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Article Dans Une Revue Mathematical Research Letters Année : 2016

On the modularity of reducible mod $l$ Galois representations

Résumé

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.
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hal-04614945 , version 1 (17-06-2024)

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Nicolas Billerey, Ricardo Menares. On the modularity of reducible mod $l$ Galois representations. Mathematical Research Letters, 2016, 23 (1), pp.15-41. ⟨10.4310/MRL.2016.v23.n1.a2⟩. ⟨hal-04614945⟩
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