  Let $(\lambda_f(n))_{n\geq 1}$ be the Hecke eigenvalues of either a
holomorphic Hecke eigencuspform or a Hecke-Maass cusp form $f$. We prove that,
for any fixed $\eta>0$, under the Ramanujan-Petersson conjecture for $\rm GL_2$
Maass forms, the Rankin-Selberg coefficients $(\lambda_f(n)^2)_{n\geq 1}$ admit
a level of distribution $\theta=2/5+1/260-\eta$ in arithmetic progressions.
