Abstract

We consider congruences between Eisenstein series and cusp forms — of weight k, level N and character χ of conductor N — modulo large prime divisors of L(1 − k,χ⁻¹). We show that such primes occur in the order of a “global torsion” group attached to the cusp form f, and (under a certain hypothesis) also in the denominator of the algebraic part of the rightmost critical value L_f(k − 1). These occurrences are linked by the Bloch–Kato conjecture.

Keywords

modular form, L-function, Bloch–Kato conjecture

Mathematical Subject Classification

Primary: 11F67, 14G10

Authors