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Slopes of modular forms and congruences

Douglas L. Ulmer — 1996

Annales de l'institut Fourier

Our aim in this paper is to prove congruences between on the one hand certain eigenforms of level p N and weight greater than 2 and on the other hand twists of eigenforms of level p N 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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