The local density of states of the adsorbate-induced two-dimensional electron system is studied in magnetic fields up to B=6 T. Landau quantization is observed and drift states with a width of about the magnetic length are found in agreement with theoretical predictions. At the tails of the Landau levels the states form closed paths indicating localization. These states show the expected energy dependence. A multifractal analysis applied to the data results in a nice parabolic shape of the characteristic f(alpha) spectra, but we find only a slight displacement of the origin from alpha=2.0 for the states in the center of the Landau level.