  Combining the recent developments of the observations of $\Omega$ sates we
calculate the $\Omega$ spectrum up to the $N=2$ shell within a nonrelativistic
constituent quark potential model. Furthermore, the strong and radiative decay
properties for the $\Omega$ resonances within the $N=2$ shell are evaluated by
using the masses and wave functions obtained from the potential model. It is
found that the newly observed $\Omega(2012)$ resonance is most likely to be the
spin-parity $J^P=3/2^-$ $1P$-wave state $\Omega(1^{2}P_{3/2^{-}})$, it also has
a large potential to be observed in the $\Omega(1672)\gamma$ channel. Our
calculation shows that the 1$P$-, 1$D$-, and 2$S$-wave $\Omega$ baryons have a
relatively narrow decay width of less than 50 MeV. Based on the obtained decay
properties and mass spectrum, we further suggest optimum channels and mass
regions to find the missing $\Omega$ resonances via the strong and/or radiative
decay processes.
