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The ionosphere of Mars is the ionized region of the atmosphere of the planet. It is affected by solar and galactic drivers from above. It is also affected by atmospheric dynamics from below. The crustal magnetic field morphology of Mars make the plasma dynamics on the planet different than those at Earth or Venus. The only in situ measurements of neutral and ion composition and plasma temperatures were obtained by the Viking Landers over 30 years ago. They triggered an era of modeling that could not justify the measurements. I model the ionosphere of Mars to find that there are many more hydrogenated ions than expected. I also calculate the electron and ion temperatures to compare with Viking 1 measurements. I simulate the magnetic field effects on plasma dynamics and compare my results to measurements made by Mars EXpress. The main ionospheric ions modeled between 80 and 400 km at Mars are shown for two extreme mixing ratios of molecular hydrogen at 80 km. The top side composition is highly sensitive to how much H2 is on the planet. Ions are summed to get electron density.