
// Make newform 33.7.b.a in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_33_b();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_33_b_Hecke();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_33_7_b_a();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_33_7_b_a();".
// 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 ConvertToHeckeField(input: pass_field := false, Kf := [])
    if not pass_field then
        poly := [32367107232497664, 0, 103653954147713024, 0, 25120735435348224, 0, 1864534894961472, 0, 64843235559312, 0, 1256133373152, 0, 14594358456, 0, 103808124, 0, 441321, 0, 1026, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [103, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-919725897194802422188656739647605849456640, -46979586314588928121839836915306960687136768, 33984449411835461974909153126802245539528704, -11451977945446114834895313215979337043059456, 7331501977865499006709960709036837770422272, -481135536011064836115704722688408011387840, 473861978170147634585994413676318241705472, 3433261982355958952428328015402424517328, 13783463828700508740992178763757386863488, 504853724455810089791642708375552861216, 213260344216584773534641450165476434240, 10926150221365792389296236077987039800, 1870868860579227922676129602691040800, 111155452029042731884353419218065788, 9305043901238470997130897504577616, 598897423145120586262667776612565, 24367521309532694943956178177536, 1645477992913509925230098367434, 26019927226645542165492964304, 1812044911305722548727895053], [-15891754264220603998228887426884015578152960, -46979586314588928121839836915306960687136768, 1061006869587665420170948387840963201295863808, -11451977945446114834895313215979337043059456, 283066055817645558396075569888295124860253184, -481135536011064836115704722688408011387840, 19424584055162512225375737997791462103748864, 3433261982355958952428328015402424517328, 574279379946733013309215727090181820795136, 504853724455810089791642708375552861216, 8902153396603051649452826656211786524160, 10926150221365792389296236077987039800, 77853158871583515439909366967510704640, 111155452029042731884353419218065788, 385436250357413917814064467069735792, 598897423145120586262667776612565, 1004620243793949104303639971340192, 1645477992913509925230098367434, 1068153974319545446790291664368, 1812044911305722548727895053], [-1267308201412983760926516625315777012039680, 10371493881410992769907044219941281139064832, 33984449411835461974909153126802245539528704, -11104395641227933496157453330311165880476416, 7331501977865499006709960709036837770422272, -481135536011064836115704722688408011387840, 473861978170147634585994413676318241705472, 3433261982355958952428328015402424517328, 13783463828700508740992178763757386863488, 504853724455810089791642708375552861216, 213260344216584773534641450165476434240, 10926150221365792389296236077987039800, 1870868860579227922676129602691040800, 111155452029042731884353419218065788, 9305043901238470997130897504577616, 598897423145120586262667776612565, 24367521309532694943956178177536, 1645477992913509925230098367434, 26019927226645542165492964304, 1812044911305722548727895053], [0, -22922228766703639602501551971866113382187008, 0, -2586118030747151275679279125281260735270144, 0, 45063507190360336612183055231196584161216, 0, 10544408957130840409868539298963582480944, 0, 374970230451303684536094489891020644960, 0, 6187673425345664900841838814918085640, 0, 55541963969824196351424040663447588, 0, 278212437841038470328727294688203, 0, 728982860376555934532369124502, 0, 776808349103473966772762515], [560772338647386497291796543138517982794481664, 46603933849275941815012859908599881584017408, 460172832997896034183740793104744450234490880, 15700034121925547581758957356829617735500544, 87842743251209757583962155383944302821185536, 1397573283244252211954449811318012732690624, 5669566257459205433922756727213161712113152, 55799485288912495370820973694137355695856, 165273892260482134873235626367930543449856, 1218079254131753502832379637094120496720, 2555717142575026554820778191189257351680, 15731392805707304302533945192697514480, 22370430228434451042884572960246158656, 122703155543360758450162781118314312, 110944524210911115473374081114887008, 564233064509688288378694411459637, 289693187470711238943640307851136, 1400462170778076942764423904758, 308512445260568631425788568288, 1440445992024970221958725485], [250296563506650137282193524309774168358912, 22999810427036559493348839265120149504000, 1334120491276528446575135769507848034775040, -193093462567246943039256551856830940565504, 323703856587080732444302185088896946732928, -41656261237872153447215685846800214604672, 21930434683965625426502363809928375601056, -2692397603239475196511331895888171827872, 648099960485759253134998932589264024808, -78315135390343799664728288430439698088, 10064297512986158159446334040602221340, -1211706501230595304174099148667479740, 