On mod p modular representations which are defined over \F_p

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.Comment: This is the final version, accepted and to appear in Glasnik Matematick