TY - JOUR
T1 - On Atkin-Swinnerton-Dyer congruence relations
AU - Li, Wen Ching Winnie
AU - Long, Ling
AU - Yang, Zifeng
N1 - Funding Information:
∗Corresponding author. E-mail addresses: [email protected] (W.-C. Winnie Li), [email protected] (L. Long), [email protected] (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.
PY - 2005/7
Y1 - 2005/7
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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U2 - 10.1016/j.jnt.2004.08.003
DO - 10.1016/j.jnt.2004.08.003
M3 - Article
AN - SCOPUS:20444385830
SN - 0022-314X
VL - 113
SP - 117
EP - 148
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -