
// Make newform 672.4.i.c in Magma, downloaded from the LMFDB on 28 December 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_672_i();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_672_4_i_c();".
// 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_672_i();"
function MakeCharacter_672_i()
    N := 672;
    order := 2;
    char_gens := [127, 421, 449, 577];
    v := [2, 1, 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_672_i_Hecke(Kf)
    return MakeCharacter_672_i();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_672_4_i_c();".
// 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_672_4_i_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_672_i();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<5,R![395329100828147712, 0, 347349051281676288, 0, 82397884120202752, 0, 6978739579684864, 0, 246895591977664, 0, 4358828758336, 0, 42479046160, 0, 239880544, 0, 782932, 0, 1372, 0, 1]>],Snew);
    return Vf;
end function;