If you are really just interested in particular examples, it might just be easier to read it off from the character table, which you can compute with $\texttt{magma}$. Since the groups are simple in this case, it is especially easy, since everything is faithful (except for the trivial representation) so you just want the first column. Here's some cheap $\texttt{magma}$ code which computes the generating function of the dimensions of all representations of a finite group $G$ for which $\texttt{magma}$ can compute the character table:

$\texttt{Q := RationalField();}$

$\texttt{P<x> := PolynomialRing(Q);}$

$\texttt{Z := Integers();}$

$\texttt{function dimensionsofrepresentations(G)}$

$\texttt{X:=CharacterTable(G);}$

$\texttt{sum:=0;}$

$\texttt{for i in [1..#X] do}$

$\texttt{sum:=sum + x^(Z!X[i,1]);}$

$\texttt{end for;}$

$\texttt{return sum;}$

$\texttt{end function;}$

$\texttt{> dimensionsofrepresentations(ProjectiveSpecialLinearGroup(4,7));}$

$\texttt{x^182400 + 4*x^159600 + 2*x^139650 + 2*x^137200 + 27*x^136800}$

$\texttt{ + 9*x^119700 + x^117649 + 56*x^115200 + 15*x^102600 + 3*x^100548}$

$\texttt{+ 48*x^98496 + 2*x^91200 + 2*x^69825 + 8*x^51300 + 2*x^50274 + 4*x^22800}$

$\texttt{ + 2*x^22400 + 5*x^19950 + x^19551 + 9*x^17100 + 2*x^2850 +
x^2450}$

$\texttt{ + 3*x^2052 + 2*x^1425 + 2*x^1026 + 2*x^400 + x^399 + x}$

$\texttt{> dimensionsofrepresentations(SymplecticGroup(6,2));}$

$\texttt{x^512 + x^420 + x^405 + x^378 + x^336 + x^315 + 2*x^280 + x^216 + 2*x^210}$

$\texttt{+ 3*x^189 + x^168 + x^120 + 3*x^105 + x^84 + x^70 + x^56 + 2*x^35 + x^27}$

$\texttt{ + 2*x^21 + x^15 + x^7 + x}$