2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146262The main result of this paper is an instance of the conjecture made by Gouvea and Mazur (Math. Res. Lett., 1995) which asserts that for certain values of r the space of r-overconvergent p-adic modular forms of tame level N and weight k should be spanned by the finite slope Hecke eigenforms. Using methods adapted from the work of Buzzard and Calegari I show that for p=2, k = 0, N = 1, this holds for all r in (5/12, 7/12). The proof relies on a certain factorisation of the U_p operator which is known in this case but I conjecture also holds for p = 3 and 5; this conjecture also implies exact formulae for the set of slopes similar to those proved for p=2 by Buzzard and Calegari. The same methods also provide an efficient approach to explicit computations of q-expansions of small slope overconvergent eigenforms, extending the computations of Gouvea and Mazur.Updated version fixing some minor typosNumber Theory11F33text