Linear representation theory of projective special linear group:PSL(3,2)

GAP implementation
The degrees of irreducible representations can be computed using GAP's CharacterDegrees and PSL functions:

gap> CharacterDegrees(PSL(3,2)); [ [ 1, 1 ], [ 3, 2 ], [ 6, 1 ], [ 7, 1 ], [ 8, 1 ] ]

The characters of irreducible representations can be computed using GAP's CharacterTable function:

gap> Irr(CharacterTable(PSL(3,2))); [ Character( CharacterTable( Group([ (4,6)(5,7), (1,2,4)(3,6,5) ]) ), [ 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( Group(   [ (4,6)(5,7), (1,2,4)(3,6,5) ]) ), [ 3, -1, 1, 0, E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4 ] ), Character( CharacterTable( Group(    [ (4,6)(5,7), (1,2,4)(3,6,5) ]) ), [ 3, -1, 1, 0, E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6 ] ), Character( CharacterTable( Group(    [ (4,6)(5,7), (1,2,4)(3,6,5) ]) ), [ 6, 2, 0, 0, -1, -1 ] ), Character( CharacterTable( Group([ (4,6)(5,7), (1,2,4)(3,6,5) ]) ), [ 7, -1, -1, 1, 0, 0     ] ), Character( CharacterTable( Group([ (4,6)(5,7), (1,2,4)(3,6,5) ]) ), [ 8, 0, 0, -1, 1, 1 ] ) ]