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# Mathematical Research Letters

## Volume 15 (2008)

### Number 3

### On modular weights of Galois representations

Pages: 537 – 542

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n3.a13

#### Author

#### Abstract

Let $F$ be a totally real field and $\rho: \Gal(\overline{F}/F) \to \GL_2(\Fpbar)$ a Galois representation whose restriction to a decomposition group at some place dividing $p$ is irreducible. Suppose that $\rho$ is modular of some weight $\sigma$. We specify a set of weights, not containing $\sigma$, such that $\rho$ is modular for at least one weight in this set.