  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 $p$.
