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In the class order $(E,8C_3,3C_2,6S_4,6{\sigma }_d)$, the 15 Cartesian nuclear displacements of methane have characters $(15,0,-1,-1,3)$. Only nuclei left fixed by an operation contribute to that operation's trace. Subtract translations $T_2$ and rotations $T_1$ to obtain the methane normal-mode representationIts dimension is $1+2+3+3=9=3(5)-6$. There are four frequency families: a nondegenerate symmetric stretch, a doubly degenerate bend, and triply degenerate stretch and bend modes.

The relevant decomposition is unchanged:Thus the same $E$ and $T_2$ vibrational symmetries are linearly Jahn-Teller active. Their coupling constants and the resulting energy surface can differ from those of a $T_1$ state. The ground-geometry methane normal-mode representation and the symmetry-allowed harmonic invariants are also unchanged; actual force constants in the excited state need not have the same values.