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A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen — 2006

Annales de l’institut Fourier

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 $ℚ$ , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

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