88178879276140053925685176885477718, -10629936707836522287932554560744550, 437213243280401797520386094901959, -52869567620673130665516463094191, 1140886642938819287866338614048, -138451825622344857636114648736, 1214091398216826191845011119, -147840495605940580485755479], [-757759711849332226173241897880596979081281536, -866844435917272932184903979686081279676448768, 1210815330871374594799696086054759972620357632, -290883990257317725819536149681523261264450816, 326742075189122584280918811869542618867489792, -24998112719975576699842698065113161806864960, 22346591490576375337233976292039376215404288, -1012372990439437067013174152472836607754832, 659774158406849028708984123140307310410880, -22714793423007772656800425127849943151904, 10215767489579173956810621915656552061760, -300460848187579883357925352555248128120, 89216256593607178619277748659806756896, -2382036658058837574732329664504421532, 440995980687809442819745058455362496, -11057972024487384083846846090648525, 1147603214778500619220525800240544, -27575897507097028156198942716986, 1218358873784241581228022408640, -28410894120486667503142542917], [60040711336228971011603670433444015022014464, -257280838791813510641670242066154281604808704, 125739164661846099544303907745188799988838400, -89326678122141832049915174416521529059443968, 37497639504771978315133980204930396627311616, -8011947215984482342537096206578781928029760, 2736419602576686655464789439890384924801792, -339746504801382994972676936167880485596496, 82947632148287674093387146067690899772416, -7908166957306464278794570181533682958112, 1300212351615842168885079490047708144000, -107437716210103822712172608237074069240, 11436662575610634557192661199782096576, -868115854038974346167012167646851036, 56826250907370730533189496855823088, -4085255623592541752124060547957885, 148515619664466503957133530837856, -10288951164308016002219713150618, 158260762733152198471971205488, -10678327981032704200199444341], [-979796154114691259288714433949380955585118208, 1418697985457437197658918649472650744585060352, -2151568073737774886349042478129952161111801856, 424613723710795692111968531607576657885577984, -461803883468177942234301366418861280393123840, 34675665827623140683900690447506088635679680, -29822132670742958684544774391095368483635712, 1339102489229878862966176126469177312585008, -860819779505226798857304335284768229185664, 28969492139557776644609613762661765108576, -13191576130157647771053185901684194751680, 373912209971821923746687320473785295880, -114653791758562366946537501440290820832, 2919469238825918749885250263925696548, -565579007713817445781022492682958640, 13431082132762669919457009399292315, -1470844831743693604396806914594816, 33322756534629992334386101195894, -1561572881007712804076781509552, 34236851690056186774994986723], [1839451794389604844377313479295211698913280, -1531108653724885708354529159888882097810898944, -67968898823670923949818306253604491079057408, -551206950574621526302848655768717593731031808, -14663003955730998013419921418073675540844544, -53893490275601246698838796129612699168610240, -947723956340295269171988827352636483410944, -2418138609178157625166871159267502361888816, -27566927657401017481984357527514773726976, -57525159857365265154701456513680143136672, -426520688433169547069282900330952868480, -783931073404193294932606929996178178920, -3741737721158455845352259205382081600, -6305465029457417308073142577572701716, -18610087802476941994261795009155232, -29472658590002655401316372681802195, -48735042619065389887912356355072, -73733819255580553075770024198838, -52039854453291084330985928608, -76080419675044826296549340251], [-7496452445933757773368443731436250357432320, -47109929678670746123866534372432524873105408, -42567457340848872803320906379919849715056640, -11451977945446114834895313215979337043059456, -9164377472331873758387450886296047213027840, -481135536011064836115704722688408011387840, -592327472712684543232493017095397802131840, 3433261982355958952428328015402424517328, -17229329785875635926240223454696733579360, 504853724455810089791642708375552861216, -266575430270730966918301812706845542800, 10926150221365792389296236077987039800, -2338586075724034903345162003363801000, 111155452029042731884353419218065788, -11631304876548088746413621880722020, 598897423145120586262667776612565, -30459401636915868679945222721920, 1645477992913509925230098367434, -32524909033306927706866205380, 1812044911305722548727895053], [-750115212194912258344621981093875536376102912, 72635243930076263378030945337251693432733696, -726669126518568329615812603860176860334362624, 29183445749063541474358114180333427619746560, -135304851274621598785320811976383386109731840, 4547035444478536379319340010870302839840704, -8286045678093086532432862589459492947336448, 274874770279027047735331561260158639385648, -232181087013893249921933417767209054267136, 7857379538813727785780955452399359616224, -3487986176718699269564584164218508944640, 