
// Make newform 20.11.d.d in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_20_d();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_20_11_d_d();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_20_d();"
function MakeCharacter_20_d()
    N := 20;
    order := 2;
    char_gens := [11, 17];
    v := [1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_20_d_Hecke(Kf)
    return MakeCharacter_20_d();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_20_11_d_d();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_20_11_d_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_20_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,11,sign)));
    Vf := Kernel([<3,R![20712001879922408790530457600, 0, -4296719597795414433792000, 0, 283487924231943782400, 0, -7756847217446400, 0, 93360281616, 0, -503592, 0, 1]>],Snew);
    return Vf;
end function;