Siegel modular forms of genus 2 and level 2

Fabien Cléry; Gerard Van Der Geer; Samuel Grushevsky

doi:10.1142/S0129167X15500342

Siegel modular forms of genus 2 and level 2

Fabien Cléry
, Gerard Van Der Geer
, Samuel Grushevsky

Simons Center for Geometry & Physics

Stony Brook University

University of Siegen
University of Amsterdam

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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.

Original language	English
Article number	1550034
Journal	International Journal of Mathematics
Volume	26
Issue number	5
DOIs	https://doi.org/10.1142/S0129167X15500342
State	Published - May 14 2015

Keywords

Siegel modular form
modular forms of level 2
theta series
vector-valued modular form

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10.1142/S0129167X15500342

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title = "Siegel modular forms of genus 2 and level 2",

abstract = "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.",

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AU - Cléry, Fabien

AU - Van Der Geer, Gerard

AU - Grushevsky, Samuel

PY - 2015/5/14

Y1 - 2015/5/14

N2 - 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.

AB - 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.

KW - Siegel modular form

KW - modular forms of level 2

KW - theta series

KW - vector-valued modular form

UR - https://www.scopus.com/pages/publications/84929291450

U2 - 10.1142/S0129167X15500342

DO - 10.1142/S0129167X15500342

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VL - 26

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 5

M1 - 1550034

ER -

Siegel modular forms of genus 2 and level 2

Abstract

Keywords

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