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The study of modulated electron beams is important because they can be used to produce coherent radiation, but the modulations can cause unwanted instabilities in some devices. Specifically, in a free electron laser, proper prebunching at the desired emission frequency can enhance performance, while bunching resulting from instabilities and bunch compression schemes can degrade performance. In a photoinjector accelerator, tailoring the shape of the drive laser pulse could be used as a technique to either enhance or mitigate the effect of these modulations. This work explores the possibility of creating deeply modulated electron beams at the photocathode by using a modified drive laser designed to produce multiple subpicosecond pulses repeated at terahertz frequencies. Longitudinal space charge forces can strongly influence the evolution of modulations by converting density modulations to energy modulations. Experiments at the Source Development Laboratory electron accelerator at Brookhaven National Laboratory and PARMELA simulations are employed to explore the dynamics of electron beams with varying charge and with varying initial modulation. Finally, terahertz light generated by a transition radiator is used to confirm the structure of the electron beam.