scholarly journals On the images of the Galois representations attached to genus 2 Siegel modular forms

2002 ◽  
Vol 2002 (553) ◽  
Author(s):  
Luis V. Dieulefait
Keyword(s):  
Modular Forms ◽  
Galois Representations ◽  
Siegel Modular Forms ◽  
Genus 2

scholarly journals Siegel modular forms of genus 2 and level 2

2015 ◽  
Vol 26 (05) ◽  
pp. 1550034 ◽  
Author(s):  
Fabien Cléry ◽  
Gerard van der Geer ◽  
Samuel Grushevsky
Keyword(s):  
Modular Forms ◽  
Generating Functions ◽  
Theta Functions ◽  
Siegel Modular Forms ◽  
Genus 2 ◽  
Vector Valued ◽  
Level 2

We study vector-valued Siegel modular forms of genus 2 on the three level 2 groups Γ[2] ◁ Γ1[2] ◁ Γ0[2] ⊂ Sp(4, ℤ). We give generating functions for the dimension of spaces of vector-valued modular forms, construct various vector-valued modular forms by using theta functions and describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued Siegel modular forms.

CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES

2021 ◽  
pp. 1-22
Author(s):  
NEIL DUMMIGAN
Keyword(s):  
Recent Work ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Siegel Modular Forms ◽  
Hecke Eigenvalues ◽  
Genus 2

Abstract Following Ryan and Tornaría, we prove that moduli of congruences of Hecke eigenvalues, between Saito–Kurokawa lifts and non-lifts (certain Siegel modular forms of genus 2), occur (squared) in denominators of central spinor L-values (divided by twists) for the non-lifts. This is conditional on Böcherer’s conjecture and its analogues and is viewed in the context of recent work of Furusawa, Morimoto and others. It requires a congruence of Fourier coefficients, which follows from a uniqueness assumption or can be proved in examples. We explain these factors in denominators via a close examination of the Bloch–Kato conjecture.

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