  The quadratic form of the isobaric multiplet mass equation (IMME), which was
originally suggested by Wigner and has been generally regarded as valid, is
seriously questioned by recent high-precision nuclear mass measurements. The
usual resolution to this problem is to add empirically the cubic and quartic
$T_z$-terms to characterize the deviations from the IMME, but finding the
origin of these terms remains an unsolved difficulty. Based on a strategy
beyond the Wigner's first-order perturbation, we derive explicitly the cubic
and quartic $T_z$-terms. These terms are shown to be generated by the effective
charge-symmetry breaking and charge-independent breaking interactions in
nuclear medium combined with the Coulomb polarization effect. Calculations for
the $sd$- and lower $fp$-shells explore a systematical emergence of the cubic
$T_z$-term, suggesting a general deviation from the original IMME.
Intriguingly, the magnitude of the deviation exhibits an oscillation-like
behavior with mass number, modulated by the shell effect.
