
// Make newform 2736.2.dc.e in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2736_dc();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2736_dc_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_2736_2_dc_e();".
// 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_2736_2_dc_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 ConvertToHeckeField(input: pass_field := false, Kf := [])
    if not pass_field then
        poly := [414864, 1645728, 3072904, 2772832, 305564, -1894880, -1551960, 179664, 827916, 231024, -211368, -110512, 30728, 24552, -2732, -3152, 208, 232, -18, -8, 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], [8873896951844027855339716452350276320, 25266758669410056204978590092108637616, 31326774111765113277095281549403765448, 14403510941675495772037035656585777116, -13600789197511252656146435058333646304, -20740168859386387469678083153892123296, -4140393219262939690330662395349696000, 8925140825286763829505881454998214516, 5102989750434358306742613129669927116, -1789974221357225856099187365231182972, -1902287669059162278503611331727506532, 155694756492590487171681448990131436, 397476082097474528665988702634316268, 775059420515620958491045704576776, -51489519973712400783356309500020044, -163499447501062404766145784096704, 3978260337437901665273536195549354, -161239095629442621126593855001550, -148593778484398162786982352379514, 16681461776043958135813810856917], [15812311700289241129964636878306874369244, 73172532736735401450953778065962907914516, 117025922681196944094935461333427588036060, 58283450565875367856710313343548647404302, -58481546667761690308150408508171038104940, -85681686588697522780759689929351648500972, -5584913650916830437622275855861548901208, 43066956964000254128795793446669803927076, 14108709472827365855769310330675426154816, -12442290715127623547740530200606298515920, -5476647550318308104401617362959860717014, 2426270466145703313384037407251069364549, 1074799105956056261033430690170830276422, -346345708169796521109486920651764372349, -108566508238176682482261966310807446226, 33048250775229752530986444416002772805, 4601208784938391233250980129074065810, -1682856364552321584500026602521420228, 26541088955141657603326243430984519, 13115868417397658456364348148848915], [-15196014837537277447126728811485926297336, -58853833372894860269744391063692532099952, -86564562655993321458641668598608686856960, -38909977031898120344633612526299355966232, 46415764506318599536314994375361223579644, 62068180354268237290482085020804335099940, 2038026794695829030456942686769678232520, -31724011830731060939399798454103173548792, -9680985296058222775530131040616068678888, 9177531727766758089198243062204095068280, 3872219881670832625764656492247423665818, -1771997806719383005068146481053787233954, -765411625428540336620863901527133815840, 246908925619128277403764558206985304184, 78222247304994335934100181496304630686, -23037695516489760537395919258811936474, -3480753380333844988776014875735762658, 1165600201318935188111787123235486558, -1255718491576450550450641877348697, -10942943876722015485581900558295253], [-29994021422201585777828603058771990495000, -60073288420591244239807879069669583122736, -22306051706803469114456980459887459681136, 64602668393764161025925905119813003999544, 65068105923859515794280726129601615123976, -17640302628378780847996556221751213215288, -46885362389683427760969544884683927853064, -4584359383832745890765462488934808829720, 