  We determine the lowest and higher order collective modes in both
spin-conserving and spin-reversed sectors by calculating energy differences of
the appropriate linear combinations of different levels of
composite-fermion-excitons and the fully spin-polarized ground states at
filling factors $\nu=1/3$, 2/5, 3/7, and 4/9. Apart from providing the detailed
study of previously reported modes that have also been observed in the
experiments, we predict additional higher energy modes at different filling
factors. The lowest and the next higher spin-conserving modes have equal number
of "magneto-rotons" and the number is the same as the number of filled
effective Landau-like levels of composite fermions. The higher energy modes at
$\nu =1/3$ merge with the lowest mode at long-wavelength. The spin-conserving
modes do not merge at other filling factors. Apart from showing zero-energy
spin-wave mode at zero momentum, thanks to Larmor's theorem, the lowest
spin-reversed modes at the ferromagnetic ground states of $\nu=2/5$, 3/7, and
4/9 display one or more "spin-rotons" at negative energies signalling the
unstable fully polarized ground states at sufficiently small Zeeman energies.
The high energy spin-reversed modes also have spin-rotons but at positive
energies. The energies of these excitations depend on the finite width of the
quantum well as the Coulomb interaction gets screened. We determine finite
thickness correction to the Coulomb interaction by the standard method of local
density approximation and use them to calculate the critical energies such as
rotons, long-wavelength, and short-wavelength modes which are detectable in
inelastic light scattering experiments.
