
// Make newform 8033.2.a.d in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8033_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8033_2_a_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_8033_a();"
function MakeCharacter_8033_a()
    N := 8033;
    order := 1;
    char_gens := [5541, 1944];
    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_8033_a_Hecke(Kf)
    return MakeCharacter_8033_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8033_2_a_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_8033_2_a_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8033_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![9648337658368, 510935933839424, 5825338915493688, -122946968181880089, -2929108510245095691, 240669658575329863, 408666181828284494473, 1731666403280664063105, -29191467747313324840528, -196104610636569292885238, 1279719620962069764877735, 11636363235856285093973746, -37178835897441777085846551, -455279987428007923043459356, 728349322997695562800798791, 12882922896062163321548472900, -8932746540284137760880092641, -277701928061641736517477757932, 35446568738246199854601843419, 4718609214664431190707995269742, 1162078583648620655903140555865, -64781147792486271707696838037303, -32543667997258470892131445228764, 732396429269894088077043211530373, 498955512547712747079570225868092, -6924205200003498090718414571941672, -5587381817068619620083229570097721, 55447042570124751570296200591380097, 49583782131474907623711101397767752, -380212527840811851268966862817592045, -362290511443121094171415361970122492, 2254006305685586091027922740251842930, 2229753858918285062650081335649580239, -11649733222096943401739596242606140923, -11741846374918198162589075149637672855, 52887715065413331190543150222607882485, 53530042045126539050472530840141058634, -212310253722289076571085263913566610572, -213254062471840845393496753395344326442, 758160847030152598402192861950251460983, 748143945542079457270185308966378488397, -2421335051257474235524701348279493315410, -2326464793357983912002411143944574670057, 6949302921803793210247900063395280540392, 6448680791532042703909298217759635508687, -18000960991025577163639594788540563953595, -16011406416095602503044556947552912266919, 42247533639684486291845589857501709603095, 35762487819488416373356969306140197808482, -90150770549387796552948730014524874906917, -72126126190430799166312763117819828159115, 175451726474504308701895363024847718422603, 131779962770146093785975603567557226211663, -312310795602198931219781417373200328011680, -218746109845951858054751511406555692458010, 509749757622155509316584218926037230781272, 330702257165517538756155153321430589502545, -764644132841767760225968680654768659599201, -456296596041915348185596146715301555438949, 1056305909506773880182994330686040006673985, 575590508618606836731778202967036232419194, -1346351233310620272708875425692644541002710, -664672177925374418957433348067406529756392, 1585985760830360288332244779915370862012594, 703250972017009906041814447800761763480981, -1729329464815085993603656022082917472949884, -681995257513471131939838119951871404130905, 1747820899297308502648890687994809358783726, 606040164719934692554578093886214341062370, -1639469567503118348637686144910479369289542, -492920845597426408592780395572693473130115, 1428865587218253990942825122500341900966576, 366077463204682676055929412398596525369394, -1158262000760675843371856956987349314827234, -247172433772791119074874367242716797968968, 874077426230107074695734512129206336685626, 150555377349545042530580740341076381910715, -614578876121879398288461627051354617786399, -81553637227922314306176052027655939643241, 402907537574254335246520607384451562364748, 38153005257330649678676564927052986804032, -246438337179081677738330524967164972956579, -14329121707766155131815435209362641925971, 140708959618961167967714373965324519930633, 3228542190140135966731286655898574685080, -75031226064235430027187556539255703650060, 827379725186690355081854918055783198848, 37378848019317998599788771792230521972363, -1641173438342887142433453537950648217574, -17401635943126086457383230016793399617726, 1319782160626138185986286223613560909121, 7571990922608740831199328881565961007538, -810192882888356588959464210095876195496, -3079772243592934261376102027577889736540, 423638730398252812837458048233821580630, 1170854803621113874479368481599968541105, -196366059426120221248984923764606741381, -416008647481032509495569297155929307538, 82241757260036746449997236385808770644, 138102891012179898957016584057309292093, -31453434156550404113660033196183352275, -42818568491479324097360838521615721007, 11055500367297065998381475485475062152, 12392317932913867634288069914840570424, -3585964497698241209352412985628096055, -3345417380574644300835934883497757210, 1076276188875590107443455830224833848, 841632638472103132039858378638396367, -299436009530394891697862208227747006, -197087339972910193377235148431872123, 77310369917642379483721967570366985, 42895749873155851340711219835385340, -18535540834769900074469853827804208, -8661093037438793341071124692462934, 4127812030701559963366790778716283, 1618409574819463843401019261653095, -853797536255888896218940776567329, -278995432090077532860208434225016, 163968088516973173756018706476524, 44184270038062483909689373767907, -29219104719398745308437771780616, -6390620079809026264477649053457, 4827240753843005193905243420464, 836846284139113864808143344508, -738521391927273473783270493752, -97844001257912613265415182875, 104483458204444774595611850251, 9961955069260987679785297642, -13646196429169402107671317568, -836619541804501552486209092, 1641993163484249548999653658, 48995630378007888085124504, -181584896106698782815321776, -84361439979970359245907, 18403479893471196921558054, -501520829139944921023063, -1703606187505587005096298, 91535645625320794116091, 143466057582545031879296, -11392324777457114852636, -10938481300308943798746, 1146000448450741736140, 750700499088293434909, -97889913033874052018, -46042783001707798320, 7232334055961431546, 2500944463630039437, -465034990059732012, -118891512312362026, 26014551611128475, 4866901011173758, -1260048060986696, -167501599851290, 52384575503051, 4658431311689, -1845037662227, -96574590701, 54043308953, 1154362372, -1282022240, 6772092, 23676691, -674469, -319504, 15629, 2803, -188, -12, 1]>],Snew);
    return Vf;
end function;