A published reference is here: msp.org/pjm/2001/197-1/pjm-v197-n1-p07-p.pdf. However note that there is an assumption of semi-simplicity, but this is easy to generalize to reductive groups.

I have a related but soft question. Are there results that quantify how many level raised $g$ exist for a given $f$ under Ribet's theorem?

I saw that paper, but I wanted to hear about the generalizations for the n-dimensional case. Also, in the 2-dimensional case, there seem to be some minor conditions placed on the representation, so I wanted someone to clarify that as well.