On the modularity of reducible mod l Galois representations
Given an odd, semisimple, reducible, 2-dimensionalGalois 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 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 .
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