Periods of modular forms on and products of Jacobi theta functions

  • YoungJu Choie

    Pohang University of Science and Technology, Pohang City, Republic of Korea
  • Yoon Kyung Park

    Gongju National University of Education, Gongju, Republic of Korea
  • Don B. Zagier

    Max Planck Institute for Mathematics, Bonn, Germany
Periods of modular forms on $\Gamma_0(N)$ and products of Jacobi theta functions cover

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 , multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level . We also show that for and this formula completely determines the Fourier expansions all Hecke eigenforms of all weights on .

Cite this article

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

DOI 10.4171/JEMS/864