# An Application of Maeda's Conjecture to the Inverse Galois Problem

@article{Wiese2012AnAO,
title={An Application of Maeda's Conjecture to the Inverse Galois Problem},
author={Gabor Wiese},
journal={Mathematical Research Letters},
year={2012},
volume={20},
pages={985-993}
}
• G. Wiese
• Published 26 October 2012
• Mathematics
• Mathematical Research Letters
It is shown that Maeda’s conjecture on eigenforms of level 1 implies that for every positive even d and every p in a density-one set of primes, the simple group PSL2(Fpd) occurs as the Galois group of a number field ramifying only at p. MSC (2010): 11F11 (primary); 11F80, 11R32, 12F12 (secondary).
4 Citations
On the irreducibility and Galois group of Hecke polynomials
Let T_{n,2k}(X) be the characteristic polynomial of the n-th Hecke operator acting on the space of cusp forms of weight 2k for the full modular group (k is any even positive integer >5). We show that
Applying modular Galois representations to the Inverse Galois Problem
For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some
Automorphic Galois representations and the inverse Galois problem
A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are

## References

SHOWING 1-10 OF 12 REFERENCES
On modular forms and the inverse Galois problem
• Mathematics
• 2009
In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL2(Fpn) occurs as the
On projective linear groups over finite fields as Galois groups over the rational numbers
Ideas and techniques from Khare´s and Wintenberger’s preprint on the proof of Serre’s conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups
A Possible Generalization of Maeda’s Conjecture
We report on observations we made on computational data that suggest a generalization of Maeda’s conjecture regarding the number of Galois orbits of newforms of level N=1, to higher levels. They also
Experimental evidence for Maeda's conjecture on modular forms
• Mathematics
• 2012
We describe a computational approach to the verification of Maeda's conjecture for the Hecke operator T2 on the space of cusp forms of level one. We provide experimental evidence for all weights less
Functoriality and the inverse Galois problem
• Mathematics
Compositio Mathematica
• 2008
Abstract We prove that, for any prime ℓ and any even integer n, there are infinitely many exponents k for which $\mathrm {PSp}_n(\mathbb {F}_{\ell ^k})$ appears as a Galois group over $\mathbb {Q}$.
Functoriality and the Inverse Galois problem II: groups of type B_n and G_2
• Mathematics
• 2008
For every finite field F and every positive integer r, there exists a finite extension F' of F such that either SO(2r+1,F') or its simple derived group can be realized as a Galois group over Q. If
on l-adic representations attached to modular forms II
• K. Ribet
• Mathematics
Glasgow Mathematical Journal
• 1985
Suppose that is a newform of weight k on Г1(N). Thus f is in particular a cusp form on Г1(N), satisfying for all n≥1. Associated with f is a Dirichlet character such that for all, .
Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
• Mathematics
• 2013
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves
NON-ABELIAN BASE CHANGE FOR TOTALLY REAL FIELDS
• Mathematics
• 1997
Let F be a number field. A cohomological Hecke eigen cusp form f on GL2(FA) for the adele ring FA of F is called a base change of f if L(s, f) = L(s, ρF ) for ρF = ρ ∣∣ Gal(Q/F ). When f exists, we