Wohlfahrt's Theorem and index formula for elementary matrix groups and $SL(2,\mathcal{O})$

The present article determines the indices of the principal congruence subgroups of the Bianchi groups $B_d$, $SL(2,\mathcal{O})$ and elementary matrix group $E$ and extends Wohlfahrt’s Theorem to $B_d$, $SL(2,\mathcal{O})$ and $E$, where $\mathcal{O}$ is the ring of integers of some number fields.