18283327311335448206801103011136330094568, 4759022729141155846042914131427061848872, -4661237926908142152669618970035273042122, -1530389839782528327655909108408707156384, 844373125155859612151397216083530296810, 266004969137992687230933313898419130788, -115227237906996608249333364185589701032, -22854896017038970535735319085504890600, 10494197114525150455504467805193335012, 524820264377727883872519017430362788, -487447826213734352512144738938508849, 43835544762926484794227641594863424], [-3504208022937383219475875967735197351784, -12481990803328201500807554127068011593400, -33468739346478510594743798561303555387812, -37311775733834007419271878323840194704744, -9662937709643706390231521859783588664960, 25880542805761323593003924920032621822624, 25058545157304506986240196515194050394804, -3548438337388519061326993632344848938780, -14811380636498267061545407849249789012182, -2132865235292925431273520999387943958112, 4776480396327888690271181632891146624502, 1042949759298375991707665169483211487662, -1005107113841820898162117175180326395372, -190048815707666208098019589372777918690, 139409765401527847633889225951837062232, 14061969206778851457432623527788194102, -11642544529720890137033980998302943067, 27719020784879128669866353090993778, 452488264323821090956200231131167937, -45396441352429200471231129097648615], [44015430934707192303408, 194224008953817686819344, 305343803120447027306372, 174384646298544210182272, -122804429110328283320416, -215042516118489255052816, -41057110277847312776644, 91165988185656377603072, 46715454745291975296686, -18666595158931711807576, -16916575613597789414324, 1726734584144648759712, 3458587877297465561562, 11658639337487252752, -448971481003687507060, -6909492216299799072, 35737623454942883911, -1021833237456926570, -1426701888785846434, 155949130665898008], [48722450699971541619563702852110214999400, 84775330933698136006355269118706484961448, 10131444874243881021607612184454684400348, -115377772446021499409114342880417062176648, -100157595193400179366046533090714390638092, 43491380068085326125967610983198267238552, 85945647914137401048646821335399546848640, 691253310070505119375996302115590219716, -38452258997660056579594875294456298624750, -5506096304862885177996330816719586246016, 10802940777032014436219614389650802464786, 1844804793691559794392241630377768723112, -2037163431744649924438918038624912754098, -271541758445924838523674036824267674452, 252420007899202066932659165974919308888, 15224697961020602431845695323200882374, -18751652082082181333622676730926909131, 437812637253555423331669552622441710, 640859972434545699418029954928713199, -66683776651226420646148135606228942], [22017477340419927121099139255417491433760, 60073141487264815804875105879487741403588, 72775728144521167214581667397058235861700, 21166971660940137148216722441026673622548, -38682682786771741759818086190193271409714, -39450597683422150770980800191669040626154, -1269501066795366315961694829323884254340, 17148630978011258669508318129336283347572, 7625259638209495836155683165784908427888, -3209799363488097639427096788214214830744, -3190685335038092035275886883532443994000, 159458775806468634079467402224736538304, 713535614855747505665039043765380080083, 34053790159432569671262476245587912563, -99065028532576253302255472011139326089, -3715451966917323678402618006025613705, 8216884964005379080169285662425776441, -194329814409292962930814277451338588, -326361834668063319019441007281826298, 