Shifted convolution sums involving theta series

Let $f$ be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by $\lambda_f(n)$ its $n$-th Hecke eigenvalue. Let $$r(n)=\#\left\{(n_1,n_2)\in \mathbb{Z}^2:n_1^2+n_2^2=n\right\}.$$ In this paper, we study the shifted convolution sum $$\mathcal{S}_h(X)=\sum_{n\leq X}\lambda_f(n+h)r(n), \qquad 1\leq h\leq X,$$ and establish uniform bounds with respect to the shift $h$ for $\mathcal{S}_h(X)$.