A detailed computational characterization of the one-photon absorption spectrum of a 2-((E)-2-[ 2,2']-bithiophenyl-5-yl-vinyl)-1-methyl-quinolinium cation in acetonitrile solution is presented. The main physico-chemical effects (solvation, vibronic progression) affecting the band position and shape are progressively introduced in the computational model, highlighting their relative role in the spectral profile. The reported results underline how an accurate reproduction of the experimental spectrum can only be obtained by going beyond oversimplified methods. Moreover, the deep interplay between the solvent effects and nuclear rearrangements permits the negative solvatochromism exhibited by hypsochromic molecules to be explained. This illustrates the potential of the computational investigation, which can shed light on the information hidden in experimental spectra.