Computing the number of certain Galois representations mod $p$

Abstract

Using the link between mod $p$ Galois representations of \qu and mod $p$ modular forms established by Serre's Conjecture, we compute, for every prime $p\leq 1999$, a lower bound for the number of isomorphism classes of continuous Galois representation of \qu on a two--dimensional vector space over \fbar which are irreducible, odd, and unramified outside $p$.Comment: 28 pages, 3 table