35209295494433949058095561342081412], [-964994322078005962600066041904330716760, -9233757337787828972264667802954314388992, -15613348826566545060936152479282324623136, -1215693627322429175828931966443190700416, 20292259532154304310621050123792537363744, 13288950780682738493525542503213343198764, -10886304446871984175941423911002969232784, -11196134760620316071539245223924460156268, 3355781630951237032751728929232507473612, 4964505607704553342016023252554169465492, -806311860834263206768666405458308121978, -1339454951944920902356635039267766592512, 188793265805292131589087998935611987802, 226699745364459051393098981275643994290, -40991369934379002968860769632286875468, -20665591772989804286649192383899143912, 5259722529090685621938717099894635886, 671871494550282380708405110615893958, -303152790641521057193940937163042239, 24329550630029425125019162115302612], [27977379055707406243313949897542693124720, 50860899321223095973487073880478350091096, 9520470024203668889906426445507469445228, -84763134875746239149064918671806536008612, -77584089963697053832085143016894244594316, 31597517719851328466205984252337953670152, 66688288741820181029864130901864732330848, 2223562085053793149811470077865334155800, -28850338168969946712245497602044179913358, -5776803041592731679786487195927545449136, 7868335529193386211539768345545938589258, 2079198299956714403317002933978241032940, -1470349455209909448885416081172919687722, -378838066142494504043060667640749448348, 199307454645123223720015418686821502976, 32727761323022738545703475278202613598, -17707496423967608864556132696908175895, -650741942830558341836515703723807250, 802632091708737018522867424795639805, -74493152490554605544655709542284197], [-33186369757339128048361740880884608118828, -102513929482764026574942475121075376746392, -136360952302424698160516907459291809046156, -51626499576394326179902452134141612760774, 71717608580709653165815512617574390445782, 86988467388268982248159832514330300367010, 3804879503306061498155588636103957386408, -41447086921082987655089282595864173027098, -15409640745111541105264081034530065785452, 10326266656983520645563843027703267647560, 6277670630961765928439973854691275220582, -1566625570153250362770738408082687250173, -1328744710908810456713018146632077312325, 171431560327345511632713637739703575240, 161179555718012112149763459626002851135, -16284061162250088205870904595540575309, -10724503735828651691893446850543484563, 1219477751153613007306537935086174263, 294847922845260114778924393880981940, -41591345973789317351839599485157581], [91834987903107898352381792620066049227584, 188795308897576535559349777537743828011032, 98067248932425528885094818362006704500012, -155145955708762556189089659580874196200796, -206207956080791709427885871185890688436952, 18413908127971468746366622635587614325740, 140018710743228950415173178450641611656316, 26823878182868280464914125015884904647056, -54541884387145001124036561415755540076130, -16126170293510814072353238379238777013788, 14163081246487181270529578005347834023688, 4335301821112490427099407814288275651368, -2584394949383529953705945026283890535550, -638990055334644746025261155081320567058, 330702890123025950566383910749758996772, 45553125773013255536362317694238999996, -26744773419431791442015275631633336741, -492864481381205451918870836166930634, 