We applied first principles molecular dynamics (MD) technique to study structure, dynamics, and magnetic interactions of the $Gd^{3+}$ aqua ion dissolved in liquid water, a prototypical system for Gd-based complexes used as contrast agents for magnetic resonance imaging. The first coordination sphere contains eight water molecules with an average Gd-O distance of 2.37 Å and an average geometric arrangement close to a square antiprism. The mean tilt angle of the electric dipole vector of these water molecules is $\theta$=145°. In our picosecond time scale simulation we observe no exchange event from the first coordination sphere but only fast “wagging” motions. The second coordination sphere is well pronounced though water molecules in this sphere are subjected to large amplitude dynamic motions. The isotropic hyperfine coupling constants for the inner sphere water molecules $[\langle A_{iso}(^{17}O_{I})\rangle=0.65\pm 0.03 MHz, \langle A_{iso}(^{1}H_{I} \rangle =0.085\pm0.005 MHz]$ are in good agreement with experimental data and with an earlier study using classical MD. Second sphere Fermi contact hyperfine coupling constants calculated are more than one order of magnitude smaller and of opposite sign as those of the first coordination sphere. The effect of spin polarization induced by the paramagnetic $Gd^{3+}$ ion on the dipolar hyperfine interaction was found to be sizable only for the $^{17}O$ nuclei of inner sphere water molecules and has a screening character.