Let $f$ be a modular form of an even weight $k$ over the modular group $SL\_2(Z).$ Denote $\lambda\_f(n)$ the $n$-th normalized Fourier coefficient of $f.$ I am doing some calculations and I am stack in finding the expression of the sum $\sum\_{d|n} \lambda\_f\left(\frac{n^2}{d^2}\right)$ in terms of $ \lambda\_f(n)$ or $ \lambda\_f(n)^2.$ Any help is appreciated.



Expression of a sum of Hecke eigenvalues in terms of one Hecke eigenvalue
From the Hecke relation, we get 
$$ \lambda\_f(n)^2 =\sum\_{d|n} \lambda\_f\left(\frac{n^2}{d^2}\right).$$