1059899090970726402417874332707552286, -99264454368073675050546328687460107], [68289015767209039162441190635750590486336, 225737961073408467342050672493869730122648, 301531798045316189801810112210954792064520, 115980895161136056353030906218855341044104, -156788556988216516041361155604772781820564, -187872355619506608541101418590895736157252, -9302561977122612233069928004367219243940, 86719925066824736484764801260532399475996, 33939050548622386234786484088617881470360, -20319673739274360314260809033725167379676, -13806347942149969448201487150789573595766, 2733567803575598827963517704888868648038, 2945121219762577352397966234690477180948, -244870005107409551497702364793961276732, -368782287023067582470100645254584362964, 22638511669651621679160264862327560536, 26177086030663471823505605677082385620, -2175315216222029797231055552823746172, -829416866311997612019946084599479839, 105207995528008854981836399678000867], [-22018771992380346456762927987918530536512, -115636397782095431426455541639364028595064, -230663322408928470364250174624017807526096, -177566421946722478247667498669613135162540, 57019072038218668913884683931826718173068, 189838569784146556855675313306686846104500, 65855269570420294051983418396816112806544, -77795968426714167035304853699102707645244, -53131701621906569235839163171745158974908, 16893828488563361958496444363853529935984, 18116135539087877116808693893808028712358, -2193914302325574349217088641256214748774, -3589167799954695264394291524336142406808, 224598193259646203867185602454288715808, 426263369412054997075403050419170922442, -26422388833183357214578617128933255950, -28563879971648745533070789316654617192, 2571260887863293589745402350957662944, 825911904031095207172812184872967579, -106969029197638398935762339672537740], [63402148837830025402604240793270553922016, 239820969674371081046896851101647753234184, 375233855193937870122545481839924868472756, 205983084273929988167894656814862481329104, -150488596908134171457156226289500784889488, -263789438827925010182358863133769334942288, -51173581259036795310102290794970563298876, 113912356468052462018279649555079444545220, 58979113654874720433552083972418643882438, -24675913396845562844955206859449386531196, -21465909027663759950069779933574560381036, 2800086224445418242888322017518628519366, 4394864282456011213403521945146260651526, -154269244864296573225632410219561503358, -553361507740906985225053039010211326876, 12390613742200141606597832538991621122, 41212384490314216649817718465566704075, -2277232232900597427067657642538386312, -1461774093363221791035597346381644116, 170589665652278063619799431868215081], [-56289902248766350154358564803480261229372, -197199707830927168186997670292014318719824, -284124688587252127404971859542943916429220, -133196065582601126839040804613109728439120, 136740230379093335239331776954041223079272, 195778687012781072646518077503165820512316, 18801884129069771246191065358195632910594, -91569722732251910873490840327192744191558, -36186199963244343423586810969042101484298, 22794268836030046605222836630025288187300, 13930631959256335630049983474986006503366, -3492670108659059798120555985167723319402, -2856387335530381004212286934706429209246, 377794045026347363640290525824497178484, 340325200961636541760660149200125843471, -34300752649525785197976151797899656893, -22559491769451811946089623325663111606, 2482797434225236600682097090744399941, 641680508772376093307279641120816255, -89023814084180728597956750331677429], [4308379572552717168083669246186828026472, 