Big image of Galois representations associated with finite slope p-adic families of modular forms

in Loeffler, David; Zerbes, Sarah Livia (Eds.) Elliptic Curves, Modular Forms and Iwasawa Theory: In Honour of John H. Coates' 70th Birthday (2016)

We consider the Galois representation associated with a finite slope, non-CM p-adic family of Hecke eigenforms, and prove that the Lie algebra of its image contains a congruence Lie subalgebra of non ... [more ▼]

We consider the Galois representation associated with a finite slope, non-CM p-adic family of Hecke eigenforms, and prove that the Lie algebra of its image contains a congruence Lie subalgebra of non-trivial level. We describe the largest such level in terms of the congruences of the family with p-adic CM eigenforms. [less ▲]