Weight Reduction for Mod l Bianchi Modular Forms

TL;DR

This paper proves that mod l systems of Hecke eigenvalues in the cohomology of certain Bianchi modular forms can be realized with trivial coefficients by increasing the level, simplifying their study.

Contribution

It establishes a weight reduction result for mod l Bianchi modular forms, connecting eigenvalues in cohomology with non-trivial coefficients to those with trivial coefficients.

Findings

Hecke eigenvalues in cohomology can be realized with trivial coefficients after level increase.

The result applies to Bianchi modular forms over imaginary quadratic fields with class number one.

Provides a method to simplify the analysis of mod l eigenvalues in Bianchi modular forms.

Abstract

Let K be an imaginary quadratic field with class number one and ring of integers O. We prove that mod l, a system of Hecke eigenvalues occurring in the first cohomology group of some congruence subgroup Gamma of SL(2,O) can be realized in the first cohomology with trivial coefficients after increasing the level of Gamma by l.