  We present the ground and excited state spectra of $\Omega^{0}_{c}$ baryons
with spin up to 7/2 from lattice quantum chromodynamics with dynamical quark
fields. Based on our lattice results, we predict the quantum numbers of five
$\Omega^{0}_{c}$ baryons, which have recently been observed by the LHCb
Collaboration. Our results strongly indicate that the observed states
$\Omega_c(3000)^0$ and $\Omega_c(3050)^0$ have spin-parity $J^P = 1/2^{-}$, the
states $\Omega_c(3066)^0$ and $\Omega_c(3090)^0$ have $J^P = 3/2^{-}$, whereas
$\Omega_c(3119)^0$ is possibly a $5/2^{-}$ state.
