Weyl-type bounds for twisted GL(2) short character sums

Let f be a Hecke-Maass or holomorphic primitive cusp form for $SL(2,\mathbb{Z})$ with Fourier coefficients $\lambda_{f}(n)$. $\chi$ Dirichlet character of modulus p, where p is prime number. In this article we prove the following Weyl-type bound: any $\epsilon >0$, $$\sum_{|n| \ll N}\lambda_{f}(n)\chi (n) \ll_{f,\epsilon}N^{3/4 }p^{1/6}(pN)^{\epsilon}.$$ We can see an improvement range $N > p^{3/4}$ to p^{2/3}$ and get bound $S_{f,\chi}(N)$ without going into $L$-function.