89010229639273607834470746150720525504, -30713389797044905771340313945047281465232, -58234923465481136420490249420849705688628, -28701628675810078894442985921142882007680, 33140882060053006699867920539706680046064, 42137814115466786109256221094629648430444, -2728119120950767745908120714688508174068, -22082216789763744663089725126430746815292, -3849282298803696116504714482983634592500, 6727067222933043986193651365108009742378, 1687125323992368596213071867366139381408, -1361405868190840864516333744464472777590, -321871417494073077627997473801404467304, 191322827129546014818615602723240680586, 27269351351439472530220683162797501052, -16930589916205081036277617595944847204, -391932226633151269059854956184800206, 737645128257416557126881891450860121, -70534788882533822890101113761257285], [-41713387361523125808496832035848548158400, -152086173282889998154413945289952923910896, -222993783773803220738367641163968178160756, -107943791577135573871841260501281311534472, 105078857648956426178106605196444461131584, 154273948546656212567085495905620178382072, 16452503594662652227762554465392408127528, -71296678543028079237406904689758549150452, -28933135210460394951663240287327075860090, 17371569464810637636215531482843894333396, 11040526992680254240924102904021441097436, -2550172056198404018920846308144517318568, -2262034068247398398011895992393708970682, 254585823990933011798132282316704950564, 273320661727770099925075644746683754634, -22288672470112467664578882838711964354, -18756250649917400270332287167816118263, 1759921364654730471493599396329243214, 578331413918091029095945980222629960, -75824552744386106785280664841832100], [-30785103785354510543867399930854392342920, -115069865859072778799050916607040829332416, -177030134746585184814959662072922873856112, -96740889772118728094552733224628769586472, 68274643887234408214958964686604280134736, 122884040227871974034572500120687008742620, 27017259079904762786255988507752439653600, -51892703021508593978638775422030071609364, -29557726158080053294248018444740923441060, 10807232568254190673155339027831980198752, 10757550010400229960941965691154576865278, -1131376933420477341817308886209580284472, -2220965729142672970990200835657716439986, 56854241168340053940968841211296913698, 280037010161159861148114416018653590384, -6317452785503034813650056033615229828, -20611966355249918601352311540748567498, 1220856346544264792243327205384793016, 703454819230384804399591380532474023, -82877048202940611495080265061638892]];
    Rf_basisdens := [1, 1363556174103278319148990106889990968, 738365668276925209819178142880930109172, 492243778851283473212785428587286739448, 1476731336553850419638356285761860218344, 1476731336553850419638356285761860218344, 3498599200269127333272, 1476731336553850419638356285761860218344, 738365668276925209819178142880930109172, 492243778851283473212785428587286739448, 1476731336553850419638356285761860218344, 738365668276925209819178142880930109172, 1476731336553850419638356285761860218344, 1476731336553850419638356285761860218344, 1476731336553850419638356285761860218344, 1476731336553850419638356285761860218344, 738365668276925209819178142880930109172, 492243778851283473212785428587286739448, 492243778851283473212785428587286739448, 492243778851283473212785428587286739448];
    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_2736_dc();"
function MakeCharacter_2736_dc()
