Capacitance spectroscopy is used to determine the allowed energy levels for electrons and holes in InAs self-assembled quantum dots embedded in GaAs. Using this technique, the relative energy of the electron and hole states is measured with respect to their respective energy band minima in the GaAs. This allows the construction of an energy level diagram for these quantum dots which correlates well with previously observed photoluminescence data. By tuning the device geometry, a fine structure in the electron ground state is revealed and attributed to Coulomb charging effects.