We measure and explain scintillator non-proportionality and gamma quenching of CaWO4 at low energies and low temperatures. Phonons that are created following an interaction in the scintillating crystal at temperatures of 15mK are used for a calorimetric measurement of the deposited energy, and the scintillation light is measured with a separate cryogenic light detector. Making use of radioactivity intrinsic to the scintillating crystal, the scintillator non-proportionality is mapped out to electron energies <5keV. The observed behavior is in agreement with a simple model based on Birks law and the stopping power dE/dx for electrons. We find for Birks constant $k_B=(18.5pm0.7)$nm/keV in CaWO4. Gamma lines allow a measurement of the reduced light yield of photons with respect to electrons, as expected in the presence of scintillator non-proportionality. In particular, we show that gamma-induced events in CaWO4 give only about 90 percent of the light yield of electrons, at energies between 40keV and 80keV.
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