Linear representation theory of special linear group:SL(2,7)

GAP implementation
The degrees of irreducible representations can be computed using CharacterDegrees:

gap> CharacterDegrees(SL(2,7)); [ [ 1, 1 ], [ 3, 2 ], [ 4, 2 ], [ 6, 3 ], [ 7, 1 ], [ 8, 2 ] ]

The character table can be computed using the Irr and CharacterTable functions:

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

The irreducible representations can be computed using the IrreducibleRepresentations functions:

gap> IrreducibleRepresentations(SL(2,7));