"Source: Text/Geometry/Lseries.text";
"Line: 2562";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Lseries.text, line: 2562
// Example: H139E28 ()
print "Example: H139E28";
ei := GetEchoInput();
SetEchoInput(true);
E := EllipticCurve("32a"); // congruent number curve
chi := DirichletGroup(32).1; // character of conductor 4 lifted
MF := ModularForms(chi, 3); // weight 3 modular forms on Gamma1(32,chi)
NF := Newforms(MF);
NF[1][1]; // q-expansion of the desired form
Parent(Coefficient(NF[1][1], 3)); // defined over Q(i)
f1, f2 := Explode(ComplexEmbeddings(NF[1][1])[1]);
L1 := LSeries(E);
L2 := LSeries(f1); // first complex embedding
L := TensorProduct(L1, L2, [ <2, 9> ]); // conductor 2^9 (guessed)
time CFENew(L);
SetEchoInput(ei);
