On cusp forms associated with binary theta series

Let f is an element of Z[x, y] be a primitive positive binary quadratic form with fundamental discriminant and let S(f, z) := Sigma(n=1)(infinity) a(f, n)e(nz) be the associated cusp form, i.e., the projection of the theta series of f onto the subspace of cusp forms. For any real beta > 0, the exact order of magnitude of the counting function Sigma(nless than or equal tox) \a(f,n)\(2beta) is given. For integral beta > 0, a meromorphic continuation of Sigma\a(f, n)\2beta n(-s) to the half plane Hs > 0 is obtained. The number of sign changes of a(f, n) for n less than or equal to x is estimated.