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

Stochastic Estimation of Nuclear Level Density in the Nuclear Shell Model: An Application to Parity-Dependent Level Density in $^{58}$Ni