"Source: Text/Geometry/ModFrm.text";
"Line: 1501";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/ModFrm.text, line: 1501
// Example: H144E12 ()
print "Example: H144E12";
ei := GetEchoInput();
SetEchoInput(true);
M := ModularForms(Gamma0(33),2); M;
Basis(M);
Basis(CuspidalSubspace(M));
Basis(EisensteinSubspace(M));
Basis(NewSubspace(M));
Basis(NewSubspace(EisensteinSubspace(M)));
Basis(NewSubspace(CuspidalSubspace(M)));
ZeroSubspace(M);
MQ := BaseChange(M, Rationals()); SetPrecision(MQ, 20);
b := Basis(MQ); b[5];
CuspidalProjection(b[5]);
EisensteinProjection(b[5]);
MQ! $1 + MQ! $2;  // Add the previous two answers, inside MQ
SetEchoInput(ei);
