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 Lf (k − 1). These occurrences are linked by the Bloch-Kato conjecture.
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