Orthogonal Eisenstein series at harmonic points and modular forms of singular weight

We investigate the behaviour of orthogonal non-holomorphic Eisenstein series at their harmonic points by using theta lifts. In the case of singular weight, we show that the orthogonal non-holomorphic Eisenstein series that can be written as a theta lift have a simple pole at s=1 whose residues yield holomorphic orthogonal modular forms that are Eisenstein series on the boundary. Moreover, we will investigate the image of this construction and give sufficient conditions for the surjectivity.