121064919183462453549492356876640960200, -29884362923503162406898842203238250368, 1062129868516536073673174712212925444, -145853964010807879536695449397662960, 5290145323843200312193245083169787, -376259270693188495056601279171104, 13877575429153409532918008409494, -397008224122138033990950966128, 14843399725118373092813557827], [31193184033845488372025203987941114374799360, 21369850507932653672910147138229416212269056, 57673341390302394842142313821663617875431680, 6986659299643516238312224554974993224719488, 11662165271284683052782484486030564315628480, 648844254210587107101483538028976849917408, 737259005547593122797238825198607440803440, 28381214521599725882884357315014030918872, 21014098274324101675204226729098276892120, 675903276448657741803022425543667263020, 319049588430493645591142279180765054060, 9345292256402695151103515729957012030, 2752921147062497487391977020349397550, 76585836741159209444464582591168799, 13502113137678124271957101668384470, 364609741517910335982040229382539, 34954229297397003423281995156130, 927121184954315581305818402201, 36977088779858231864684461670, 969825372312616429518997595], [354260368234889578969134241472786212835033088, -1339156598707128548342122786077101926729187328, 734396828079027676514501298077854672568070144, -424266506325905353872436019432172033501910272, 153498695318774166238565534947726172929547264, -36710169919596461918120025940084454491451968, 9782115573680197265617339603948477422635776, -1422463644386711232303806960655470948974160, 279207104134471771531678965749614492615680, -29965648676878362456998495592641978205216, 4237810829882923255845024359896567264640, -372316299374475291670950139205568914680, 36545465933583445430970040258321308352, -2795300569918228020262009907725914332, 179165449995949750155441634734469872, -12411404291425965375393400684956909, 463707777678018789800329495891808, -29876568591615269663603161688890, 490492226254423926992487622000, -29941078979952710033688993893], [48046448094736202418468176393043859432538112, -337213233809075176921392753046474290012291072, -338395444581686565715987117960723370824073216, -155080565300897736535377087240417431934543616, -113358080805716725647714993254609563896504320, -21352172042170467990828143737426068772808896, -8200611108856799814577082147880729444349952, -1209981713449343458770574105159613158194544, -249310174908856104927782007627810551604224, -33485040220008672464073457206671397247840, -3938991333524514200484087829989390087680, -506309317683239635353313270204656332200, -34928290347863241283941892284639763712, -4387828767496922084476585886157483508, -174702740828600544885267635579997440, -21667438769631417156281372752832623, -458846962580278929684685741335296, -56483086886187978264333313244542, -490680932700784818858421436672, -60127805464107441894459062935], [-1690064759182741556245983558693250644918140928, 6069767462487991391985771305717129636509581312, -4441809376492496771368749475788468322948284416, -253796115746533659893647631421853440937795328, -931614718621280336842172557797533726719385600, -238984890096308707972891084435989331366367936, -59347625558818707387176643318183820024174592, -18042187367221407469916875064785134274212848, -1697905700716013515724109157076913616300544, -547870514330964204002204521386597093943328, -25847210689740288007699976953968578420480, -8590702822554101802380377362980854891400, -223471862277909906806770171875907939712, -75594695961435681104367757622194391972, -1097702826249178621614012278288027840, -375682838228076487122252200448828623, -2844879102453023201410199425174016, -981701235215439987880332836836334, -3011945222484306775045169523392, -1045671781162003279890798391799], [469728413199344383372447836941806671339454464, 2152870680820593540418873146839731504880812032, 251514904309881975453325696481097423781173248, 760992341205806700650267415195182383816663808, 39138548623399400715600545513244698205785600, 118654380079115727880230747390387990718757312, 2324776728779035143171707214397571737582976, 7092902158571697808268561230774962573360560, 64706518340521715120839991374449729324032, 198968164778864341144841337530969337238784, 968594354286534005372923209061823783360, 3006319590018615627084296471046001813880, 8265778133335854249442820422034737376, 25913974393577153460602443886653840508, 40158038285329350803370026658922040, 127148307605603758212496023779089751, 103103073584323879918583622350768, 329442472856111183141513087394230, 108289321147071110920979092856, 348838177531886382659327558207]];
    Rf_basisdens := [1, 1, 1, 1042746912654544016213579657004513487749120, 1042746912654544016213579657004513487749120, 347582304218181338737859885668171162583040, 86895576054545334684464971417042790645760, 130343364081818002026697457125564185968640, 5924698367355363728486248051162008453120, 1042746912654544016213579657004513487749120, 347582304218181338737859885668171162583040, 1042746912654544016213579657004513487749120, 2085493825309088032427159314009026975498240, 43447788027272667342232485708521395322880, 347582304218181338737859885668171162583040, 16292920510227250253337182140695523246080, 347582304218181338737859885668171162583040, 347582304218181338737859885668171162583040, 2085493825309088032427159314009026975498240, 521373456327272008106789828502256743874560];
