Murmurations of modular forms in the weight aspect

We prove the existence of “murmurations” in the family of holomorphic modular forms of level $1$ and weight $k\to \mathrm{\infty }$, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family.