  In this preprint we prove that any finite slope modular form fits into a
p-adic family of modular forms which is indexed by the weight. Here, the term
p-adic family means that p-adic congruences between weights entail certain
p-adic congruences between the corresponding modular forms. We also show that
the dimension of the slope subspace of the space of modular forms does not
depend on the weight. Both statements are predicted by the Mazur-Gouvea
Conjecture, which has been proven by Coleman using methods from rigid analytic
geometry. In contrast our proof is based on a comparison of (topological) trace
formulas.
