Approximate Atkin-Serre Conjecture

Let $lambda(m)$ be the $m$th coefficient of a modular form $f(z)=sum_{mgeq 1} lambda(m)q^m$ of weight $kgeq 4$, let $p^n$ be a prime power, and let $varepsilon>0$ be a small number. An approximate of the Atkin-Serre conjecture on the lower bound of the form $left |lambdaleft (p^nright )right | geq p^{(k-1)n/2-2k+2varepsilon}$ is presented in this note.