Galois representations with quaternion multiplication associated to noncongruence modular forms
In this paper we study the compatible family of degree-4 Scholl representations ρℓ associated with a space S of weight κ > 2 noncongruence cusp forms satisfying QuaternionMultiplication over a biquadratic extension of ℚ. It is shown that ρℓ is automorphic, that is, its associated L-function has the same Euler factors as the L-function of an automorphic form for GL4 over ℚ. Further, it yields a relation between the Fourier coefficients of noncongruence cusp forms in S and those of certain automorphic forms via the three-term Atkin and Swinnerton-Dyer congruences. © 2013 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
Atkin, A., Li, W., Liu, T., & Long, L. (2013). Galois representations with quaternion multiplication associated to noncongruence modular forms. Transactions of the American Mathematical Society, 365 (12), 6217-6242. https://doi.org/10.1090/S0002-9947-2013-06019-9