A detailed analytical and numerical study of the spin wave modes of the free layer of a nanopillar spin torque nano-oscillator (STNO) has been performed as a function of the magnetostatic interaction between the free and the fixed magnetic layers. Results for higher frequency normal modes show that the magnetostatic interaction does not appreciably affect the spin wave frequencies and the critical current densities, due to more relevance of the exchange interaction in these modes. For lower frequency normal modes we observe a decrease in frequency and in the critical current density for auto-oscillations when the strength of the magnetostatic interaction between the layers increases, an effect that may be appreciable.