Slopes of modular forms and congruences

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2 Scopus citations

Abstract

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 Up. Curiously, we also find a relation between the leading terms of the p-adic expansions of the eigenvalues for Up 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.

Original languageEnglish (US)
Pages (from-to)1-32
Number of pages32
JournalAnnales de l'Institut Fourier
Volume46
Issue number1
DOIs
StatePublished - Jan 1 1996

Keywords

  • Congruences between modular forms
  • Galois representations
  • Slopes of modular forms

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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