Murmurations of Modular Forms and $p$-power Coefficients

Abstract

We extend the work of N. Zubrilina on murmuration of modular forms to the case when prime-indexed coefficients are replaced by squares of primes. Our key observation is that the shape of the murmuration density is the same.

Accepted for publication (Math. Proc. Camb. Philos. Soc.). This version has more details than the accepted journal version