The fluorescence and fluorescence-excitation spectra of C-60 in a hydrocarbon glass at 1.2 K are reported. The fluorescence spectrum resembles that of a molecular X-trap in crystalline C-60. The vibronic bands in these spectra are assigned, and the intensity distribution among the false origins points to vibronic coupling within the singlet manifold. The lowest excited singlet state of C-60 shows predominantly T-1g and G(g) character. Additionally, we show that a reduction of the symmetry of C-60 by either an intra- or an intermolecular perturbation leads to a fluorescence spectrum with a strong 0-0 transition and a different vibronic structure.