We investigate thermodynamic properties of the rotating Bose gas in a trap, taking the charged ideal Bose gas in a magnetic field as an example.The system is equivalent to a neutral gas in a synthetic magnetic field.It is indicated that the Bose-Einstein condensation temperature is irrelevant to the magnetic field, conflicting with established intuition that the critical temperature decreases with the field increasing.The specific heat and Landau diamagnetization also exhibit intriguing behaviors.