Mean value theorems for automorphic L-functions

Let f be a holomorphic Hecke eigencuspform of even weight k≥ 12 for SL(2, Z) and let L(s, sym²f) be the symmetric square L-function of f. Let $C(x)$ be the summatory function of the coefficients of L(s,sym² f). The true order is found for {equation*} ∫ ˣ₀C(y)^2 dy. {equation*}