Date of Award
Master of Science (MS)
Xue , Hui
Let f be a normalized eigenform of level Npα for some positive integer α and some odd prime p satisfying gcd(p,N)=1. A construction of Deligne, Shimura, et. al., attaches a p-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 p.
In this presentation we present a proof of Ribet which allows us to 'strip' these powers of p from the level while still retaining the original Galois representation, i.e., the residual of our new representation arising from level N will remain isomorphic to the residual of our original representation arising from level Npα.
Keaton, Rodney, "Explicit Level Lowering of 2-Dimensional Modular Galois Representations" (2010). All Theses. 986.