Abstract Let $\pi $ be a Hecke–Maass cusp form for $\textrm{SL}_3(\mathbb{Z})$ with normalized Hecke eigenvalues $\lambda _{\pi }(n,r)$. $f$ holomorphic or Maass $\textrm{SL}_2(\mathbb{Z})$ _f(n)$. In this paper, we are concerned obtaining nontrivial estimates the sum $$\begin{align*}& \sum_{r,n\geq 1}\lambda_{\pi}(n,r)\lambda_f(n)e\left(t\,\varphi(r^2n/N)\right)V\left(r^2n/N\right), \end{a...