The Dielectron Spectrometer HADES operated at the SIS18 synchrotron, FAIR/GSI Darmstadt recently provided new intriguing results on production of electron pairs and of strangeness from nucleus-nucleus collisions, as well as from elementary reactions, in energy region of $1 - 2$ A GeV. In 2019 the spectrometer was complemented by an electromagnetic calorimeter based on lead-glass modules, which allows us to measure photons and thus to study the production of $\pi^0$ and $\eta$ mesons via their two-photon decay. Knowledge of the neutral-meson production is a mandatory prerequisite for the interpretation of dielectron data. In particular, the directed and elliptic flow of neutral mesons will be shown with respect to transverse momentum and rapidity for different centrality classes in Ag + Ag collisions at 1.58 A GeV. The results of the analysis corresponding to the $14\times10^9$ events will be confronted with the results of other experiments and with the current model calculations.