The Wikipedia pages for $E_6$ and $E_7$ list three series of groups notated as each of $E_6(q)$, $^2E_6(q)$, and $E_7(q)$:

 - The simple form, analogous to $PSL_n(q)$
 - The adjoint form, analogous to $PGL_n(q)$
 - The universal form, analogous to $SL_n(q)$

Is there a fourth series analogous to $GL_n(q)$?