The magnetic susceptibility of the Ising model is defined in terms of the two-point spin correlation function as \[ k_BT\cdot\chi=\sum_{M=-\infty}^{\infty}\sum_{N=-\infty}^{\infty}\{<\sigma_{0,0}\sigma_{M,N}>-\mathcal{M}^2\}, \] where \(\mathcal{M}\) is the spontaneous magnetization of the Ising model. The authors present the exact expressions of the partial susceptibilities \(\chi_d^{(3)}\) and \(\chi_d^{(4)}\) for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau equations.