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Computing the number of certain Galois representations mod $p$

Tommaso Giorgio Centeleghe — 2011

Journal de Théorie des Nombres de Bordeaux

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

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Computing the number of certain Galois representations mod p

Computing the number of certain Galois representations mod $p$