On the Fourier coefficients of modular forms. II.
Slopes of modular forms and congruences
On the Fourier coefficients of modular forms
Slopes of modular forms and congruences
Our aim in this paper is to prove congruences between on the one hand certain eigenforms of level and weight greater than 2 and on the other hand twists of eigenforms of level 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 . Curiously, we also find a relation between the leading terms of the -adic...
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