    Rf_basisnums := ChangeUniverse([[z : z in elt] : elt in Rf_num], Kf);
    Rfbasis := [Rf_basisnums[i]/Rf_basisdens[i] : i in [1..Degree(Kf)]];
    inp_vec := Vector(Rfbasis)*ChangeRing(Transpose(Matrix([[elt : elt in row] : row in input])),Kf);
    return Eltseq(inp_vec);
end function;


// To make the character of type GrpDrchElt, type "MakeCharacter_33_b();"
function MakeCharacter_33_b()
    N := 33;
    order := 2;
    char_gens := [23, 13];
    v := [1, 2];
    // 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_33_b_Hecke();"
function MakeCharacter_33_b_Hecke(Kf)
    N := 33;
    order := 2;
    char_gens := [23, 13];
    char_values := [[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    values := ConvertToHeckeField(char_values : pass_field := true, Kf := Kf); // the value of chi on the gens as elements in the Hecke field
    F := Universe(values);// the Hecke field
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),values);
    return chi;
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..(prec+1)]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 7;
    raw_aps := [[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [41, -1, -1, 1, 0, 0, -1, 1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, -28, -1, 1, 1, 1, 11, 0, 0, 0, -1, 0, 2, 0, 0, 1, 0, 0, 2, 0], [271, 2, 42, 38, 4, 0, 3, -1, 6, 0, -1, 1, 0, -3, 3, -3, 0, -1, 0, 0], [-3, -114, -1, 19, 2, 0, 7, -1, 6, -2, 1, 3, 10, -3, 1, 0, 0, 0, -2, 6], [68, -245, -16, -225, -4, 7, 3, 2, 1, 6, -3, 3, 18, -9, -3, -15, 14, 1, -6, 2], [-4493, 31, -44, -194, 0, 0, 6, -14, -14, 12, 6, 20, 0, 7, -16, -6, 0, -4, 0, 0], [11874, -61, -27, 471, 14, 0, 6, -3, 38, 14, 15, -1, 0, -20, -37, 16, 0, -14, 0, 0], [130, 966, -53, -259, -21, -11, 199, 6, -94, 6, -3, 8, 58, -2, 6, 1, 20, -12, -2, -16], [-6003, 125, -273, -904, 35, 0, 5, 9, 3, -6, -17, -20, 0, 40, 46, 15, 0, 18, 0, 0], [-2, 19, -1, 299, -38, 8, 121, -11, -146, -18, 51, -43, 82, 22, 27, 40, -48, -16, -14, 18], [-347, 1587, 130, 901, 48, -2, -64, -4, 232, 27, -28, -54, 44, 18, -39, -50, -4, 43, 44, 20], [82, 7087, -125, -70, -12, -190, -301, -1, -156, -53, 21, 99, 42, -33, 46, 82, -12, -45, -42, -6], [55885, -360, -718, -385, -13, 0, -243, -37, -556, -24, -41, 19, 0, -1, -171, -77, 0, 7, 0, 0], [30879, -221, -1174, 1956, 502, 0, -26, 18, 122, 18, -138, -100, 0, -155, 66, -48, 0, -28, 0, 0], [164, -8310, -106, 791, -158, 182, -1484, -4, -690, 23, 72, -104, -280, 95, 71, 22, 44, -67, 8, 68], [-68124, 49, -1413, -1138, -221, 0, -80, -138, -61, -112, -36, -251, 0, -33, 75, 110, 0, 7, 0, 0], [18434, 231, -1737, -1005, -516, 0, -116, 20, -189, 94, -314, -101, 0, 9, 143, -80, 0, 39, 0, 0], [-2544, -12330, 914, 8086, 262, 152, 1276, 20, 1306, 70, -196, 178, -752, 164, -176, -308, 172, 156, -32, 52], [2789, 13633, -778, -12945, -56, -88, 67, -36, -74, -13, 118, -168, -704, -408, 23, 4, -112, 13, -32, 104], [-159474, -199, 7321, -2117, -212, 0, -218, -189, -18, -344, 273, -123, 0, -78, -389, -190, 0, -242, 0, 0], [86, 16606, -163, -2529, 277, 151, -1993, 10, 330, -38, -233, 116, -1186, -50, -26, 235, -44, 16, 362, -104], [37541, 1608, -4567, -5624, -972, 0, 513, -117, 952, -381, 371, 231, 0, 184, 386, -378, 0, -137, 0, 0], [-1302, -21495, 653, 6786, -45, 838, 3878, 106, -311, -2, -154, 339, -928, 477, -11, 128, 110, -95, -40, -526], [477789, 116, -4508, -6513, 203, 0, -271, 341, -406, -450, -31, -685, 0, 459, 655, 649, 0, 445, 0, 0], [393, 20123, -470, -6059, 408, -926, 3209, -116, 1076, -257, 32, 142, -308, -514, 49, 298, -348, 67, 100, 348], [547350, 3898, -1622, -24313, 1377, 0, 972, -128, 680, 378, 848, 1160, 0, 1292, -266, 54, 0, -12, 0, 0], [-7302, -75871, 1829, 32880, 109, 890, 2020, -56, -1113, -26, -104, -493, 224, 1339, 133, 640, -326, -77, 860, 10], [-8423, -41793, 2138, 34029, -392, -1682, 1151, 132, -368, 659, -212, -678, -1268, 1206, -319, -1010, 716, 187, 124, -76], [75261, -4072, -15246, 42284, -2898, 0, 443, -65, 3110, 148, 407, -287, 0, -2021, -1113, -159, 0, -1001, 0, 0], [-7952, -36078, 881, 51751, -827, 289, 1149, 142, -5308, -220, 17, 1214, 1434, 1672, 746, 601, 1016, -888, -282, 164], [335898, -1563, 2283, -28345, 4518, 0, -2912, 764, -2423, -2044, -174, -1135, 0, 377, -1445, -1834, 0, -751, 0, 0], [853, -9339, -6312, 12769, 1588, 0, -4611, 292, -9616, -601, -1634, -1364, 0, -548, -1351, 154, 0, 1025, 0, 0], [-20651, 5350, 6387, -8668, -5182, 0, 2773, 815, 6218, 175, 1515, 37, 0, 1310, 1136, 1706, 0, 53, 0, 0], [312, 97837, 3695, -6646, -863, 3626, -6002, 90, 2555, 1090, 606, -2739, 468, 1113, -1013, -1880, -662, 923, -576, -1202], [-13162, 25977, 2592, 44201, 