The spectral distribution of parametrically excited dipole-exchange magnons in an in-plane magnetized epitaxial film of yttrium-iron garnet was studied by means of frequency- and wavevector-resolved Brillouin light scattering spectroscopy. The experiment was performed in a parallel pumping geometry, where an exciting microwave magnetic field was parallel to the magnetizing field. It was found that for both dipolar and exchange spectral areas parallel pumping excites the lowest volume magnon modes propagating in the film plane perpendicularly to the magnetization direction. No excitation of the high-order volume modes has been registered. In order to interpret the experimental observations, we used a microscopic Heisenberg model that includes exchange as well as dipole-dipole interactions to calculate the magnon spectrum and construct the eigenstates. As proven in our calculations, the observed magnons are characterized by having the highest possible ellipticity of precession, which suggests the lowest threshold of parametric generation. Applying different pumping powers we observe modifications in the magnon spectrum that are described theoretically by a softening of the spin stiffness.