The electronic properties of defects resulting from electron irradiation of germanium at low temperatures have been investigated. The recent success in preparing ${n}^{+}p$ junctions on germanium has opened a new opportunity to address fundamental questions regarding point defects and their related energy levels by allowing an access to the lower half of the band gap. In this work we apply various space-charge capacitance-transient spectroscopy techniques connected on line with the electron-beam facility. In $n$-type germanium we identify a level at about 0.14 eV below the conduction band whose properties resemble in many respects those of a defect assigned previously to the close vacancy-interstitial or Frenkel pair. This pair seems to annihilate over a small barrier at about 70 K, and its stability is particularly sensitive to the irradiation temperature and energy. We also observe two coupled levels at 0.08 and 0.24 eV below the conduction band stable up to 160 K. Recent independent theoretical work has predicted the existence of the single and double donor of the germanium interstitial with energy levels matching exactly these two values. Given these identifications hold, they mark a major difference with silicon where both the Frenkel pair and self-interstitial have never been caught. In $p$-type germanium, two levels were found. The shallower one, located at about 0.14 eV above the valence band, is tentatively assigned to the vacancy. It exhibits a field-driven instability at about 80 K making its analysis quite difficult. The application of a reverse bias, required by the space-charge spectroscopy, leads to a strong drift process sweeping this defect out of the observation area without necessarily provoking its annealing. Unlike silicon, in which the vacancy has four charge states, only one vacancy-related level seems to exist in germanium and this level is very likely a double acceptor. Finally, a very peculiar observation is made on a hole midgap trap, which, in many respects, behaves as the boron interstitial in silicon. This has led us to suggest that it may stem from the gallium interstitial, a natural dopant of our germanium materials, whose presence would be the fingerprint of the Watkins replacement mechanism in germanium.