.jnt.2004.08.003