  Given a cuspidal automorphic form $\pi$ on $\GL_2$, we study smoothed sums of
the form $\sum_{n\in\mathbb{N}} a_{\pi}(n^2+d)W(\frac{n}{Y})$. The error term
we get is sharp in that it is uniform in both $d$ and $Y$ and depends directly
on bounds towards Ramanujan for forms of half-integral weight and Selberg
eigenvalue conjecture. Moreover, we identify (at least in the case where the
level is square-free) the main term as a simple factor times the residue as
$s=1$ of the symmetric square L-function $L(s,\Msym^2\pi)$. In particular there
is no main term unless $d>0$ and $\pi$ is a dihedral form.
