Sturm type theorem for Siegel modular forms of degree 2

2011/01/15 by Toshiyuki Kikuta, Kikuta, Toshiyuki
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1101.2986

Abstract

We attempt to generalize a congruence property of elliptic modular forms proved by Sturm to that of Haupttypus of Siegel modular forms of degree 2 with level. Namely, we give an explicit bound of Fourier coefficients required to determine the congruence of modular forms. We give the analog of Sturm's theorem for Jacobi forms, which is required in the proof. In the case that Nebentypus of Siegel modular forms with prime level, in order to prove the congruence between two modular forms, we show that it suffices to check the congruence of the finitely many Fourier coefficients. Finally, we give two examples of our main theorem.

Cited by

• Congruences for Hermitan modular forms of degree 2

Related

• Bounds for Siegel Modular Forms of genus 2 modulo p
• Sturm bounds for Siegel modular forms of degree 2 and odd weights
• Sturm Bounds for Siegel Modular Forms
• Some relations on Fourier coefficients of degree 2 Siegel forms of\n arbitrary level
• On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups