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.
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