Linear representation theory of projective special linear group:PSL(2,13)

Degrees of irreducible representations
These can be computed using the CharacterDegrees, GAP:CharacterTable, and PSL functions:

gap> CharacterDegrees(CharacterTable(PSL(2,13))); [ [ 1, 1 ], [ 7, 2 ], [ 12, 3 ], [ 13, 1 ], [ 14, 2 ] ]

Character table
This can be computed using the Irr, CharacterTable, and PSL functions:

gap> Irr(CharacterTable(PSL(2,13))); [ Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),     (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ), [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),     (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ),    [ 7, 0, 0, 0, 1, -1, -1, -E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10-E(13)^12,      -E(13)^2-E(13)^5-E(13)^6-E(13)^7-E(13)^8-E(13)^11 ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),     (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ),    [ 7, 0, 0, 0, 1, -1, -1, -E(13)^2-E(13)^5-E(13)^6-E(13)^7-E(13)^8-E(13)^11       , -E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10-E(13)^12 ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),     (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ),    [ 12, -E(7)^3-E(7)^4, -E(7)-E(7)^6, -E(7)^2-E(7)^5, 0, 0, 0, -1, -1 ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),     (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ),    [ 12, -E(7)^2-E(7)^5, -E(7)^3-E(7)^4, -E(7)-E(7)^6, 0, 0, 0, -1, -1 ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),     (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ),    [ 12, -E(7)-E(7)^6, -E(7)^2-E(7)^5, -E(7)^3-E(7)^4, 0, 0, 0, -1, -1 ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),     (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ), [ 13, -1, -1, -1, 1, 1, 1, 0, 0     ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),      (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ), [ 14, 0, 0, 0, -1, 2, -1, 1, 1     ] ), Character( CharacterTable( Group([ (3,13,11,9,7,5)(4,14,12,10,8,6),      (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]) ), [ 14, 0, 0, 0, -1, -2, 1, 1, 1     ] ) ]