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 language | English (US) |
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Pages (from-to) | 1-32 |
Number of pages | 32 |
Journal | Annales de l'Institut Fourier |
Volume | 46 |
Issue number | 1 |
DOIs | |
State | Published - 1996 |
Keywords
- Congruences between modular forms
- Galois representations
- Slopes of modular forms
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology