<abstract><p>Let $ F $ be a normlized Hecke-Maaß form for the congruent subgroup $ \Gamma_0(N) $ with trivial nebentypus. In this paper, we study the problem of the level aspect estimates for the exponential sum</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathscr{L}_F(\alpha) = \sum\limits_{n\le X} A_F(n, 1)e(n \alpha). $\end{document} </tex-math></disp-formula></p> <p>As a result, we present an explicit non-trivial bound for the sum $ \mathscr{L}_F(\alpha) $ in the case of $ N = P $. In addition, we investigate the magnitude for the non-linear exponential sums with the level being explicitly determined from the sup-norm's point of view as well.</p></abstract>