"Source: Text/Geometry/ModSym.text";
"Line: 748";
"Date: Mon Aug 27 15:40:50 2018";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Geometry/ModSym.text, line: 748
// Example: H142E7 ()
print "Example: H142E7";
ei := GetEchoInput();
SetEchoInput(true);
M := ModularSymbols(1,12);
Basis(M);
IntegralBasis(M);
R<X,Y> := PolynomialRing(Rationals(),2);
[M!<X^i*Y^(10-i),[Cusps()|0,Infinity()]> : i in [0..10]];
C := CuspidalSubspace(M);
IntegralBasis(C);
M := ModularSymbols(1,12);
E := EisensteinSubspace(M);
IntegralBasis(E);
ManinSymbol(IntegralBasis(E)[1]);
function EisZ(k)
   E := EisensteinSubspace(ModularSymbols(1,k));
   B := IntegralBasis(E);
   return [ManinSymbol(z) : z in B];
end function;
EisZ(12);
EisZ(16);
EisZ(18);
EisZ(20);
EisZ(22);
SetEchoInput(ei);
