
// Make newform 560.2.bb.c in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_560_bb();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_560_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_560_bb();"
function MakeCharacter_560_bb()
    N := 560;
    order := 4;
    char_gens := [351, 421, 337, 241];
    v := [4, 3, 2, 4];
    // 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_560_bb_Hecke(Kf)
    return MakeCharacter_560_bb();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_560_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_560_2_bb_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_560_bb();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![819200, -29327360, 524959744, 1970012160, -13903093760, -110316445696, 15227451920384, 172467366887424, 965148755218432, 1697346063372288, 1359177655527424, 610914947383296, 15234290871968768, 20021715155567616, 12915500733493760, 248680452952064, 67878903507359360, 79340166141280896, 46364827660830528, 1193721688310784, 110334722723394336, 126651610241304608, 72705609577732752, 246079087842688, 74219001468737792, 85463495187250368, 49185463901434432, -961414961524800, 23953703051348784, 27711062426560560, 16024385012642008, -619186280313568, 4458831782349400, 5117371668294152, 2942591273078556, -150128567956784, 528543583396034, 591783235210850, 333358309604481, -18289874385008, 41652590245456, 44962583854096, 24503801702568, -1236872530416, 2202344585624, 2288015855096, 1200647539116, -48568812656, 77464823648, 77939951552, 39514770896, -1111935632, 1775083820, 1747662476, 863999094, -14291152, 25614192, 24964592, 12182648, -93712, 220968, 215496, 105076, -240, 1032, 1016, 500, 0, 2, 2, 1]>],Snew);
    return Vf;
end function;