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Generalizing a result of  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 .
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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. 1379–1410DOI 10.4171/JEMS/864