RADEX excitation best-fit model (T_kin = 9 K, n_H2 = 1.3 × 10⁵ cm⁻³, A/E = 1, and N_col(A) = 1.8 × 10¹⁴ cm⁻² and 0.7 × 10¹⁴ cm⁻² for the G₁ and G₂ velocity components in Table 2, respectively), overlaid in red on top of the ALMA methanol spectra toward the southwest image of PKS 1830−211. The methanol type, quantum numbers (J_K), and rest frequency (GHz) are given in the bottom right corner for each transition. The ALMA band is given in the bottom left of each frame. The last row shows the ¹³CH₃OH spectra (all of A type), with the RADEX fit of the corresponding transitions of the main isotopologue, scaled down by a factor 62; hence, these lines were not taken into account in the χ² minimization.