Orthogonality of cusp forms and holomorphic Eisenstein series
= Orthogonality of cusp forms and holomorphic Eisenstein series
For the full modular group, a cusp form is orthogonal under the <Petersson inner product> to every holomorphic Eisenstein series of the same weight. Unfolding reduces the integral to the constant Fourier coefficient of the cusp form, which is zero.