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We report that the suppressed vibrational modes in nanoconfined water lead to an apparent solid-like behavior at terahertz frequencies, as observed experimentally. Terahertz nano-trenches composed of two gold films are realized using atomic layer lithography and a dilution method, with widths controlled to range from 2 to 20 nm. One reason for the anomalously low dielectric constant of thin water films is believed to be the interfacial water layers with a thickness of 0.8 nm (4 water layers). However, we found that the remaining water layers in the nano-trenches also contribute to the reduction of the dielectric constant at terahertz frequencies. Using a vibrational density of states (VDOS) model, the vibrational degrees of freedom of water molecules align with experimental results, featuring a number of vibrational modes (P) proportional to the nanoconfined volume (P~V). Through low-temperature measurements, we observed the absence of phase transition in 1.5 nm nano-trenches, which consist solely of interfacial water layers. Phase transitions in water emerged with increasing gap width, and at 20 nm, the behavior closely resembled that of bulk water.