"Source: Text/Geometry/RepLoc.text";
"Line: 296";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/RepLoc.text, line: 296
// Example: H152E3 ()
print "Example: H152E3";
ei := GetEchoInput();
SetEchoInput(true);
S := CuspidalSubspace(ModularSymbols(Gamma1(7), 5, 1));
newforms := NewformDecomposition(S);
Eigenform(newforms[1], 15);
pi := LocalComponent(newforms[1], 7);
pi;
chi := CentralCharacter(pi);
Conductor(chi);
assert $1 eq 7;
parameters := PrincipalSeriesParameters(pi);
Conductor(parameters[1]), Order(parameters[1]);
Conductor(parameters[2]), Order(parameters[2]);
rho := WeilRepresentation(pi); rho;
IsAbelian(Group(rho));
assert $1;
Decomposition(rho);
assert #$1 eq 2;
SetEchoInput(ei);
