  Magnetized plasmas are well known to exhibit a rich spectrum of collective
modes. Here, we focus on the density modes in dense or cold plasmas, where
strong coupling effects alter the mode spectrum known from traditional weakly
coupled plasmas. In particular, we study the dynamic structure factor (DSF) of
the magnetized one-component plasma with molecular dynamics simulations.
Extending our previous results [H.~K\"ahlert and M.~Bonitz, Phys. Rev. Research
\textbf{2022}, 4, 013197], it is shown that Bernstein modes can be observed in
the weakly magnetized regime, where they are found below the upper hybrid
frequency, provided the coupling strength is sufficiently low. We investigate
the DSF for a variety of different wave numbers and plasma parameters and show
that even small magnetization can give rise to a strong zero-frequency mode
perpendicular to the magnetic field and change the dispersion as well as the
damping of the upper hybrid mode.
