Estimates for fourier coefficients of cusp forms in weight aspect

Let f be a holomorphic Hecke eigenform of weight k for the modular group Γ = SL2(Z) and let λf (n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum\limits_{n \leqslant x} {{\lambda _f}\left( {{n^2}} \right)} \ll {x^{\frac{1}{2}}}{k^{\frac{1}{2}}}{\left( {\log \left( {x + k} \right)} \right)^6}$$\end{document} is established, which improves the previous result.