Weight reduction for cohomological mod p modular forms over imaginary quadratic fields
Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2014), pp. 45-71.

Let F be an imaginary quadratic field and 𝒪 its ring of integers. Let 𝔫𝒪 be a non-zero ideal and let p>5 be a rational inert prime in F and coprime with 𝔫. Let V be an irreducible finite dimensional representation of 𝔽 ¯ p [ GL 2 (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 𝔽 ¯ p det e for some e0; except possibly in some few cases.

Soient F un corps quadratique imaginaire et 𝒪 son anneau d’entiers. Soient 𝔫𝒪 un idéal non nul et p>5 un nombre premier inerte dans F copremier avec 𝔫. Soit V une représentation irréductible de dimension finie de 𝔽 ¯ p [ GL 2 (𝔽 p 2 )]. Nous établissons qu’un système de valeurs propres de Hecke appartenant au groupe de cohomologie â ?¡ coefficients dans V appartient aussi au groupe de cohomologie â ?¡ coefficients dans 𝔽 ¯ p det e pour e0 à l’exception, éventuellement, de quelques cas.

Received:
Published online:
DOI: 10.5802/pmb.4
Classification: 11F75,  11F67,  11F25,  11F41
Keywords: Modular forms modulo p, imaginary quadratic fields, Hecke operators, Serre weight
Mohamed, Adam 1

1 Universität Duisburg-Essen, Institut für Experimentelle Mathematik, Ellernstr 29, 45326 Essen, Germany
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Mohamed, Adam. Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fields. Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2014), pp. 45-71. doi : 10.5802/pmb.4. http://www.numdam.org/articles/10.5802/pmb.4/

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