    N := 2736;
    order := 6;
    char_gens := [1711, 2053, 1217, 1009];
    v := [6, 6, 3, 5];
    // 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_2736_dc_Hecke();"
function MakeCharacter_2736_dc_Hecke(Kf)
    N := 2736;
    order := 6;
    char_gens := [1711, 2053, 1217, 1009];
    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], [-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, 1, 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 := 2;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -1, 0, 0, -1, 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, 1, 0], [1, 0, -1, 0, 0, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, -1, 0, 1, 0, 2, -1, 0, 0, 1, 0, 0, 0, 1, -2, 0, 1, 2, -1, 1], [0, 2, 0, -1, 0, 0, 1, 0, 1, -1, 0, 1, 1, -1, 1, 0, 0, -1, 0, -1], [0, 0, 1, 1, -1, 0, 0, 1, -1, -1, -1, 2, 1, 1, -1, 1, 1, 0, 0, 0], [0, 1, 0, -1, 0, -1, 1, 0, 1, -1, -1, -1, 1, -1, 1, -1, 0, -1, 1, -1], [-1, 0, 0, 0, -1, -1, 0, 0, 0, -1, -1, -1, 0, -1, 1, 0, 0, 0, 2, 0], [0, 0, 0, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 2, -1, 2, 0, 1, -1, 0], [0, 1, 1, 1, 1, 0, 2, 2, -2, 0, -1, 2, 0, 1, -1, 0, 0, 0, 1, -1], [-1, 1, -1, -3, 1, -1, 2, -2, 2, 0, 0, -3, 0, -3, 3, 0, -2, 0, 2, 0], [-1, 1, -1, -2, 1, 0, 2, -2, 2, 1, 0, -1, 0, 0, 2, 0, -1, -1, 0, -1], [1, 2, 0, 1, 1, -1, 4, 1, 0, -2, -1, -1, -1, 0, 1, 1, -1, 0, 3, -3], [-1, 0, -1, -2, 1, -1, 1, -1, 2, 0, -1, -2, 0, 0, 1, 0, -1, 0, 2, 0], [-1, -2, 1, 1, -2, -2, -2, 2, -2, 0, -1, 0, -1, 0, 1, 1, 1, 0, 0, 1], [-1, 0, 3, 0, -1, 0, 2, 2, -1, -1, -1, 2, 0, -1, 0, 0, 0, 0, 0, -1], [-1, 0, 2, 1, -1, -1, 1, 1, -1, -1, -1, 0, 0, 0, 1, 3, -1, 0, 1, 1], [2, 0, 0, 1, 1, 2, 2, 1, -1, 1, 2, 3, 0, 1, -1, 0, 1, 0, -2, -2], [-4, -2, 0, 0, -2, -4, -2, -1, -2, -1, -3, -1, 0, 0, 1, 0, 0, 0, 1, -1], [2, -2, -1, -1, 1, 1, 4, -1, 1, 1, 0, -1, 0, -2, 2, 0, -2, 1, 0, 0], [4, -1, 0, 2, 1, -1, 6, 4, -2, -2, 0, 0, -2, 0, 2, 2, -1, 1, 1, -2], [2, 0, 0, 1, -1, 2, -1, 0, 1, 2, 0, 0, 0, 1, -4, 0, 1, 2, -1, 1], [-2, 1, 5, -1, 0, -1, 2, 1, 0, -1, -3, 0, 1, -1, 1, 1, 0, -1, 1, 0], [0, -4, -1, -2, -1, -1, -1, -1, 2, 0, -3, -3, 1, 0, -1, -2, 3, 0, -1, 1], [-2, 3, 1, -3, 1, -3, 2, 1, 3, -1, 0, -1, 2, -2, 2, 0, 0, -3, 2, -2], [0, -2, -2, 0, -2, 0, -2, -1, -2, 1, 2, 1, 0, 0, 3, 0, -2, 0, -1, 1], [-1, -2, -1, 2, -1, 3, -2, -1, -2, 1, 1, 1, 1, 2, -3, 0, 1, 2, -2, 2], [-1, 1, 1, -2, 0, -1, 2, 1, -4, -1, 1, 0, 0, 0, 2, 0, -1, -1, 1, -1], [4, -1, -3, 4, 1, 0, 3, -2, -1, 1, -1, -2, -4, 2, 1, 2, -3, 4, 2, -2], [-1, 0, -3, -1, 3, -1, 3, 0, 3, 2, 3, -2, -1, 1, 1, -1, -1, 0, 1, -2], [-2, 2, 1, 2, 0, 1, -2, 2, -1, 1, 1, 2, -2, 0, 2, 2, 0, 0, 1, 0], [-4, 0, 0, -1, -3, -4, -3, -4, 1, 0, -5, -2, 2, 0, 3, -1, 1, 0, 1, -1], [-1, -5, 1, 3, 1, 1, -1, 4, -3, 0, 1, 3, -2, 1, 1, 4, 0, 1, 1, -1], [1, -1, 0, -1, 1, 1, 2, -1, 2, 1, 1, 0, 0, 0, 1, 1, -1, 0, -1, -1], [2, -1, -1, 2, -2, -2, 0, 4, 0, -1, 1, 2, -1, 3, 0, 0, 0, 2, 0, -1], [0, 2, -2, -2, 2, 6, -2, -2, 4, 4, 2, 0, 2, 1, -4, -2, 0, 2, -2, 2], [-3, -1, 1, -1, -1, -3, 6, 1, 2, -3, -1, -2, 0, -1, 2, 2, -2, 0, 5, 1], [3, 2, 0, -1, 0, 0, 0, 0, 3, -2, 1, 0, 3, 2, 1, 0, 1, -1, 0, 2], [-2, 1, -1, -2, -1, -2, 0, -1, 0, -3, -1, -2, 0, -3, 2, 0, -1, -1, 2, 2], [-1, 4, 0, 1, 2, 2, -1, 2, -1, -2, 1, 2, -1, -1, 2, 2, -3, 1, 1, -4], [-2, 0, -1, 1, 3, -2, 3, -2, -1, -2, -2, -2, -2, 0, 5, 1, -2, 0, 3, -3], [2, 0, 1, 2, 2, 2, 8, 3, -2, -3, 2, 4, -1, -2, 3, 2, -2, 0, 4, -5], [2, 5, -1, -2, 1, 6, -2, -4, 6, 5, 