  Using ab-initio calculations, we study the electronic structure of
gallium-doped germanium, which was found recently to be a superconductor, with
a critical temperature of 0.5 Kelvins, and a particularly low density of Cooper
pairs. The calculations of the electronic properties reveal that no sign of an
impurity band is observed, and that the Fermi level lies in the valence band of
Germanium. Moreover, the calculation of the phonon frequencies shows that a new
mode associated to the Ga atom is appearing, around 175$ cm-1.
