On congruences between normalized eigenforms with different sign at a Steinberg prime

  • Luis Victor Dieulefait

    Universitat de Barcelona, Spain
  • Eduardo Soto

    Universitat de Barcelona, Spain
On congruences between normalized eigenforms with different sign at a Steinberg prime cover
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Abstract

Let be a newform of weight on with Fourier -expansion , where denotes the group of invertible matrices with integer coefficients, upper triangular mod . Let be a prime dividing once, , a Steinberg prime. Then, it is well known that . We denote by the field of coefficients of . Let be a finite place in not dividing and assume that the mod Galois representation attached to is irreducible. In this paper we will give necessary and sufficient conditions for the existence of another Hecke eigenform -new of weight on and a finite place of such that and the Galois representations and are isomorphic.

Cite this article

Luis Victor Dieulefait, Eduardo Soto, On congruences between normalized eigenforms with different sign at a Steinberg prime. Rev. Mat. Iberoam. 34 (2018), no. 1, pp. 413–421

DOI 10.4171/RMI/990