
// Make newform 430.2.q.c in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_430_q();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_430_2_q_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_430_q();"
function MakeCharacter_430_q()
    N := 430;
    order := 21;
    char_gens := [87, 261];
    v := [21, 17];
    // 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_430_q_Hecke(Kf)
    return MakeCharacter_430_q();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_430_2_q_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_430_2_q_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_430_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![116488849, -1517538972, 2380539743, 13373688466, 50236948068, 80961344819, -4242275082, -412480305671, -728612430756, -39439751884, 1815152916259, 3945491279565, 5445325616310, 5914982477018, 5320422621137, 3887047913980, 2176900211805, 908696725016, 357859060115, 231933695882, 196324104753, 138764569560, 66718587528, 14875646796, -1632895596, -822942094, 200981019, 516718293, 840837206, 478552988, 128559372, 56698388, 22722433, 2454789, 2500125, 1794441, 208150, -138021, -70365, -31669, -3550, 3112, 1342, -45, -198, -41, 12, 7, 1]>],Snew);
    return Vf;
end function;