A twist of the Gauss circle problem by holomorphic cusp forms

Let f be a holomorphic cusp form of even weight k for the group Gamma(0)(4N) with N is an element of N. We prove that S-f(X) := Sigma(k,l is an element of Z)Sigma(k2+l2 <= X)lambda(f)(k(2) + l(2)) <<(k,N,epsilon) X1/2+epsilon for any epsilon > 0, where lambda(f)(n) denotes the normalized n-th Fourier coefficients of f.