The dynamics of fluctuations in a fast rotating spherical Couette flow experiment in the presence of a strong dipolar magnetic field is investigated in detail, through a thorough analysis of the experimental data as well as a numerical study. Fluctuations within the conducting fluid (liquid sodium) are characterized by the presence of several oscillation modes, identified as magneto-Coriolis (MC) modes, with definite symmetry and azimuthal number. A numerical simulation provides eigensolutions which exhibit oscillation frequencies and magnetic signature comparable to the observation. The main characteristics of these hydromagnetic modes is that the magnetic contribution has a fundamental influence on the dynamical properties through the Lorentz forces, although its importance remains weak in an energetical point of view. Another specificity is that the Lorentz forces are confined near the inner sphere where the dipolar magnetic field is the strongest, while the Coriolis forces are concentrated in the outer fluid volume close to the outer sphere.