  We report on the timing analysis of RXTE observations of the Galactic
micro-quasar GRS 1915+105 performed in 2003. Out of a total of six times ~20
ks, we focus here only on the three observations during which GRS 1915+105 is
found in a steady C-state (referred to as class $\chi$) resulting in a total of
\~50 ks. During these observations, we detect low frequency quasi-periodic
oscillations with high (~14 %) rms amplitude in the 2-40 keV energy range.
Contrary to what is usually observed in GRS 1915+105, in most of our
observations the QPO frequency presents no correlation with the RXTE/PCA count
rate, nor with the RXTE/ASM count rate. We present, for the first time, high
resolution (22 spectral channels) 2-40 keV spectral fits of the energy
dependence of the QPO amplitude (``QPO spectra''). The QPO spectra are well
modeled with a cut-off power law except on one occasion where a single power
law gives a satisfactory fit (with no cut-off at least up to ~40 keV). The
cut-off energy evolves significantly from one observation to the other, from a
value of ~21.8 keV to ~30 keV in the other observations where it is detected.
We discuss the possible origin of this behavior and suggest that the compact
jet detected in the radio contributes to the hard X-ray (> 20 keV) mostly
through synchrotron emission, whereas the X-ray emitted below 20 keV would
originate through inverse Compton scattering. The dependence of the QPO
amplitude on the energy can be understood if the modulation of the X-ray flux
is contained in the Comptonized photons and not in the synchrotron ones.
