In this contribution, a new class of planar coprime MIMO radar systems based on quadratic integers is proposed where the antenna locations are represented by lattice points generated by prime integers in quadratic number fields. By exploiting the coprimality of certain quadratic integers, the virtual coarrays of proposed structures enjoy a quadratic gain in parameter identifiability according to the Chinese Remainder Theorem (CRT). To avoid holes in the coarray, we present Hole-free CRT arrays with guaranteed full-rank autocorrelation matrices for subspace-based target estimation. The ring of Gaussian integers and the ring of Eisenstein integers are chosen as examples of designing coprime MIMO radar systems. It is shown that the proposed arrays achieve enhanced angular resolutions and improve the side lobe suppression. In the context of target estimation, simulations show the superior performance of the coprime MIMO structures based on CRT.