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On Atkin-Swinnerton-Dyer congruence relations
by
Ling Long
Iowa State University
Coauthors: Wen-Ching Winnie Li and Zifeng Yang
A cuspform of noncongruence subgroup and a newform are said to satisfy the Atkin-Swinnerton-Dyer congruence relation if their coefficients are related by some congruence relation given by Atkin and Swinnerton-Dyer. We will exhibit a noncongruence subgroup whose space of weight 3 cusp forms 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 the space of weight 3 forms of the noncongruence subgroup by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.
Date received: April 30, 2004
Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caok-20.