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

Periods of modular forms on Γ0(N)\Gamma_0(N) 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
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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 Γ0(N)\Gamma_0(N), multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level NN . We also show that for N=2,3N = 2, 3 and 55 this formula completely determines the Fourier expansions all Hecke eigenforms of all weights on Γ0(N)\Gamma_0(N).

Cite this article

YoungJu Choie, Yoon Kyung Park, Don B. Zagier, Periods of modular forms on Γ0(N)\Gamma_0(N) and products of Jacobi theta functions. J. Eur. Math. Soc. 21 (2019), no. 5, pp. 1379–1410

DOI 10.4171/JEMS/864