
// Make newform 441.2.bb.c in Magma, downloaded from the LMFDB on 10 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_441_bb();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_441_2_bb_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_441_bb();"
function MakeCharacter_441_bb()
    N := 441;
    order := 21;
    char_gens := [344, 199];
    v := [21, 16];
    // 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_441_bb_Hecke( : Kf := Kf)
    return MakeCharacter_441_bb();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_441_2_bb_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_441_2_bb_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_441_bb();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1681, -67650, 794998, -2037571, 664507, 290591, 6519914, -10918434, 29086251, -43480464, 26379556, 5695537, 34664346, 21893625, -121731052, 8168195, -6287702, 184521159, -37641322, 61785561, 52537497, -211737064, 315974536, -225086287, 140937360, -39914208, -6798801, 13604129, -2929504, -2883777, 2105581, -270255, -194520, 60683, -93517, 75361, 4119, -24778, 10794, 1464, -2615, 258, 317, -63, -12, 10, -5, -1, 1]>],Snew);
    return Vf;
end function;