A generalization of level-raising congruences for algebraic modular forms
Annales de l'Institut Fourier, Volume 56 (2006) no. 6, pp. 1735-1766.

In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field F. We do this for automorphic representations of an arbitrary reductive group G over F, which is compact at infinity. In the special case where G is an inner form of GSp (4) over , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

Dans cet article, on étend des résultats d’augmentation du niveau de Ribet et Taylor, au cas de formes modulaires algébriques pour une algèbre à division sur un corps totalement réel F. On travaille avec des représentations automorphes d’un groupe réductif G sur F, compact à l’infini. Dans le cas particulier où G est une forme intérieure de GSp (4) sur , on utilise ces résultats pour construire des congruences entre des formes de Saito-Kurokawa et des formes avec des composantes locales génériques.

DOI: 10.5802/aif.2226
Classification: 11F33,  11F70
Keywords: Level-raising, algebraic modular forms
Mazanti Sorensen, Claus 1

1 California Institute of Technology Department of Mathematics 253-37 Caltech, Pasadena, CA 91125 (USA)
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Mazanti Sorensen, Claus. A generalization of level-raising congruences for algebraic modular forms. Annales de l'Institut Fourier, Volume 56 (2006) no. 6, pp. 1735-1766. doi : 10.5802/aif.2226. https://aif.centre-mersenne.org/articles/10.5802/aif.2226/

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