The overtone spectroscopy and intramolecular vibrational relaxation dynamics of CH chromophore in the fluoroform molecule is studied by a three-dimensional (3D) time-dependent wave-packet method, and the results are compared with the experiment and with those of a 2D (stretch-bend) wave-packet method. A third mode (CF symmetrical stretch) is included in order to explain the long time dynamics and the combination bands between the CF stretch fundamental and the Fermi polyad frequencies. The comparison with the 2D study is carried out by the use of a full set of dynamical and spectroscopic variables, based on the autocorrelation function of the bright states of each polyad. The spectroscopic variables then follow by Fourier transforming the autocorrelation function, while the dynamical ones emerge via survival probability in the frame of the dynamical statistical ensemble. These include several relaxation times and the number of cells and rates of phase-space exploration. The specific effect of the third mode is monitored by following the reduced dynamics of the system irrespective of the polyad stretch-bend dynamics, through population evolution. Dynamical results clearly reveal the third mode effects at very short and long times. In the last regime, we can observe a great span of different behaviors, depending on how the third mode excited states are involved. This richer variety of dynamical patterns cannot be observed in a two-mode model and justifies the present work. The spectroscopic results of both models are in good agreement with the experimental results.