The linear Vlasov stability of a class of electron velocity distributions which model those observed within the earth's bow shock is examined. The study is restricted to electrostatic waves which propagate parallel to the ambient magnetic field B. Two instabilities are identified which are driven by free energy in the direction parallel to B: an ion acoustic wave with real frequency below the ion plasma frequency and an electron acoustic wave with real frequency of several times the ion plasma frequency. The characteristics of the unstable waves are in accord with observations obtained within the bow shock, in particular, with the trend of the observed electrostatic waves to be polarized parallel to the magnetic field. The instabilities identified here may contribute to electron dissipation in collisionless shocks.