Galois level and congruence ideal for -adic families of finite slope Siegel modular forms

Big image of Galois representations associated with finite slope p-adic families of modular forms

Level Stripping for Siegel Modular Forms with Reducible Galois Representations

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 nat...

Galois 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...

Congruence Properties of Siegel Modular Forms

Let X35 be a Siegel cusp form of degree 2 and weight 35. Kikuta, Kodama and Nagaoka [4] proved that det T a(T, X35) ≡ 0 mod 23 for every half integral positive symmetric matrix T . In this paper, we give a finite number of examples of Hecke eigenforms of degree 2 and odd weights that have the same type of congruence relation above. We also introduce congruence relations for the Hecke eigenvalue...

Galois characterization of Endoscopy for rational Siegel modular forms

We establish a relation between Galois reducibility and Endoscopy for genus 2 Siegel cusp forms which have rational eigenvalues and are unramified at 3.