An Exercise in Benford's Law

This article is a generalisation of the results of Thorner etal concerning Benford's law for the Fourier coefficients of a primitive i.e. a normalised newform $f$ of weight $k$ on $\Gamma_0 (N)$ without complex multiplication to the Fourier coefficients of ${\rm sym}^2f$, where ${\rm sym}^2 f$ is the symmetric square lift of $f$.