A generalization of level-raising congruences for algebraic modular forms

Mazanti Sorensen, Claus

Annales de l'Institut Fourier, Tome 56 (2006) no. 6, pp. 1735-1766.

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 $\mathrm{GSp}\left(4\right)$ sur $\mathbb{Q}$, on utilise ces résultats pour construire des congruences entre des formes de Saito-Kurokawa et des formes avec des composantes locales génériques.

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 $\mathrm{GSp}\left(4\right)$ over $\mathbb{Q}$, we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

Classification : 11F33, 11F70
Keywords: Level-raising, algebraic modular forms
Mot clés : augmentation du niveau, formes modulaires algébriques

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