We use molecular dynamics simulations in a constant potential ensemble to study the effects of solution composition on the electrochemical response of a double layer capacitor. We find that the capacitance first increases with ion concentration following its expected ideal solution behavior but decreases upon approaching a pure ionic liquid in agreement with recent experimental observations. The nonmonotonic behavior of the capacitance as a function of ion concentration results from the competition between the independent motion of solvated ions in the dilute regime and solvation fluctuations in the concentrated regime. Mirroring the capacitance, we find that the characteristic decay length of charge density correlations away from the electrode is also nonmonotonic. The correlation length first decreases with ion concentration as a result of better electrostatic screening but increases with ion concentration as a result of enhanced steric interactions. When charge fluctuations induced by correlated ion-solvent fluctuations are large relative to those induced by the pure ionic liquid, such capacitive behavior is expected to be generic.