2196, -289, 21, -106, 6221, -420, -1291, 2455, -4094, -97, -273, -495, 1134, 379, 274, 1770], [5759, -88345, -1140, -47760, 3348, 1352, -2218, 210, 10932, 348, -2682, 1626, -1644, -2385, -1434, -792, 816, 1224, 1956, -444], [-225693, -299, -8856, -11611, -660, 0, 483, -204, -7822, 2899, 2126, 6022, 0, 2748, -3261, 284, 0, 1281, 0, 0], [-12946, 361508, 2734, 29043, 2036, -2162, 14006, -218, 5068, -807, -682, 1040, -10332, 421, -111, 1298, -1056, 329, 1020, 252], [-537004, 1850, 48144, -17566, 1648, 0, 246, 228, -376, 2862, -672, -756, 0, 1652, -1018, 3872, 0, 926, 0, 0], [6812, -55947, -4814, -10857, -2262, -4385, -9291, 278, -7153, 1154, 133, 453, -3542, -1167, 419, -2795, 3778, -697, -1454, 2110], [-34429, -2404, -17065, 23534, 5618, 0, 2927, -1079, 8120, -591, 4745, -1299, 0, -828, -2250, 4430, 0, -1023, 0, 0], [-3251993, -10047, -32445, -6538, -6773, 0, -5987, 1549, -19263, 1100, -233, 4710, 0, 2746, -4790, -1779, 0, 2064, 0, 0], [3357765, -14315, 73864, 122352, -8154, 0, -278, -1214, -7090, 1924, -1290, 2672, 0, -4327, 412, -714, 0, 1324, 0, 0], [-886, -655171, -5955, -26126, 1819, -8350, 6714, -502, -835, -622, -966, 591, -21840, -2499, 773, 1508, 502, -271, 2736, 3514], [4163470, 841, -49393, 46927, 9212, 0, 3166, -1419, 1980, 5206, -2293, 4437, 0, -2598, -499, -2276, 0, -752, 0, 0], [-12196, 488031, 4830, 4961, 4714, -4019, -8299, -674, 23873, -722, -797, 2935, 1518, -4033, -1847, -3841, 270, 2521, -2466, 4314], [7512, 67942, -2898, -25164, 680, -184, 11890, -186, 124, -2358, 766, 4378, 1932, -1918, 1284, 2656, -1040, -1098, -2268, 76], [1884062, 8838, 46922, -67334, 5352, 0, -552, 2178, 19160, -3604, -50, -8926, 0, -248, -1478, 692, 0, -4580, 0, 0], [18365, 260695, -1542, -88234, 4030, 13400, 45294, 474, 7146, -1006, -3194, 2228, 188, -659, -778, 4628, -2516, 304, 4388, -5360], [-1810, 629112, 2562, 72214, -7130, 9060, -7652, 496, -24114, 4218, 1692, -10382, 12536, 7322, 228, -2248, 1508, -724, 3008, -1468], [23640, -496753, -2755, -118544, -2573, 1274, -57950, -418, -8255, -3104, 4562, -1781, -16412, 89, 1951, 7228, -8306, -1533, -2288, -5798], [39113, -115975, -17792, -97799, -8754, -9262, -4032, -268, -39590, 1611, 4316, -11340, 18332, 672, 3363, 4750, -2608, -3095, 4460, -1000], [-2541176, -28490, -48570, 37945, -3201, 0, -15254, 9326, -16432, -7466, -2706, -3482, 0, -934, -5716, -7324, 0, -634, 0, 0], [-4556793, -54714, 40286, 264529, 5719, 0, -13189, -657, -33256, -978, -4713, 1051, 0, -11409, -4913, -4157, 0, 2585, 0, 0], [-37538, -1765, 15136, 9945, 10278, -13171, 333, -384, 46753, 1336, -4595, -3271, -8746, -1961, -6251, -3545, -4746, 6635, 4874, -2442], [-200953, -21493, -97953, 171430, 26925, 0, 1737, 3445, 16683, -8338, 707, -10064, 0, -9382, 9518, 2583, 0, 150, 0, 0], [-24048, -1066678, 4383, 159745, 3295, -1117, 27793, 1830, 9964, 1108, -6345, 11246, 46750, 880, -1718, -4453, 9192, -112, -1382, -1788], [5423377, 23732, 92470, 106784, -28140, 0, 19321, -10367, 45656, 5578, 5077, -1435, 0, -8497, 693, 4117, 0, -7973, 0, 0], [-43375, -366287, 18416, 214063, 3308, 18314, 45470, -214, 10932, -389, -1430, 168, 34792, 7182, -1061, 726, -1632, 1275, 2020, -348], [-263560, -4815, -148109, 72005, 11514, 0, 7676, -53, 27752, -3370, 10617, -5617, 0, -3064, -2989, 9446, 0, -3418, 0, 0], [57470, -168938, -13964, -232662, -3284, 4864, 61079, -1620, 1224, -338, 5712, -1592, -8368, -10792, 1150, -6816, 1784, 470, -8344, 11504], [2892721, 71851, 233130, -413624, -35304, 0, 10506, 6930, 20208, -9064, 2218, -5542, 0, 22139, 23990, 5334, 0, 6638, 0, 0], [-12419172, 42101, -268529, -188264, -70783, 0, 12696, -8068, -99, 19692, 14810, 26677, 0, 16233, -26433, 3198, 0, -4627, 0, 0], [17470, -1129909, 7379, -89544, 869, 7298, -26994, -1626, 18363, -5332, 7254, 5, 34732, -3083, 461, 4320, -12278, 1165, -8720, -2522], [-23986345, 2527, -27523, -89401, -4918, 0, -12251, 5357, -23755, -1790, -19485, -13526, 0, 3254, 18092, 1319, 0, 9068, 0, 0], [-100363, -739663, 25686, 576051, -8176, 28264, -78335, 2556, -52514, 1143, -2690, 4552, -19128, 27524, 4611, 6988, 7480, -7167, 4296, -7856], [-75738, 734141, 22461, 374844, -11581, 474, 163406, -2302, -31495, 3868, 10150, -22537, 9932, 16003, 2167, -3956, -4162, 135, 536, 9650], [-16373687, 35775, -28902, -472900, -42744, 0, -13834, -8302, -24568, 6916, -2070, -15822, 0, 20779, -16470, 22878, 0, 2210, 0, 0], [23389921, -114215, 5501, 784327, -50640, 0, -9141, 13919, -40381, 3916, -5671, -2806, 0, -16872, 12026, 20463, 0, 19412, 0, 0], [-3407983, 27981, 13000, -105200, -59010, 0, -8574, -10090, 40330, -4532, -19534, -37408, 0, -12907, 412, -1738, 0, -15080, 0, 0], [212619, -254498, -83051, -678711, -24288, -39992, 140335, 4059, -101552, 2368, 4693, 4469, 24554, -17741, 9109, 5020, 12564, -13168, -7114, -11790], [-275814, -176648, 71226, 940642, 23510, -42560, -86243, -760, 82354, -13582, -6640, 35726, -46152, 15634, -1768, 7612, -5268, 2528, -10632, -708], [18241269, 91368, -20911, -466762, 41956, 0, 10695, -573, 