Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fields

Details Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fields Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fields

2011-08-23

arxiv.org/abs/1108.4619v1

Mathematics

Number Theory

30 pages

Scientific paper

Let $ F$ be an imaginary quadratic field and $\mathcal{O}$ its ring of integers. Let $ \mathfrak{n} \subset \mathcal{O} $ be a non-zero ideal and let $ p> 5$ be a rational inert prime in $F$ and coprime with $\mathfrak{n}$. Let $ V$ be an irreducible finite dimensional representation of $ \bar{\mathbb{F}}_{p}[{\rm GL}_2(\mathbb{F}_{p^2})].$ We establish that a system of Hecke eigenvalues appearing in the cohomology with coefficients in $ V$ already lives in the cohomology with coefficients in $ \bar{\mathbb{F}}_{p}\otimes det^e$ for some $ e \geq 0$; except possibly in some few cases.

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