
// Make newform 441.2.bb.d in Magma, downloaded from the LMFDB on 25 April 2024.
// 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_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_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)
    return MakeCharacter_441_bb();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_441_2_bb_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_441_2_bb_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_441_bb();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![729, 8748, 94770, 120285, -2429514, -13553568, 14881428, 164732643, 176107320, -1029066183, 1054628136, 460195632, -2725523000, 3457721601, -596908112, -4764576089, 8486973495, -6794434022, 471275179, 4819406471, -4799895474, 1255417912, 1581095860, -2034512224, 1095013975, -179961202, -139112732, 73154844, 22061348, -34010633, 11095130, 4462552, -6578229, 3320702, -823626, 12909, 79166, -54238, 41812, -36353, 27882, -17506, 9018, -3829, 1339, -382, 85, -13, 1]>],Snew);
    return Vf;
end function;