59944, 1457, -16825, -21409, 0, 6498, 17204, -2818, 0, -8859, 0, 0], [-2962, 2326998, 386, -36732, 15342, -1158, 117266, -212, 44272, -6362, -6874, 16608, 42524, -8568, -1682, 7034, -3736, 1894, 1820, -2464], [-3247142, -105436, -381478, 860142, 68206, 0, 8380, -13760, -5156, 6058, 3800, 5996, 0, -40046, -398, 4942, 0, 1080, 0, 0], [-86669, 1228600, -7865, 428020, -17352, -68522, -124491, 725, -67568, 12885, 1175, -21987, -14182, 11970, 1842, -13826, 17060, -2567, 8594, 12710], [29941278, -81862, 161020, 21454, -10152, 0, -28424, -9988, -121298, -8082, 25952, 27714, 0, 11856, -32920, 3530, 0, 13374, 0, 0], [132424, 194463, -55383, -716784, 3831, -82858, 40686, 4094, 16849, -572, -8130, 17827, -29020, -28939, -3317, 984, 4606, -777, -4312, -19958], [4948540, 55645, -636849, -564573, 39464, 0, -8900, -4167, -28178, 12206, -3353, 21187, 0, 19934, -25241, -19822, 0, -7488, 0, 0], [44900486, -60575, 25555, 603655, 166884, 0, 19978, -7838, -25769, 35586, -3260, 49045, 0, -23487, -7927, -12298, 0, 4421, 0, 0], [-86060, 2890985, 6155, 44972, 19068, -33658, -117937, -5325, 42636, 4309, -7247, -29861, -97710, -2641, -5480, 2726, -11764, 10805, 34566, 20186], [-27621, -4654233, -638, 138045, -8084, -28608, 135463, -8584, -38042, -7387, 23430, -39232, 93616, 4540, 9209, 21420, -35016, -625, 8968, 16488], [-2103394, 188334, 400676, -1185824, 29442, 0, 40428, -1806, 19560, -12806, 28854, 22690, 0, 62458, 42780, 11758, 0, 18400, 0, 0], [-75214, 2236935, 2250, 163413, 28066, -9945, 200591, -6726, 47219, -23988, 101, 26345, -26166, -10367, 9273, 34613, -22894, -2547, 6714, 17462], [-14947735, -11303, -257704, -77112, 25654, 0, 19370, -11906, -73014, 18916, 37986, 36328, 0, 32153, -5772, 52334, 0, 31760, 0, 0], [-44234, 1450747, 44099, 323222, 11104, 108906, 73503, 2355, 40400, -8501, -7311, 39867, -870, 11655, -2, 10, 9652, -2353, -16746, -4478], [-359862, -1864275, 135349, 1581740, -36017, 10438, -156050, 6462, -25223, 24228, 9422, -15989, -121964, 65999, -10557, -57288, 33214, 4095, -37640, -5558], [14616683, -4111, 714730, 129298, -85594, 0, -27006, 42454, 12084, 3364, -76378, -78558, 0, -707, 73466, 33002, 0, 27458, 0, 0], [631298, 3897318, -198096, -2557144, 5374, 68596, 32034, -362, -58810, 6322, -15386, -13388, -37392, -76738, 4414, 13136, 10716, -4052, 42252, 12888], [-37192323, 181272, 164839, -1292760, 232176, 0, 20017, 15727, 12124, 9721, -5553, 50543, 0, 49558, 12396, -49828, 0, -3453, 0, 0], [132152, -469512, -63552, -94720, -16034, 30360, -332350, 5666, -87422, 3930, -9314, 40788, 50524, -13176, 10086, -16180, 51332, -15752, -16004, 17336], [289590, 2107238, -62034, -822940, -37554, 93990, -128739, -2728, -174148, 2814, 25238, -67952, 121708, 13436, 14958, 41046, -39096, -12230, 29620, -22728], [-318319, -2529479, 116620, 1605885, -23614, 48862, 30985, -956, -52862, 2667, 18848, -22132, 90252, 65584, 4011, -3574, -8208, -3055, -14220, -2472], [45485795, 305712, -726120, -2784786, -70354, 0, -22241, -13997, -114576, -13880, 22711, 63431, 0, 120135, -34739, -58267, 0, -3667, 0, 0], [-51492897, -41757, 82235, 157191, -93598, 0, -9271, -13833, 194691, -81724, 46325, -126126, 0, -42354, -24342, 40257, 0, -50470, 0, 0], [2795621, 277197, -95625, -679936, -97607, 0, 90023, -28121, 227617, -22688, -6311, -52520, 0, 3516, 107436, 11935, 0, -11586, 0, 0], [410106, 2986720, -76065, -2225281, 46107, 11827, 404547, -6938, 173700, -27998, 3347, 8498, 65022, -76460, -7580, 43755, -69200, 14518, 5226, -27572], [321570, -8512212, -32162, -1282128, -51524, 95684, -88570, -16266, -94716, -8102, 74562, -84014, -82408, -16828, 17596, 2556, -58192, -1330, -39412, 39404], [-596684, 6594507, 191742, 2609043, -36852, 4557, 1675, -12020, -113965, -13066, 55377, -75589, 32686, 113089, 18581, 41931, -72166, -6561, -3518, -46], [46260967, -98975, 376765, 351310, -51605, 0, -20699, 26665, -95439, 7850, 48467, 127746, 0, 8944, -100536, -94949, 0, -23520, 0, 0], [16650955, 124731, -253206, -521801, -11612, 0, 11043, 44530, -56354, 87735, -48856, 109784, 0, 50128, -21243, -64312, 0, 6593, 0, 0], [-529204, -622958, 93178, 2163516, 1834, -28428, 262156, -248, -134314, -8148, -11016, -9738, -246780, 91998, 17826, 62280, -15860, -17578, 57744, -14372], [108888, -3977619, -6258, -308483, 55100, 183827, -57907, 6016, 76061, -2730, -53701, 27105, 174194, 3807, -10701, 42133, -3818, 4685, 72326, -39914], [-638661, 11251769, 152074, 2226481, 14902, -105622, -62366, 2926, 7762, -17207, -8210, 31134, -315992, 81216, 4663, 42138, -21676, -7589, 7156, -39232], [-33505016, -18059, -2304105, -406616, 348049, 0, -54388, 21908, 49241, -9196, -60494, -53927, 0, -33247, -25789, -56854, 0, -41091, 0, 0], [-48881404, 59561, -332697, 746925, 175620, 0, 111546, 3414, 138093, 8060, 41804, 84407, 0, -21481, 63685, -32540, 0, 2003, 0, 0], [49894597, 28228, -1420922, -464049, -172641, 0, -7075, 60451, -6632, -34024, 48791, 41135, 0, 59395, -15943, -20469, 0, 5899, 0, 0], [-257686, -2725076, 7900, 102756, 