# Eliminate symmetric Gammas in Majorana bilinears

I am working in d=11 supergravity with the following convention for the charge-conjugation matrix:
$$C^T=-C$$

$$(C\Gamma^{m1\dots mr})^T=+C\Gamma^{m1\dots mr} \quad r=(1,2)mod4$$

and with an anticommuting Majorana spinor $\eta$.

How to set automatically to zero all the expressions of the type
$$\bar \eta \Gamma^{m1\dots mr} \eta=0\qquad r=(1,2)mod4$$
when for ex. $\Gamma^{m1\dots mr}$ is the result of a "join_gamma()"?