Minimal lifts of dihedral 2-dimensional Galois representations

Abstract

In this paper we study the connection between odd dihedral 2-dimensional modulo p Galois representations and modular forms with complex multiplication. More precisely, we prove that, for every such representation satisfying some explicit conditions, there exists a modular form giving rise to it of the type given by Serre’s conjecture (in its strong version) with the additional property of having complex multiplication.