
// Make newform 387.3.j.f in Magma, downloaded from the LMFDB on 08 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_387_j();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_387_3_j_f();".
// 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_387_j();"
function MakeCharacter_387_j()
    N := 387;
    order := 6;
    char_gens := [173, 46];
    v := [6, 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_387_j_Hecke(Kf)
    return MakeCharacter_387_j();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_387_3_j_f();".
// 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_387_3_j_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_387_j();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<2,R![51381, 0, 142468, 0, 120479, 0, 46229, 0, 9075, 0, 942, 0, 49, 0, 1]>],Snew);
    return Vf;
end function;