  We present a detailed analysis of the multimode quantum state embedded in an
optical frequency comb generated by a Synchronously Pumped Optical Parametric
Oscillator (SPOPO). The full covariance matrix of the state is obtained with
homodyne detection where the local oscillator is spectrally controlled with
pulse shaping techniques. The resulting matrix reveals genuine multipartite
entanglement. Additionally, the beam is comprised of several independent
eigenmodes that correspond to specific pulse shapes. The experimental data is
confirmed with numerical simulations. Finally, the potential to create
continuous-variable cluster states from the quantum comb is analyzed. Multiple
cluster states are shown to be simultaneously embedded in the SPOPO state, and
these states can be revealed by a suitable basis change applied to the measured
covariance matrix.
