Let \(\pi=\otimes\pi_p\) be a cuspidal automorphic representation of \(\text{GL}_m({\mathbb A}_{\mathbb Q})\). For \(p\) a prime at which \(\pi_p\) is unramified, let \(\text{diag}(\alpha_{1,p},\ldots,\alpha_{m,p})\) be the corresponding Satake parameter. For a positive integer \(k\), let \(a_\pi(p^k)=\alpha_{1,p}^k+\ldots +\alpha_{m,p}^k\). Rudnick and Sarnak made the Hypothesis H: For any fixed \(k\geq 2\), \[ \sum_p\frac{(\log p)^2| a_\pi(p^k)| ^2}{p^k}<\infty. \] They proved it for \(m=2,3\). The author proves the case \(m=4\) and the case when \(\pi\) is the fourth symmetric power of a cuspidal representation of \(\text{GL}_2\).