1, 0, 2, 1, -4, -2, 3, 3, -4, 4], [7, -3, 0, -1, 1, 3, 3, -2, -2, 2, 0, -1, 2, 0, -2, -1, 1, 0, 0, 0], [2, 4, -2, -1, -1, 2, -1, 0, 3, 2, 5, 2, 0, -1, -2, 0, -3, -2, -1, 1], [7, -2, -1, 0, 3, -1, 2, -1, -4, 1, -1, -3, -1, 0, 1, 0, -1, 0, 2, -2], [-3, 2, 2, 1, -2, 0, -1, -2, 5, 0, -5, 2, 1, 1, -2, 0, 2, 1, -1, 0], [8, -4, 2, 1, -2, 2, 1, 0, -3, 3, -2, 0, 0, 1, -4, 0, 3, 2, -1, 1], [3, -3, -4, -6, 1, 1, 1, -8, 6, 4, -1, -7, 2, -6, 4, -4, 1, 2, -5, 3], [-3, 0, 0, -1, 0, -3, 2, 1, 7, -3, -2, -2, -1, -4, 1, -1, -1, 0, 3, 1], [1, -1, 2, 2, -3, 4, -5, -3, 4, 1, -2, 0, 0, -2, -2, 0, 1, 1, -4, 4], [-1, -2, 2, 2, 0, 1, -1, 5, -4, 1, 2, 4, -2, 2, -2, 2, 0, -2, 1, 0], [-1, 0, 2, 3, -1, 3, -3, 3, 1, 3, -1, 0, -2, 2, -1, 1, 3, 4, -1, 1], [1, 3, -3, -6, 2, 1, 7, -5, 3, 1, 0, -4, 0, -7, 5, -3, -3, 0, 0, -2], [2, 0, 4, 8, -2, 2, -2, 6, -8, 0, 2, 8, 0, 6, -6, 2, 4, 0, -4, 0], [1, 0, -3, -4, 2, -4, 3, -3, -4, -1, 0, -2, 1, -3, 4, 0, -3, -4, 3, -3], [7, 5, -1, 3, 0, 0, 7, 2, -1, 0, 5, 4, -3, 3, -3, 3, -6, -1, 0, 0], [2, -4, -1, 0, 2, 2, 1, -2, 4, 4, 2, 0, 0, -3, 1, -1, 1, 0, -4, 0], [-9, 2, -2, -1, 0, -4, 2, -2, 3, -4, -3, 0, 1, 1, 2, 0, -1, -1, 2, 0], [0, 2, 2, 2, 4, 4, 2, 3, 0, 1, 2, 1, -4, 0, -3, 2, 0, 0, 1, -1], [5, 1, 3, 4, 3, 3, 11, 9, -4, -3, 1, 9, -1, 3, -2, 2, 3, -2, 1, -6], [-2, -11, -1, -5, -1, 1, -5, -6, -1, 2, -1, -2, 5, -3, 1, -5, 2, -1, -3, 3], [3, -1, 2, -1, -6, -8, 2, 1, -1, -2, -5, -3, 1, -3, 5, -1, 2, -3, 2, 1], [-2, -6, -1, -1, 3, 3, -4, 1, 1, 6, 0, 1, 0, 7, -7, 0, 1, 1, 0, 3], [-2, -2, 1, 2, 4, 2, 2, 7, -2, -1, 2, -1, -2, 1, 2, 1, 1, 2, 1, -1], [-5, 0, 3, 1, 1, -3, 0, 7, -3, -3, 1, 2, -4, -1, 5, 2, 0, -2, 1, -1], [3, 2, -2, -5, 0, -6, 3, -6, -1, -2, -5, 0, 3, -1, 6, 0, -2, -5, 3, -4], [-6, -7, 1, 2, -2, -2, -17, 1, -2, 1, 0, 0, -1, 1, 0, 2, 2, 0, -5, 3], [9, 11, 1, -5, 2, -7, 10, 3, 8, -4, 0, -2, 2, -4, 4, -1, -2, -8, 5, -5], [2, 1, -1, -8, -3, 0, -4, -10, 8, 3, -3, -4, 8, -3, -2, -8, 5, -1, -6, 6], [-2, 1, 1, 3, -2, -2, -1, 3, -3, -3, -1, 0, -2, 2, 0, 4, -2, 1, 3, -1], [-5, -9, 0, -2, -4, -4, -11, -3, 2, -2, -3, -4, 2, -4, 2, -4, -1, -2, -1, 2], [1, 5, 1, -1, 1, 1, 2, -1, -4, 1, 3, 0, 0, -9, 5, 0, -2, 0, -1, -1], [2, 1, 2, -2, -1, -5, -4, 2, -1, -6, -4, -2, 0, 0, 2, 0, -1, -1, 5, 2], [-1, 3, 3, 2, -2, -1, 6, 1, -5, -1, -1, 0, 0, 2, -2, 0, -1, 0, 0, 2], [1, -6, -1, 1, -1, 1, -2, -3, 5, 3, 3, -2, 0, 5, -3, 0, 2, 0, -5, 3], [3, 0, 4, 0, 3, 3, -2, -2, -4, 6, 0, -2, 0, -1, 0, 0, 0, 0, -3, -1], [-3, 6, 1, 1, 2, 2, -6, 1, -1, -1, 3, 4, 0, 1, -1, 0, -3, -1, 0, -3], [-10, 0, -1, 0, -2, -4, -5, -1, -2, -1, 0, 1, -2, -1, 0, 1, -3, -2, 1, -1], [-15, -1, 3, -2, -3, -4, -18, 0, 0, -1, -2, 1, 2, 0, -2, -2, 5, -3, -4, 3], [0, -2, 4, 4, -3, 5, -3, -2, 2, 2, -4, 2, 0, 1, -4, 0, 2, 2, -5, 3], [4, -4, 0, -1, -3, 0, -1, 1, -5, 1, 3, 3, 0, -1, 5, 0, -1, -2, -2, 2], [-1, 0, 1, -2, 2, -1, 2, 0, -2, 1, 0, -3, -2, -5, 2, -2, -2, 0, 1, -1], [4, -5, 3, 2, 2, 2, 0, 3, -8, 5, 0, -2, -5, -3, -2, 0, 0, 2, 0, -3], [-4, 4, -6, 4, -1, 3, -2, -1, 12, 1, 4, 1, -2, 7, 1, 0, -2, 4, -2, 2], [-3, 7, 1, -6, -2, -5, -1, -3, 7, -3, -2, 0, 6, -3, 1, -3, 1, -6, 0, 0], [-3, -1, 5, 3, -1, -7, 3, 9, 1, -8, -6, 1, 0, 3, -3, 0, 4, 3, 3, 1], [3, -8, 3, 3, -2, -2, 5, 3, -3, 1, 1, 4, 0, 3, -3, 0, 3, -3, -1, 3], [3, 2, -1, -4, 0, -3, -2, 0, 3, -3, 0, -1, 0, -5, 4, 0, -2, -2, 3, -1], [-2, 2, -1, -2, 1, 1, -7, -2, 2, 0, 0, -1, 1, -4, 3, -2, -1, 0, -3, -1], [-5, 0, 6, -1, -1, -9, 1, 7, -3, -5, -5, 0, -2, -2, 5, 1, 3, -4, 