"Source: Text/Geometry/Lseries.text";
"Line: 2902";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Lseries.text, line: 2902
// Example: H139E35 ()
print "Example: H139E35";
ei := GetEchoInput();
SetEchoInput(true);
x := PolynomialRing(Integers()).1;
Lf := LSeries(Newforms(ModularForms(25,4))[1][1]);
S2 := Symmetrization(Lf,[2] : BadPrimes:=[<5,2,1+125*x>]);
CFENew(S2);
S31 := Symmetrization(Lf,[3,1] : BadPrimes:=[<5,2,1+5^7*x>]);
CFENew(S31);
LSetPrecision(Lf,10);
S3 := Symmetrization(Lf,[3] : BadPrimes:=[<5,4,1>]);
CFENew(S3);
S4 := Symmetrization(Lf,[4] : BadPrimes:=[<5,4,1-125^2*x>]);
CFENew(S4);
f := Newforms(CuspForms(FullDirichletGroup(13).1^2,2))[1][1];
L := LSeries(f : Embedding:=func<x|Conjugates(x)[1]>);
BP := [<13,2,Polynomial([1,-(-Coefficient(EulerFactor(L,13),1))^2])>];
S2 := Symmetrization(L,[2] : BadPrimes:=BP);
CFENew(S2); // deg 3, conductor 169
LSetPrecision(L,15);
BP := [<13,3,Polynomial([1,-(-Coefficient(EulerFactor(L,13),1))^3])>];
S3 := Symmetrization(L,[3] : BadPrimes:=BP);
CFENew(S3); // deg 4, conductor 13^3
LSetPrecision(L,5);
BP := [<13,4,Polynomial([1,-(-Coefficient(EulerFactor(L,13),1))^4])>];
S4 := Symmetrization(L,[4] : BadPrimes:=BP);
CFENew(S4); // deg 5, conductor 13^4
SetEchoInput(ei);
