Flach classes and generalised Hecke eigenvalues

Alice Pozzi; Henri Darmon

Flach classes and generalised Hecke eigenvalues

School of Mathematics

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Abstract

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.

Original language	English
Title of host publication	Elliptic Curves and Modular Forms in Arithmetic Geometry
Subtitle of host publication	Celebrating Massimo Bertolini's 60th birthday. Milano, Italy, September 16-20, 2022.
Publisher	Springer Nature
Publication status	Accepted/In press - 23 Feb 2025
Event	Elliptic curves and modular forms in arithmetic geometry : Celebrating Massimo Bertolini's 60th birthday - , Italy Duration: 12 May 2022 → 16 May 2022 https://sites.google.com/view/bertolini60/home-page

Conference

Conference	Elliptic curves and modular forms in arithmetic geometry
Country/Territory	Italy
Period	12/05/22 → 16/05/22
Internet address	https://sites.google.com/view/bertolini60/home-page

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@inproceedings{7ef122f8673b4365931746eaf9b1b177,

title = "Flach classes and generalised Hecke eigenvalues",

abstract = "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.",

author = "Alice Pozzi and Henri Darmon",

year = "2025",

month = feb,

day = "23",

language = "English",

booktitle = "Elliptic Curves and Modular Forms in Arithmetic Geometry",

publisher = "Springer Nature",

address = "United Kingdom",

note = "Elliptic curves and modular forms in arithmetic geometry<br/> : Celebrating Massimo Bertolini's 60th birthday ; Conference date: 12-05-2022 Through 16-05-2022",

url = "https://sites.google.com/view/bertolini60/home-page",

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TY - GEN

T1 - Flach classes and generalised Hecke eigenvalues

AU - Pozzi, Alice

AU - Darmon, Henri

PY - 2025/2/23

Y1 - 2025/2/23

N2 - 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.

AB - 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.

UR - https://sites.google.com/view/bertolini60/home-page

M3 - Conference Contribution (Conference Proceeding)

BT - Elliptic Curves and Modular Forms in Arithmetic Geometry

PB - Springer Nature

T2 - Elliptic curves and modular forms in arithmetic geometry<br/>

Y2 - 12 May 2022 through 16 May 2022

ER -

Flach classes and generalised Hecke eigenvalues

Abstract

Conference

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