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Density and time-dependent density functional theory have been used to simulate the vibronic structure of the emission and absorption spectra of a typical trimethine cyanine dye. This approach combines the BH and HLYP exchange-correlation functional with the Doktorov scheme to evaluate the Franck-Condon factors. The absorption and emission spectra present a dominant band and a shoulder, which nicely reproduce the experimental data. The theoretical calculations demonstrate that the simplicity of the shape results from rather small geometry relaxations in the first excited state, though many vibrational normal modes contribute to it.