Murmurations in the depth aspect

TL;DR

This paper analyzes the murmuration density function for Hecke forms of a specific weight and prime power level, providing insights into their distribution as the level increases.

Contribution

It introduces a new computation of murmuration density for Hecke forms with prime power levels, extending understanding of their distribution patterns.

Findings

Density function computed explicitly for large levels

Distribution patterns identified for Hecke forms

Asymptotic behavior characterized as level increases

Abstract

We compute the murmuration density function for the family of Hecke forms of weight $k$ and prime power level $N=\ell^a$, with $\ell$ a fixed odd prime and $a\to \infty$.