Asymptotics for the second moment of the Dirichlet coefficients of symmetric power L-functions

Let m >= 2 be an integer. Let f be a holomorphic Hecke eigenform of even weight k for the full modular group SL(2, Z). Denote by lambda(m)(Sym)(f) (n) the nth normalized Dirichlet coefficient of the corresponding symmetric power L-function L(s, Sym(m) (f)) related to f. In this paper, we study the average behavior of the second moment of the Dirichlet coefficients lambda(m)(Sym)(f) (n) and establish its asymptotic formula.