  Let $\pi$ be a cuspidal representation on $\GL(2,\mathbb{A}_{\mathbb{Q}}).$
We give nontrivial lower and upper bounds for average of absolute values of
Dirichlet coefficients associated to $\pi;$ and nontrivial upper bound in the
case of $\Sym^k\pi,$ $k=2, 3.$ These bounds generalize the known estimates in
holomorphic case to Maass forms, without assuming Ramanujan-Petersson
conjecture.
