Computing the number of certain Galois representations mod $p$

Using the link between mod $p$ Galois representations of $\text{qu}$ 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 $\text{qu}$ on a two–dimensional vector space over $\text{fbar}$ which are irreducible, odd, and unramified outside $p$.