The excitation of low-frequency parametric instabilities by a finite wavelength pump in a system consisting of a warm electron plasma traversed by a warm electron beam is investigated in a fluid dissipationless model. The dispersion relation for the three-dimensional problem in a magnetized plasma with arbitrary directions for the waves is derived, and the one-dimensional case is analyzed numerically. For the one-dimensional back-scattering decay process, it is found that when the plasma-electron Debye length (λ Dp) is larger than the beam-electron Debye length (λDb), two low-frequency electrostatic instability branches with different growth rates may exist simultaneously. When λDp≃λDb, the large growth rate instability found in the analysis depends strongly on the amplitude of the pump field. For the case λDp <λDb, only one low-frequency instability branch is generally excited.