Periods of modular forms on $\Gamma_0(N)$ and products of Jacobi theta functions

YoungJu Choie; Yoon Kyung Park; Don B. Zagier

doi:10.4171/jems/864

JournalsjemsVol. 21, No. 5pp. 1379–1410

Periods of modular forms on $Γ_{0} (N)$ and products of Jacobi theta functions

YoungJu Choie
Pohang University of Science and Technology, Pohang City, Republic of Korea
- MathSciNet
- zbMATH Open
Yoon Kyung Park
Gongju National University of Education, Gongju, Republic of Korea
- MathSciNet
- zbMATH Open
Don B. Zagier
Max Planck Institute for Mathematics, Bonn, Germany
- MathSciNet
- zbMATH Open

$Periods of modular forms on $\Gamma_0(N)$ and products of Jacobi theta functions cover$

Download PDF

A subscription is required to access this article.

Abstract

Generalizing a result of [15] for modular forms of level one, we give a closed formula for the sum of all Hecke eigenforms on $Γ_{0} (N)$ , multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level $N$ . We also show that for $N = 2, 3$ and $5$ this formula completely determines the Fourier expansions all Hecke eigenforms of all weights on $Γ_{0} (N)$ .

Cite this article

YoungJu Choie, Yoon Kyung Park, Don B. Zagier, Periods of modular forms on $Γ_{0} (N)$ and products of Jacobi theta functions. J. Eur. Math. Soc. 21 (2019), no. 5, pp. 1379–1410

DOI 10.4171/JEMS/864