Weight aspect exponential sums for Fourier coefficients of cusp forms

Let k >= 2 be an even integer. Let f be a primitive holomorphic cusp form of weight k, with lambda(f) (n) being its n-th Fourier coefficient. We explicitly determine the dependence on the weight aspect by proving Sigma(n <= X) lambda(f)(n)e(n(2)alpha + n beta) << (Xk)(epsilon) X-21/22 k(31/22) uniformly for k, and any alpha, beta is an element of R, where the implied constant depends only on epsilon. In addition we obtain an analogue of the Prime Number Theorem associated to the Fourier coefficients of cusp forms Sigma(n <= X) Lambda(n)lambda(f)(n)e(n(2)alpha + n beta) << X exp (-c log X/root log X + log k) uniformly for k < X1/31-epsilon and any alpha, beta is an element of R, where the implied constant is absolute.