On the modularity of reducible mod l Galois representations

Resumen

Given an odd, semisimple, reducible, 2-dimensional mod l Galois representation, we investigate the possible levels of the modular forms giving rise to it. When the representation is the direct sum of the trivial character and a power of the mod l cyclotomic character, we are able to characterize the primes that can arise as levels of the associated newforms. As an application, we determine a new explicit lower bound for the highest degree among the fields of coefficients of newforms of trivial Nebentypus and prime level. The bound is valid in a subset of the primes with natural (lower) density at least 3/4.

Autores: Billerey, N., Menares, R.

Journal: Mathematical Research Letters

Journal Volume: 23

Journal Issue: 1

Journal Page: 15-41

Tipo de publicación: ISI

Fecha de publicación: 2016

Topics: Galois representations, Modular forms

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n1.a2

URL de la publicación: http://intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0023/0001/a002/index.html