On the Endomorphism Algebra of Abelian Varieties Associated with Hilbert Modular Forms

TL;DR

This paper generalizes a formula for the endomorphism algebra of abelian varieties linked to modular forms, extending it to Hilbert modular forms of weight 2 over fields with odd degree.

Contribution

It extends Quer’s explicit formula for the Brauer class of endomorphism algebras to Hilbert modular forms of parallel weight 2 over odd degree fields.

Findings

Generalized Quer’s formula to Hilbert modular forms

Derived explicit description of endomorphism algebras

Applicable to fields with odd degree over Q

Abstract

In this article, we will generalize an explicit formula proved by Quer for the Brauer class of the endomorphism algebra of abelian varieties associated to modular forms of weight 2 to the case of Hilbert modular forms of parallel weight 2, under the condition that the degree of the base field over Q is an odd number.