Level Stripping for Siegel Modular Forms with Reducible Galois Representations
نویسنده
چکیده
In this paper we consider level stripping for genus 2 cuspidal Siegel eigenforms. In particular, we show that it is possible to strip primes from the level of Saito-Kurokawa lifts that arise as theta lifts and weak endoscopic lifts with a mild condition on the associated character. The main ingredients into our results are a level stripping result for elliptic modular forms and the explicit nature of the forms under consideration.
منابع مشابه
Uniform behavior of families of Galois representations on Siegel modular forms
We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of level 1, weight k > 3 and with multiplicity one is reducible (for a prime p > 4k − 5) then almost all the representations in the family are reducible. The result will be proved more generally for compatible families of geometric, pure and symplectic four-di...
متن کاملUniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecture
We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of weight k > 3, “semistable” and with multiplicity one, is reducible (for an odd prime p), then all the representations in the family are reducible. This, combined with Serre’s conjecture (which is now a theorem) gives a proof of the Endoscopy Conjecture.
متن کاملOn the images of the Galois representations attached to genus 2 Siegel modular forms
We address the problem of the determination of the images of the Galois representations attached to genus 2 Siegel cusp forms of level 1 having multiplicity one. These representations are symplectic. We prove that the images are as large as possible for almost every prime, if the Siegel cusp form is not a Maass spezialform and verifies two easy to check conditions. Mathematics Subject Classific...
متن کاملGalois Representations for Holomorphic Siegel Modular Forms
We prove local global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert-Siegel modular forms in many cases (induced from Borel or Klingen parabolic). For Siegel modular forms, when the local representation is an irreducible principal series we get local global compatibility without a twist. We achieve this by proving a version of rigidity (stron...
متن کاملp-ADIC FAMILIES AND GALOIS REPRESENTATIONS FOR GSp(4) AND GL(2)
In this brief article we prove local-global compatibility for holomorphic Siegel modular forms with Iwahori level. In previous work we proved a weaker version of this result (up to a quadratic twist) and one of the goals of this article is to remove this quadratic twist by different methods, using p-adic families. We further study the local Galois representation at p for nonregular holomorphic ...
متن کامل