Coefficients of symmetric power L-functions on integers under digital constraints

Let $\lambda_{{\rm sym}^{r}f}(n)$ be the n-th coefficient in the Dirichlet series representing the symmetric power L-function attached to a primitive form f of weight k and level N. In this paper, we give asymptotic formulas for the arithmetic mean of $\lambda_{{\rm sym}^{r}f}(n)$ on integers under digital constraints related to the sum of digits function. Our results throw the light on the behavior of the classical function $\lambda_{{\rm sym}^{r}f}(n)$ on integers in arithmetic progression related to the sum of digits function.