  We study the effects of the Coulomb interactions between electrons on the
Hofstadter butterfly, which characterizes the subband structure of the Landau
levels of a two-dimensional electron gas in a perpendicular homogeneous
magnetic field and a periodic lateral superlattice potential. The interactions
essentially preserve the intricate gap structure of the Hofstadter spectra, but
with a lower symmetry that depends on the filling of the Landau bands. For
short enough periods and strong enough modulation the miniband structure can be
resolved in the thermodynamic density of states.
