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arXiv · 1706.07885

Periods of modular forms on $Γ_0(N)$ and products of Jacobi theta functions

Y. Choie·Y. Park·D. Zagier
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Abstract

Generalizing a result of~\cite{Z1991} 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 of all Hecke eigenforms of all weights on $Γ_0(N)$.

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Y. Choie, Y. Park, D. Zagier. 2017-06-23. Periods of modular forms on $Γ_0(N)$ and products of Jacobi theta functions. https://arxiv.org/abs/1706.07885

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