Periods of modular forms on ${\Gamma }_0(N)$ and products of Jacobi theta functions

Y. Choie, Y. Park, D. Zagier

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 ${\Gamma }_0(N)$, multiplied by their odd period polyn…