Slopes of modular forms and congruences

Our aim in this paper is to prove congruences between on the one hand certain eigenforms of level pN and weight greater than 2 and on the other hand twists of eigenforms of level pN and weight 2. One knows a priori that such congruences exist; the novelty here is that we determine the character of the form of weight 2 and the twist in terms of the slope of the higher weight form, i.e., in terms of the valuation of its eigenvalue for U_p. Curiously, we also find a relation between the leading terms of the p-adic expansions of the eigenvalues for U_p of the two forms. This allows us to determine the restriction to the decomposition group at p of the Galois representation modulo p attached to the higher weight form.