  Recently the point defect responsible for the intra-3$d$ luminescence of
cobalt in doped ZnO samples has been indentified\,\cite{pssb2019}. In this work
we further extend our investigation to other point defects in Co-doped ZnO. We
use density-functional theory and GW calculations to determined the
orbital-resolved band structure of cobalt doped zinc oxide (ZnO).
  We show that mainly O-p and Co-d orbitals take part in the process and
confirm that an oxygen interstitial nearby a cobalt atom is a likely defect to
occur in Co-implanted ZnO samples. We also rule out that other common point
defects in ZnO can be responsible for the observed intra-3$d$ transition.
Finally, we suggest that defect complexes involving oxygen interstitials could
be used to promote ferromagnetism in cobalt doped ZnO samples.
