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We describe the action of Hecke operators on generalised eigenspaces attached to certain mod p cuspidal eigenforms of weight two in terms of certain extension classes of Galois representations constructed by Matthias Flach. This description can be viewed as a partial generalisation to cusp forms of a formula of Barry Mazur for the Eisenstein series of weight two and prime level.

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Flach Classes and Generalised Hecke Eigenvalues

  • 会议论文

  • 发表日期：

    2026年

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  • Henri Darmon,
  • Alice Pozzi

摘要

We describe the action of Hecke operators on generalised eigenspaces attached to certain mod p cuspidal eigenforms of weight two in terms of certain extension classes of Galois representations constructed by Matthias Flach. This description can be viewed as a partial generalisation to cusp forms of a formula of Barry Mazur for the Eisenstein series of weight two and prime level.