142392, -174886, -171154, -5444, 426354, -74850, -52886, 208402, -105900, -94954, -3768, 48934, -9028, 9212, -31548, 23636], [51653555, 114225, -716238, -130376, 122970, 0, 25684, 59100, 300062, 26270, -36808, -33326, 0, -27219, -41912, -55346, 0, -78134, 0, 0], [56316263, 217095, -737096, -1664566, 505872, 0, 53006, -40430, 33798, -48908, -2290, -89864, 0, 46271, 165028, 99490, 0, 60824, 0, 0], [296205, 4987847, -66064, -995029, -53710, 7292, -24381, -116, -149388, -11133, 44222, -5642, -70040, -10906, 20853, 15324, -17956, -20737, -50816, -17260], [34603311, -257335, -460726, 1001664, -509794, 0, -84476, -9044, -368686, 67282, 22768, 132806, 0, 24425, -145584, -13814, 0, 28942, 0, 0], [269533, -10097160, -93731, -1696961, 69906, 7428, -774987, -13731, 288270, -40876, -4453, 133481, -323922, -139937, 2885, -44708, 41200, 10846, -80814, 123586], [-708454, 11612498, 181266, 2957972, 15770, -67062, -715047, -1080, 46388, -29374, 4554, 69760, -5572, 73196, 11210, 21778, -4992, -10130, -38284, 1488], [374084, 282182, 8618, -2020652, -22156, -11528, -41462, 19662, 200576, 30678, -2906, 40046, -188776, -54986, -44940, -115128, 47816, 25278, -109852, -70156], [-80971637, -73481, 1320548, -215335, 111198, 0, -46597, -83714, -262550, 104641, -22732, 68560, 0, 4086, -119965, 21890, 0, 8541, 0, 0], [17256668, 139430, -687306, 2449482, -139192, 0, 229698, -50686, 453042, 98696, -15682, -12156, 0, -111832, 130596, 79082, 0, -16088, 0, 0], [-514906, -13990298, 148625, 2888871, -67475, -27373, 1342807, -10146, -200474, -47398, 85903, 27804, 206470, 90618, 49262, 47311, -44836, -39116, -102950, 16040], [-1038779, -4013372, 463725, 3730288, 4572, 143314, 1687123, -5669, 186676, 9711, 32737, -119041, -45466, 189478, -35682, 4482, -114252, 41351, 8174, -80238], [87345167, -372235, -1243118, 2418000, -180978, 0, -105896, 44880, 52354, -86702, -106444, -205302, 0, -143039, 80268, 5174, 0, -6982, 0, 0], [838, 14227158, -91237, -247139, 20843, -225887, -928791, 7046, 123654, 48010, -51671, 18804, 8290, -74118, -31274, -121299, 117468, 24228, 5254, 75192], [-11968502, -176275, -288861, -282085, 677668, 0, -134750, 19609, -339776, 30558, -136441, 51997, 0, -30534, -9923, -138936, 0, 18944, 0, 0], [-1112424, 23123488, 362068, 4279951, -15610, -79646, 228282, 11382, 107146, 72797, -25386, -104106, -51516, 165105, -54565, -109318, 36956, 43183, 27516, -31336], [-80130349, 223069, 2084014, -2019794, -117938, 0, -83478, 1770, -233140, 90796, -120670, 83710, 0, 75165, -61482, -121462, 0, -7878, 0, 0], [38400217, -480510, 1675866, 2591505, 70763, 0, -58151, 47583, -311614, -43818, 6575, 47069, 0, -50489, 77005, 13601, 0, 97913, 0, 0], [18000587, -302921, 1910613, 3207054, -216345, 0, 58679, 84403, 274533, 5298, 150645, 252456, 0, -118172, -259878, -259127, 0, -162614, 0, 0], [435010, -16095460, -124754, -1017698, -146450, -17808, 776460, -24716, -496646, -30326, 153172, -146022, 96760, 18330, 73036, 82716, -114532, -48320, -56960, 33764], [-48339713, -272695, -1662386, 714766, -603162, 0, -36598, -94738, -246608, -5124, 192054, 54182, 0, 36413, -211282, 144994, 0, 12246, 0, 0], [-163297348, 48940, 1329444, 457146, -111310, 0, 104514, -18550, 43668, 175696, 143890, 321926, 0, 36574, -302630, -89898, 0, -87558, 0, 0], [891110, 3140322, -304357, -3480381, 17265, -47079, 250449, -1952, -11300, -64982, 12755, 156000, 82226, -163704, 38866, 59201, 3824, -36914, -77662, 15536], [83428210, -1378789, -1053643, 8443264, 190439, 0, -209650, 79808, -250355, -47776, -146022, -231287, 0, -359117, 55223, 108564, 0, 71075, 0, 0], [-604527, 14459381, 173124, 3119625, 59598, 52034, 1928616, 4504, 223682, -1753, -47952, 100496, 646924, 33748, -18901, -52674, 67328, 14397, -21740, 40304], [14003841, 174321, -105025, 1774840, -618335, 0, 246391, 53959, 302753, -169720, 143441, 50424, 0, 15408, 369452, 20079, 0, 96782, 0, 0], [675226, 1478676, -17186, -3773458, -134258, -171952, -662073, 660, 6922, 99234, 98372, -307334, -128240, -31798, -64668, -151428, -75620, 64008, -53312, -79580], [737394, -19230792, -477387, -2437763, 83897, -168235, -1226361, -14174, -255496, -81846, -50827, 98586, 500162, -143760, 77124, 232381, -41480, -62950, 162038, 43564], [62969501, -348815, 1714375, 710568, 396083, 0, -192591, 54165, 314147, -321926, -100069, -509912, 0, -188928, 161778, 20291, 0, -67626, 0, 0], [-1270456, -43132671, 168990, 6535071, -49946, -77621, -2044139, -14074, -479529, -10850, 18929, -39627, 140546, 199689, 70015, 81041, 25986, -55941, 82634, 110430], [19783109, -885807, 2901648, 7998496, 1037038, 0, 159870, 21638, 470470, -46084, 140186, 107388, 0, -395367, -52472, -131526, 0, -118240, 0, 0], [-512972, 1317575, 348681, 1551732, -6927, 240450, 1409128, -11036, 107435, 1322, 53844, -176509, -13616, 155749, -26167, 59424, -176638, 37203, 41332, -110422], [308864460, 293757, -3541485, 1500175, -72520, 0, 301176, -160067, 48978, 142406, 50595, 245419, 0, -25726, 182119, 21526, 0, 73944, 0, 0], [354639, 