  We introduce a novel method to obtain level densities in large-scale
shell-model calculations. Our method is a stochastic estimation of eigenvalue
count based on a shifted Krylov-subspace method, which enables us to obtain
level densities of huge Hamiltonian matrices. This framework leads to a
successful description of both low-lying spectroscopy and the experimentally
observed equilibration of $J^\pi=2^+$ and $2^-$ states in $^{58}$Ni in a
unified manner.
