To extend the research on the atomic structure of tungsten ions with an open 4f-shell, we conducted an investigation into the M1 transitions originating from the ground configuration of W23+ using the SHHtscEBIT in the 420–600 nm range. Three different calculational methods, including the relativistic configuration interactions (RCI) and the relativistic many-body perturbation theory (RMBPT) implemented in FAC, as well as the multiconfiguration Dirac-Hartree-Fock (MCDHF) in GRASP2018, are performed to investigate the energy level structure of W23+. The excitation energies obtained through RCI and RMBPT are in good agreement, with an average difference of 0.62 %. When comparing RCI and MCDHF, this difference increases to 1.20 %. The observed 12 lines of W23+are identified using the detailed collisional-radiative model with the atomic data calculated by RCI. The average wavelength deviations from experimental results are 0.77 %, 1.38 %, and 2.02 % for RCI, RMBPT, and MCDHF, respectively.