Explicit Large Image Theorems for Modular Forms

Abstract

Let $k$ and $N$ be positive integers with $k\ge 2$ even. In this paper we give general explicit upper-bounds in terms of $k$ and $N$ from which all the residual representations ${\bar{\rho }}_{f,\lambda }$ attached to non-CM newforms of weight $k$ and level ${\Gamma }_0(N)$ with $\lambda$ of residue characteristic greater than these bounds are "as large as possible". The results split into different cases according to the possible types for the residual images and each of them is illustrated on some numerical examples.

References in corpus (2)

• On the computation of local components of a newform
• On uniform large Galois images for modular abelian varieties

Cited by in corpus (3)

• The Eisenstein ideal with squarefree level
• On the effective version of Serre's open image theorem
• Modular forms of arbitrary even weight with no exceptional primes