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 $p\le 1999$, 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 $p$.

28 pages, 3 tables