The COBRA collaboration aims to search for neutrinoless double beta-decay of $^{116}$Cd. A demonstrator setup with 64 CdZnTe semiconductor detectors, each with a volume of 1cm$^3$, is currently being operated at the LNGS underground laboratory in Italy. This paper reports on the characterization of a large (2 $times$ 2 $times$ 1.5)cm$^3$ CdZnTe detector with a new coplanar-grid design for applications in $gamma$-ray spectroscopy and low-background operation. Several studies of electric properties as well as of the spectrometric performance, like energy response and resolution, are conducted. Furthermore, measurements including investigating the operational stability and a possibility to identify multiple-scattered photons are presented.
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