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Using the link between Galois representations and modular forms established by Serre’s Conjecture, we compute, for every prime $p\le 2593$, a lower bound for the number of isomorphism classes of Galois representation of $\mathbf{Q}$ on a two–dimensional vector space over ${\overline{\mathbf{F}}}_p$ which are irreducible, odd, and unramified outside $p$.