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

GW electronic structure calculations of Co doped ZnO