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A novel-designed compact, ultrafast electro-optic slow light modulator based on two-dimensional coupled photonic crystal resonator arrays (2D CPCRAs) has been studied. The 2D CPCRAs, realized in silicon-on-insulator (SOI) slabs with nonlinear polymer as filling material, exhibit a single guided mode with low group velocity in all crystal directions. We realize fast electro-optic tuning of the slow mode in a wide frequency range with low modulating voltage in this structure. Numerical analysis shows that the frequency shift is nearly linearly increasing with the applied voltage. In addition, for a certain frequency, changing the modulating voltage can tune the group delay of slow mode easily.