11776138, -167963, -231751, -92860, -6072, -2428733, 30983, -382076, 87604, -49847, -44891, 258354, 27119, -6863, -81988, 149092, -24120, 50118, -36806], [47407327, -343840, -2028454, -2955413, 424455, 0, -426517, 42747, -113990, -114832, -72273, -361455, 0, -14093, -406833, 6929, 0, -167421, 0, 0], [1023252, -13625349, -133522, -3735571, -72806, 190449, 2347853, -9610, 36621, -12706, 98847, -8981, 328166, -123949, 5885, -74693, -21994, 3725, -170122, 35666], [-16312087, 358057, -2058004, -2549020, 25126, 0, 224650, -58382, -244510, 122140, 489990, 801956, 0, 261989, -470744, -273090, 0, -83264, 0, 0], [-388877, 8966877, -75714, 820417, 131338, -579142, -222110, 17830, 280542, -45279, -104706, 178690, 470552, -64300, -17013, 98330, -9820, -817, 58988, -116800], [96392911, 478767, 1809359, -1144549, -243262, 0, 229681, -22049, 119447, 173812, 117773, 307550, 0, 139010, -56746, -10807, 0, 5158, 0, 0], [-2082695, 23412643, 436866, 7987665, 76076, -711934, 3478195, 13768, 416352, -76945, -24788, 343806, 65764, 89586, -1879, -48758, 83556, -11889, -219164, 948], [-284592361, 134038, 229619, 708876, -648110, 0, 43495, 156653, 531318, -269409, -13495, -247161, 0, -44404, 306142, -56000, 0, -20257, 0, 0], [-148266, -24252836, -93454, -28090, 98120, -166224, 323782, 16230, 132640, -60332, -87934, 267074, -623796, -60350, 17686, 68232, 71304, -33916, -13188, -26076], [53486811, 1135214, 1916229, -5501604, -1379082, 0, 66103, 195765, 980294, -239607, -81167, -407905, 0, 184138, 264668, -35078, 0, -122209, 0, 0], [104516, -33342385, -26367, -1865581, 242754, 284108, 50719, -7381, 774134, 46884, -182107, 74083, -378218, -163162, -92769, -147540, 136728, 100150, 150478, 181014], [337758468, -1863871, -3270881, 11766757, -626360, 0, -379818, -5342, -1091999, 51056, -371408, -96137, 0, -459393, 152113, -12636, 0, 211579, 0, 0], [544760, 19074564, -286718, -1857874, -63754, -563102, 1391866, -28728, -224940, -178212, 179254, 178884, 599476, -153912, 120168, 210482, -178128, -91440, -239012, -5760], [-81896056, 164303, 6322127, -3492972, 261451, 0, -186212, -173530, 81305, -149266, 68776, -42253, 0, -77841, -398225, -330740, 0, -292503, 0, 0], [-1045320, -32920443, 408346, 579475, 326822, -245141, -718223, 18354, 1447063, -91618, -156123, 465993, -1158654, -136455, -115789, -95743, 38642, 97435, -177918, -71482], [748681, 18097229, -279640, -2592942, 137400, 508580, -1302178, -7466, -120920, -136106, -72286, 241998, -299740, -71493, 85924, 302132, -65464, -78458, 124604, -20668], [-1335328, -16966958, 577235, 4739925, 131067, 59679, 360855, 23542, 793636, 177436, -161773, -237210, 1143302, 159336, -193814, -256513, 54200, 170272, 189506, -87052], [-328158832, 1120875, -2216529, -4670675, 518788, 0, 354444, 76376, -387675, 571440, -156978, 577129, 0, 447219, 237887, 135238, 0, 297905, 0, 0], [633028, 10337055, 88421, -2616236, 19500, 539530, -2009787, -68571, 237676, -126189, 194487, -99947, 474830, -75799, 49344, 127658, -292028, 19227, -113494, 119398], [-345393, -9673395, 460190, 468543, -119888, 352662, 135199, 28860, 226492, 225725, -6632, -375438, -641900, 179430, -156925, -365450, 87092, 128065, 6052, -86068], [2348975, -8438426, -1005519, -6577831, -233900, -314528, 1489975, 53083, -1195924, 5608, -5915, 211201, 397074, -216613, 128041, 65180, 249900, -181124, -76938, -68598], [-244388829, 557964, -5539725, 960946, -1320274, 0, 152831, -137359, 374376, 300421, -271471, -57051, 0, -92200, 49370, 11490, 0, -74511, 0, 0], [138659853, -718789, 4028931, 9200391, -773206, 0, 245755, -63865, 14757, 41900, -104139, -310996, 0, -238886, 669936, 610699, 0, 361942, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_33_b_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_33_7_b_a();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
function MakeNewformModFrm_33_7_b_a(:prec:=20)
    chi := MakeCharacter_33_b();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 7));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(997) - 1;
    while true do
        trunc_vec := Vector(Kf, [0] cat [f_vec[i]: i in [1..prec]]);
        B := Basis(S, prec + 1);
        S_basismat := Matrix([AbsEltseq(g): g in B]);
        if Rank(S_basismat) eq Min(NumberOfRows(S_basismat), NumberOfColumns(S_basismat)) then
            S_basismat := ChangeRing(S_basismat,Kf);
            f_lincom := Solution(S_basismat,trunc_vec);
            f := &+[f_lincom[i]*Basis(S)[i] : i in [1..#Basis(S)]];
            return f;
        end if;
        error if prec eq maxprec, "Unable to distinguish newform within newspace";
        prec := Min(Ceiling(1.25 * prec), maxprec);
    end while;
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_33_7_b_a();".
// 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_33_7_b_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_33_b();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,7,sign)));
    Vf := Kernel([],Snew);
    return Vf;
end function;