### On the Fourier coefficients of modular forms. II.

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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 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...

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