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arXiv · 1309.3717

On the modularity of reducible mod l Galois representations

Nicolas Billerey·Ricardo Menares
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Abstract

We prove that every odd semisimple reducible (2-dimensional) mod l Galois representation arises from a cuspidal eigenform. In addition, we investigate the possible different types (level, weight, character) of such a modular form. 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 one half.

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Nicolas Billerey, Ricardo Menares. 2013-09-15. On the modularity of reducible mod l Galois representations. https://arxiv.org/abs/1309.3717

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