Landau level splitting in a two-dimensional electron gas (2DEG) confined in an ultrapure GaN/AlGaN heterostructure grown by molecular beam epitaxy on bulk GaN is verified spectroscopically. The Landau level fan reconstructed from magneto-photoluminescence (PL) data yields an effective mass of 0.24m₀ for the 2D electrons. Narrow excitonic PL line widths < 100 μeV, an atomically flat surface of the layer stack, as well as the absence of the 2DEG in the dark environment, are important ancillary experimental findings while focusing on magneto-PL investigations of the heterostructure. Simultaneously recorded Shubnikov-de Haas and magneto-PL intensity oscillations under steady UV illumination exhibit an identical frequency and allow for two independent ways of determining the 2D density.