The COBRA collaboration aims to search for neutrinoless double beta-decay of 116Cd. A demonstrator setup with 64 CdZnTe semiconductor detectors, each with a volume of 1cm3, is currently being operated at the LNGS underground laboratory in Italy. This paper reports on the characterization of a large 2×2×1.5cm3 CdZnTe detector with a new coplanar-grid design for applications in γ-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.