Recently the HADES Collaboration has published the invariant mass spectrum of $e^+e^-$ pairs, $dN/dM_{e^+e^-}$, produced in C + C collisions at 2A GeV. Using electromagnetic probes, one hopes to get information from this experiment on hadron properties at high density and temperature. Simulations show that firm conclusions on possible in-medium modifications of meson properties will only be possible when the elementary meson production cross sections, especially in the pn channel, as well as production cross sections of baryonic resonances are better known. Presently one can conclude that (i) simulations overpredict by far the cross section at $Me^+e^-\simM_{\omega}^0$ if free production cross sections are used and that (ii) the upper limit of the $\eta$ decay into $e^+e^-$ is smaller than the present upper limit of the Particle Data Group. This is the result of simulations using the isospin quantum molecular dynamics approach.