Document Type
Article
Publication Date
2-1-2008
Abstract
In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the p-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigenforms. We also show that there is an automorphic L-function over mathbb{Q} whose local factors agree with those of the l-adic Scholl representations attached to the space of noncongruence cusp forms. © 2007 Springer-Verlag.
Publication Source (Journal or Book title)
Mathematische Annalen
First Page
335
Last Page
358
Recommended Citation
Atkin, A., Li, W., & Long, L. (2008). On Atkin and Swinnerton-Dyer congruence relations (2). Mathematische Annalen, 340 (2), 335-358. https://doi.org/10.1007/s00208-007-0154-7