Let f be a normalized eigenform of level N` for some positive integer α and some odd prime ` satisfying gcd(`, n) = 1. A construction of Deligne, Shimura, et. al., attaches an `-adic continuous two-dimensional Galois representation to f . The Refined Conjecture of Serre states that such a representation should in fact arise from a normalized eigenform of level prime to `. In this thesis we pres...
