In this paper we examine the spectral changes in a white light laser filament due to different pulse shapes generated by a pulse shaping setup. We particularly explore how the properties of the filament spectra can be controlled by parametrically tailored white light pulses. The experiments are carried out in a gas cell with up to 9 bar of argon. Plasma generation and self-phase modulation strongly affect the pulse in the spectral and temporal domain. By exploiting these effects we show that the pulse spectrum can be modified in a desired way by either using second order parametric chirp functions to shift the filament spectrum to higher or lower wavelengths, or by optimizing pulse shapes with a genetic algorithm to generate more complex filament spectra. This paper is one of the first examples of the application of complex, parametrically shaped white light pulses.