Let $\{e_1,e_2,e_3,e_4\}$ be a basis for $V=C^4$, where $V$ is a $C[\mathbb{S}_3]$-module. If for every $\sigma \in \mathbb{S}_3$ $\sigma(e_i)=e_{\sigma(i)}$ and $\sigma(e_4)=e_4$ find $\chi(1 2)$ and $\chi(1 2 3)$.
I thought of finding the character table of $\mathbb{S}_3$ and think of $\chi$ as the standard character