On a short spectral sum involving inner products of a holomorphic cusp form and Maass forms
We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.
We have for is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue to which the Hecke series is attached. This result yields the new bound