# Number theory days

23-27 June 2014
Université Lille 1
Europe/Paris timezone

## On the modularity of reducible mod l Galois representations

24 Jun 2014, 11:45
1h
Salle de réunions (Université Lille 1)

### Salle de réunions

#### Université Lille 1

U.M.R. CNRS 8524 U.F.R. de Mathématiques 59 655 Villeneuve d'Ascq Cédex
Galois representations and modular forms

### Speaker

Nicolas Billerey (Université Clermont-Ferrand 2)

### Description

In this talk, I'll give a modularity result for reducible mod l Galois representations. By analogy with the irreducible case, I'll state some questions regarding characterization and optimization of the different types of modular forms attached to such a given representation. Finally, I'll give an application of these results to the determination of an explicit lower bound for the highest degree of the coefficient fields of newforms of prime level and trivial Nebentypus. This is a joint work with Ricardo Menares.

 Paper