Non-vanishing of Hilbert Poincaré series

We prove some non-vanishing results of Hilbert Poincaré series. We derive these results, by showing that the Fourier coefficients of Hilbert Poincaré series satisfy some nice orthogonality relations for sufficiently large weight as well as for sufficiently large level. To prove later results, we generalize a method of E. Kowalski et al.