
// Make newform 8033.2.a.e 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_e();".
// 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_e();".
// 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_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8033_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![712050240, 408045214064, 37292115930568, 724951147191891, -26205563437937652, -790052326402088524, 6211215640906495040, 265616648879155688084, -560551411911642410071, -41208100583859234186296, 9568155452998148776021, 3508612029546969453092393, 1149356184863723057965537, -186260833888888311956088729, -68143344213101711978963175, 6732321256467448272023525979, 1317865540324583559788089773, -175711265953525367415630422959, 7881698874925602821060039641, 3451947383045726695903008902555, -1015268374394349431989077478121, -52685825179845465055378837098540, 27772149844227328620167062092771, 640812098069838019611917400924053, -472087471362583784289582740141805, -6343385306425655542824908188723152, 5857528736004653168093997469976921, 52017972007507182270542398971550578, -56737398536449413001564954475597427, -358708313566716107355950674494841297, 445833878577942136139547422745658371, 2106842602220511925747847743675286588, -2915868924940178980995765609442127871, -10655375156491154297754163371411396216, 16172736175807946626538097368609230124, 46840634673495655920310700194167476458, -77176848727785687911731581732557442419, -180426352671185719184184406738785891244, 320547804545121279818927605449553068784, 613234229873576020380544304894528996217, -1169820556307379836670975946183897515536, -1850192414870813060868104972276795783163, 3781082135283325125443281760994141228835, 4981144667039341179734573198382580425621, -10897259237573574653108056037312797863641, -12020012305164109455446635441471383080726, 28167507791427748401520989894877743318232, 26097553796763468296057939226010924703154, -65630462920145150629052365540397494195081, -51144860450715707848088581969096447460953, 138456547138681350647300195839436209920666, 90706616441643934629331331345451642895768, -265504510697386710826616886126654517436278, -145871327948657987761505700584817305646831, 464397303987854022909277996143635523737814, 212989923252461988700714610562040009360324, -743213313120836344621096300504832029093445, -282500598989496140737210692200524467162378, 1091314815121000102766070191415393989237620, 340179494964472711973443505838414622215224, -1473956402145337343803817905906194846287673, -371136163297998106178884301143616920028816, 1835253096615095092923005667750900168422094, 365242980324304877886830791377529471959758, -2110904936601763629925542489836163688843243, -321477398203620258590388744311453020090985, 2247003121396743261846086947892265570951271, 248856219744461872994141513042310179385249, -2217311998614355812232828749442313484184458, -163324514120130460530655163481218607032888, 2031403210411875544463530799114188617745049, 82101517117658179865899416457123809219469, -1730246980535462935542617958421850885469316, -18198814822430491475050444037037855452056, 1371837688569514443186700920593523676168344, -22580677668903809113899373558225616881714, -1013603367237411299218129198793285640982205, 41434188100138643255845366475349094830368, 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30683252746210849560661914490765062492, 45129700920698956332530365451805442087, -9982893016952061314503620214983168764, -13254061224405789011878348329427956067, 3033571000128786382405103151365517769, 3649020191229367698619924132700557796, -861297204118461725042999234983195195, -941517401127152027458403856755954699, 228523112195730182840815376150250189, 227588068610568670681730379333888488, -56661647623551233756935203638424811, -51515989929634253332134026862872786, 13127005881118496293491194253502566, 10913496053138368266563313328678735, -2840726712142871719462790284259382, -2162346450410379686964250282216828, 573965544495435891908096058941455, 400391737635121437707651884115810, -108211876211136925221029991430353, -69222380309287751346031160591437, 19022596661571031967195474446497, 11162247709559292193582521132991, -3115107457811026775351409236446, -1676776929455198244505926303758, 474692158867223097646205503449, 234324351749223126318687986322, -67225323308622695495513359211, -30415450084928492120835868982, 8834707846373622253110679262, 3660389431336575697065487900, -1075591010425141512507678934, -407596329630501713646827020, 121071840783842240219971295, 41897964414641985522620385, -12571816321819673280747237, -3965164355942784441516025, 1201110154258011630336639, 344439025792269461820131, -105268234288343031704168, -27366781441035911241276, 8434105785634261343740, 1980763544482569279231, -615266786304821778217, -129982352565540468904, 40675449501660069002, 7690658090451453041, -2423511564764033597, -407568676854544964, 129284368266568333, 19193094141663955, -6126269930415540, -795389496465240, 255382068510353, 28658589857430, -9253126834106, -884038152364, 286946520784, 22877593891, -7463082824, -483027112, 158324083, 7990158, -2630845, -97109, 32112, 771, -256, -3, 1]>],Snew);
    return Vf;
end function;