 Solution

For a real nonmagnetic $T_1$ electronic triplet, the symmetric square of a group representation decomposes asThe $A_1$ coordinate shifts all components equally and does not remove the degeneracy. The linear Jahn-Teller selection rule therefore permits $E$ and $T_2$ vibrational modes to couple and split the triplet. Both methane $T_2$ vibrational triplets are symmetry-eligible. A nonzero allowed coupling generally produces a symmetry-lowering instability, although symmetry alone does not determine its strength or the preferred minimum.