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gap> gamma:=HAP_CongruenceSubgroupGamma0(39);;
gap> p:=2;;k:=2;;T2:=HeckeOperator(gamma,p,k);;
gap> Display(T2);
[ [ -2, -2, 2, 2, 1, 2, 0, 0, 0 ],
[ -2, 0, 1, 2, -2, 2, 2, 2, -2 ],
[ -2, -1, 2, 2, -1, 2, 1, 1, -1 ],
[ -2, -1, 2, 2, 1, 1, 0, 0, 0 ],
[ -1, 0, 0, 2, -3, 2, 3, 3, -3 ],
[ 0, 1, 1, 1, -1, 0, 1, 1, -1 ],
[ -1, 1, 1, -1, 0, 1, 2, -1, 1 ],
[ -1, -1, 0, 2, -3, 2, 1, 4, -1 ],
[ 0, 1, 0, -1, -2, 1, 1, 1, 2 ] ]
gap> Eigenvalues(Rationals,T2);
[ 3, 1 ]
gap> p:=5;;k:=2;;h:=HeckeOperator(gamma,p,k);;
gap> Display(T5);
[ [ -1, -1, 3, 4, 0, 0, 1, 1, -1 ],
[ -5, -1, 5, 4, 0, 0, 3, 3, -3 ],
[ -2, 0, 4, 4, 1, 0, -1, -1, 1 ],
[ -2, 0, 3, 2, -3, 2, 4, 4, -4 ],
[ -4, -2, 4, 4, 3, 0, 1, 1, -1 ],
[ -6, -4, 5, 6, 1, 2, 2, 2, -2 ],
[ 1, 5, 0, -4, -3, 2, 5, -1, 1 ],
[ -2, -2, 2, 4, 0, 0, -2, 4, 2 ],
[ 1, 3, 0, -4, -4, 2, 2, 2, 4 ] ]
gap> Eigenvalues(Rationals,T5);
[ 6, 2 ]
gap>T2*T5=T5*T2;
true
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