  We present theoretical calculations for the cyclotron resonance and various
magnetoplasmon modes of a Coulomb interacting two-dimensional GaAs electron gas
(2DEG) modulated as a lateral superlattice of quantum dots subjected to an
external perpendicular constant magnetic field. We use a real-time excitation
approach based on the Liouville-von Neumann equation for the density operator,
that can go beyond linear response delivering information of all longitudinal
and transverse collective modes of interest to the same order. We perform an
extensive analysis of the coexisting collective modes due to the lateral
confinement and the magnetic field for a different number of electrons in each
dot. In the limit of vanishing dot modulation of the 2DEG we find signs of the
structure of the Hofstadter butterfly in the excitation spectra.
