Seminar des SFB/TRR 326 GAUS Quantitative level lowering for modular forms

  • Freitag, 13. Juni 2025, 13:30 Uhr
  • INF 205, SR A und Livestream
    • Dr. Mohaned Moakher (University of Pittsburgh)
  • Adresse

    INF 205, SR A und Livestream

  • Livestream

  • Veranstalter

  • Veranstaltungstyp

Given a Hilbert modular form f of weight two over a totally real field F, we can associate to it a finite module Phi(f) known as the congruence module for f, which measures the congruences that f satisfies with other forms. When f is transferred to a quaternionic modular form f_D over a quaternion algebra D via the Jacquet-Langlands correspondence, we can similarly define a congruence module Phi(f_D) for f_D. Pollack and Weston proposed a quantitative relationship between the sizes of Phi(f) and Phi(f_D), expressed in terms of invariants associated to f and D. In this talk, I will outline the ideas underlying the proof of this relationship. The approach combines a method of Ribet and Takahashi with new techniques introduced by Böckle, Khare, and Manning.

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