De Haas-van Alphen ͑dHvA͒ oscillations are observed for Landau levels ͑LLs͒ with filling factors between 4 and 52, at temperatures in the range 50 mK to 1 K, in experiments on high-mobility GaAs/͑Al, Ga͒As heterojunctions. The oscillations become sawtooth-shaped at low filling factors, and theoretical fits to the data, assuming the two-dimensional electron gas to be a non-interacting Fermi system, show the shape of LLs to be close to a ␦ function. The small residual width ͑ϳ0.4 meV or less͒ fits equally well to either a Gaussian or a Lorentzian density-of-states model. In almost all cases, a constant background density of states has to be included to obtain a satisfactory fit. Weak odd-filling-factor dHvA peaks are detected at high fields, from which a g-factor enhancement of 15 can be inferred. Comparison of the scattering time derived from the fits before and after illumination, with the momentum relaxation time derived from transport, reveals a counterintuitive behavior in the bulk-modulation-doped sample.