TY - JOUR
T1 - Galois representations with quaternion multiplication associated to noncongruence modular forms
AU - Atkin, A. O.L.
AU - Li, Wen Ching Winnie
AU - Liu, Tong
AU - Long, Ling
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
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U2 - 10.1090/S0002-9947-2013-06019-9
DO - 10.1090/S0002-9947-2013-06019-9
M3 - Article
AN - SCOPUS:84884677289
SN - 0002-9947
VL - 365
SP - 6217
EP - 6242
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 12
ER -