
// Make newform 6005.2.a.g in Magma, downloaded from the LMFDB on 17 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6005_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6005_2_a_g();".
// 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_6005_a();"
function MakeCharacter_6005_a()
    N := 6005;
    order := 1;
    char_gens := [1202, 11];
    v := [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_6005_a_Hecke(Kf)
    return MakeCharacter_6005_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6005_2_a_g();".
// 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_6005_2_a_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6005_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-28158256848, -637367847724, 6173161166108, 182415613450838, -225980537145775, -19208534514948742, -30468534186553421, 968459052091890152, 2766505979654002706, -27966125356826243485, -101977462876908806128, 513937527780828616403, 2209672529414771492916, -6438735932501548460725, -32044076828891992841145, 57726684691827606220796, 334638213454790515614203, -382758024870044304126727, -2642511607446428970773255, 1911258004524540238849164, 16342441988832215110542988, -7182629263926348100196868, -81271811241108089040684384, 19550888278074206084849823, 331733768497013275767603399, -32244405806423772035699055, -1129689794356520945535317067, -9215550912969640791500788, 3252501335448529055607108638, 281857900952988362218040742, -8004568976923905726454928104, -1166202827917348178615250701, 16995228751915121835165140625, 3234795282932008603333639612, -31375242019084138068776357541, -7033896531859775667754458799, 50703212444908916648388984198, 12668554925682071189461489177, -72142766183997818961478313435, -19426918947271345222948898172, 90834267317523884469715191673, 25790243492731223708934407362, -101652543240278604380608796221, -29976806281260740465192457548, 101501254385909011841073197425, 30759450469241865426154019441, -90734902379488833652394731802, -28040656272045911399676029310, 72829783765149826512375629272, 22824319763339282730614126782, -52625149676931579646756716799, -16656172289141075818596776074, 34308116647207643264306874581, 10933706717252112905933163097, -20218681188458060991006448639, -6473868270374104731822579345, 10788660150455171600280302420, 3465283699707043663901907060, -5219484184288398603135798871, -1679891852074005327182597982, 2291950331814267810404601186, 738612389541058483559513358, -914242585766347567185425203, -294863388291824696390975880, 331472930317218987099007223, 106962583974841847918843824, -109271663913552606241694004, -35274074483100380876745002, 32754543993222313461744817, 10577173860095571906848874, -8926012386354138048945947, -2883524778494065134714238, 2210360750460895374255618, 714393414504794622823080, -497003198936678267899159, -160729403341313956456158, 101362808268050515165739, 32804857879493109077554, -18724210268835359006628, -6065283231363473050414, 3127138599041232957894, 1014021671423985177934, -471119831837925967378, -152948742984801454549, 63849467675885187174, 20756010031148105877, -7758299716941404704, -2525675430685887769, 841765586213007467, 274456129186869553, -81149506297192522, -26501995805902975, 6909340976046225, 2260341880143390, -515742786937524, -169021993713796, 33441618254888, 10979732976810, -1861934347759, -612462746694, 87694062721, 28900650905, -3425160126, -1130959591, 107939281, 35708941, -2636588, -873916, 46831, 15552, -538, -179, 3, 1]>],Snew);
    return Vf;
end function;