On mod p modular representations which are defined over \F_p

Mathematics – Number Theory

Scientific paper

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This is the final version, accepted and to appear in Glasnik Matematicki

Scientific paper

In this paper, we use techniques of Conrey, Farmer and Wallace to find spaces
of modular forms $S_k(\Gamma_0(N))$ where all of the eigenspaces have Hecke
eigenvalues defined over $\F_p$, and give a heuristic indicating that these are
all such spaces.

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