Year: 2022
Type: preprint
Abstract: Let $ρ$ be a mod $\ell$ Galois representation attached to a newform $f$. Explicit methods are sometimes able to determine the image of $ρ$, or even the number field cut out by $ρ$, provided that $\ell$ and the level $N$ of $f$ are small enough; however these methods are not amenable to the case where $\ell$ or $N$ are large. The purpose of this short note is to establish a sufficient condition for the image of $ρ$ to be large and which remains easy to test for moderately large $\ell$ and $N$.
Source: arXiv (Cornell University)
Author: Mascot, Nicolas
Institution: Trinity College Dublin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4320458162