2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142332In this paper, we use techniques of Conrey, Farmer and Wallace to find spaces of modular forms $S_k(Γ_0(N))$ where all of the eigenspaces have Hecke eigenvalues defined over $\F_p$, and give a heuristic indicating that these are all such spaces.This is the final version, accepted and to appear in Glasnik MatematickiNumber Theory11F11; 11F33text