Title

Computing mod ℓ Galois representations associated to modular forms for small primes

Publication Name

AIMS Mathematics

Abstract

In this paper, we propose an algorithm for computing mod ℓ Galois representations associated to modular forms of weight k when ℓ < k − 1. We also present the corresponding results for the projective Galois representations. Moreover, we apply our algorithms to explicitly compute the mod ℓ projective Galois representations associated to ∆k for k = 16, 20, 22, 26 and all the unexceptional primes ℓ, with ℓ < k − 1. As an application, for k = 16, 20, 22, 26, we obtain the new bounds Bk of n such that (Math Presents).

Open Access Status

This publication may be available as open access

Volume

8

Issue

12

First Page

28766

Last Page

28779

Funding Number

RGPIN-2019-04209

Funding Sponsor

Natural Sciences and Engineering Research Council of Canada

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Link to publisher version (DOI)

http://dx.doi.org/10.3934/math.20231473