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# On the modularity of reducible mod l Galois representations

## Resumen

Given an odd, semisimple, reducible, 2-dimensional mol 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 mol 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

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