The coreless linear synchronous motor is essential for improving the operational speed and stability of electrodynamic suspension (EDS) trains. This paper presents a three-dimensional analytical model to examine its magnetic field and electromagnetic characteristics. Initially, the Biot-Savart law is used to determine the spatial magnetic field distribution functions of the primary. Then, a two-dimensional Discrete Fourier transformation(2D-DFT) is applied to derive a unified analytical expression for the motor's three-dimensional magnetic field. Based on the second-order vector potential (SOVP), three-dimensional force equations are formulated and validated through finite element analysis (FEA). The proposed model's effectiveness is further confirmed using FEA and data from the Yamanashi test line. Additionally, an in-depth analysis of the motor's performance under various conditions is conducted.