201005.4105v2 Galois Representations with Quaternion Multiplications Associated to Noncongruence Modular Forms

In this paper we study the compatible family of degree-4 Scholl representations ρℓassociated with a space S of weight κ > 2 noncongruence cusp forms satisfying Quaternion Multiplications 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 G..