Charge density waves (CDWs) involved with electronic and phononic sub\x{FFFE}systems simultaneously are a common quantum state in solid-state physics, especially in low-dimensional materials. However, CDW phase dynamics in various dimensions are yet to be studied, and their phase transition mechan\x{FFFE}ism is currently moot. Here we show that using the distinct temperature evolution of orientation-dependent ultrafast electron and phonon dynamics, different dimensional CDW phases are verified in CuTe. When the temperature decreases, the shrinking of c-axis length accompanied with the appearance of interchain and interlayer interactions causes the quantum fluctuations (QF) of the CDW phase until 220 K. At T < 220 K, the CDWs on the different ab-planes are finally locked with each other in anti-phase to form a CDW phase along the c-axis. This study shows the dimension evolution of CDW phases in one CDW system and their stabilized mechanisms in different temperature regimes.