Modularity of Scholl representations of low degrees, slides

To the space of d-dimensional cusp forms of weight k > 2 for a noncongruence subgroup of SL(2, Z), Scholl has attached a family of 2d-dimensional compatible l-adic representations of the Galois group over Q. Since his construction is motivic, the associated L-functions of these representations are expected to agree with certain automorphic L-functions according to Langlands´ philosophy. In this talk we shall survey recent progress on this topic. More precisely, we´ll see that this is indeed the case when d=1. This also holds true when d=2, provided that the representation space admits quaternion multiplications. This is a joint work with Atkin, Liu and Long.