3, -3], [1, 5, -4, -8, 4, 1, 4, -8, 3, 4, 2, -7, 0, -5, 4, -5, -4, 0, -1, -1], [-6, 1, 0, -1, 0, -1, 3, 0, 5, -1, 3, -3, 1, 5, 1, 1, 0, -1, 1, 3], [5, 1, -1, -2, -1, 0, 2, -8, 4, 1, -2, -3, 2, 0, -2, -2, 3, 3, -4, 3], [-1, 1, -4, 2, 3, 7, -2, 0, 4, 4, 9, -3, -4, 1, 1, 0, -3, 2, -2, 3], [0, -1, 4, 4, -3, 1, -6, 1, 5, -2, -2, 0, 2, 1, -4, 2, 3, 1, -1, 6], [-5, -13, 2, -4, -1, -1, -7, -2, -5, 0, 0, 2, 4, -1, -2, -4, 3, -5, -3, 2], [-12, 2, 7, -3, -4, -2, 11, 5, -6, -6, 1, 2, 1, -4, 3, 1, -1, -2, 2, 1], [7, -2, -1, 2, -2, 3, -4, 0, -9, 1, -2, 5, -2, 3, -2, -2, 0, 2, -3, -3], [7, 0, -4, 1, -4, 6, -5, -6, 1, 4, 3, 4, 1, -2, -5, 0, -1, 1, -5, 2], [-6, 1, -4, -5, 5, -3, 4, -4, -3, -2, 2, -5, 1, -5, 4, 0, -4, -5, 4, -1], [-4, -3, 3, -4, 4, -4, 4, 0, -10, -1, -3, -4, 1, 1, 8, 0, 0, -4, 4, -3], [15, -8, -6, 10, 5, 9, -2, 3, -6, 7, 8, -5, -8, 5, -7, 0, -2, 10, -2, 2], [5, 5, 2, 1, -4, 3, -3, 3, 6, 2, 2, 4, 0, 1, -2, 0, 3, 2, -5, 5], [6, -3, 2, 5, -4, 5, -5, 4, -4, 1, 3, 7, -1, 2, -5, -1, 2, 3, -5, -1], [-2, -9, 0, 1, -4, -3, -5, 4, -5, 1, -1, -1, -1, 0, 1, 1, 0, 1, -1, 3], [-5, -3, -2, -3, -3, -3, -12, -9, 3, 3, 1, -7, 1, -8, 7, -2, 1, 1, -2, 6], [-8, -7, -1, -3, 0, 0, -15, -4, 3, -1, 0, -2, 2, -2, 0, -4, -2, -1, 1, -1], [-2, -4, 1, 5, -1, -2, -2, 6, -1, -2, -2, 4, 0, 6, -5, 1, 4, 0, 3, 1], [16, -4, -1, 6, 0, 6, -17, 1, -5, 6, 6, 1, -2, 5, -6, -2, 2, 4, -6, 1], [1, 14, -1, -7, 2, -6, 4, -4, 21, -5, -2, -2, 2, -4, 8, 0, -3, -7, 4, -1], [0, -6, -2, -4, -4, -4, 0, -5, 2, 0, -8, -10, 4, -4, 4, -4, 2, 2, 4, 0], [-2, -2, 1, 5, -5, -2, -14, 0, -3, 0, 1, -2, 0, 3, -5, -2, 4, 0, -3, 7], [1, 3, 2, -2, 0, 1, 6, -2, -1, 0, -2, -1, 0, -1, 0, -3, -4, 0, -1, -1], [-7, 0, 1, 1, -2, -2, -16, -3, -1, 5, 3, 0, 0, 2, -2, 0, -1, -1, -2, 7], [-2, -5, -1, -1, 3, 3, -4, -1, 1, 1, 2, 1, 0, -4, 4, 0, -6, 1, 0, -2], [-17, -4, -2, 1, -3, 1, -20, -3, -2, 4, 1, -1, -1, -2, 5, 1, -3, 2, 1, 3], [-1, -1, -1, 1, -2, 4, -3, -2, 9, 2, 5, -2, -1, 2, -1, -1, 0, 1, -4, 4], [-1, 7, 4, 5, -1, -1, -6, 9, -5, 3, -1, 7, -1, 6, -5, 2, 5, -3, -4, 4], [-3, 0, -4, 3, 2, 6, -2, 0, 3, 2, 7, -2, -5, -3, -4, 0, -3, 3, -2, 4], [11, 0, 1, -6, -3, -7, 2, 5, -6, -9, 3, 3, 3, -6, 3, 0, -1, -6, 2, 2], [14, 2, -4, 2, 0, 0, 0, -2, 6, 4, 0, 0, -2, 2, 0, 0, -2, 2, 0, -4], [-16, 8, 2, 2, 4, -8, 0, 0, 6, -6, -8, -4, -4, 0, 3, 2, 0, 0, 6, -6], [6, -13, 0, 0, -4, -2, 1, 0, -7, 2, 2, 2, 0, 0, 0, 0, -1, -1, -4, 5], [-2, 15, 3, -4, 0, -4, 1, 0, 13, -6, 0, 4, 2, -3, 2, -1, 1, -6, -2, 2], [-2, 4, 0, 0, -2, -2, -4, 1, -4, -3, -1, -1, 0, -6, 5, 4, 0, 0, 3, 1], [4, -3, 1, -3, 6, -4, 5, 1, -9, 3, -1, -6, -6, -2, 10, 0, -4, -3, 5, -7], [-3, -5, -7, -8, 2, -3, 11, -6, 13, 0, -4, -9, 0, -4, 3, -6, -1, 0, 5, 1], [1, -9, 5, 9, -7, 1, -12, 7, 0, -5, -1, 8, 0, 9, -7, 4, 4, 0, -3, 1], [1, -3, -7, 4, 2, -1, -4, -2, 10, 1, -1, -4, -2, 6, -4, -2, 1, 3, 1, 3], [3, -3, 2, 9, -1, 3, -2, 4, -6, 4, 3, 7, 0, 12, -10, 1, 7, 0, -8, 2], [4, 1, 2, 0, -8, -8, 3, 0, 0, -2, -6, -4, 2, 0, -2, -4, 4, -4, -5, 6], [3, -10, -2, 0, 6, 12, 3, -2, -4, 6, 6, 4, 0, 2, -4, 0, -2, 2, 0, 0], [6, -8, 1, 0, -2, -2, 3, 3, -1, 0, -6, -5, 0, 0, 0, 0, 8, 6, -4, 3], [2, 1, 1, -2, 4, 4, 6, 2, 2, -1, 1, 6, 3, -9, 6, -6, 0, -4, 2, -5], [-13, -10, 4, 1, 0, -2, 1, 8, -19, 0, 1, 0, -3, 0, 1, 0, 1, 1, 1, -2], [-6, 0, 3, 3, 3, 3, -11, 9, -3, -3, 0, 9, 0, 2, -2, 0, 6, -3, 1, -6], [4, 2, -8, -5, 10, -1, -1, -9, -5, 9, 2, -10, -1, -2, 5, -1, -3, -2, 1, -3], [-8, 5, -2, -6, -1, -3, 6, -4, 15, -4, 0, -2, 4, -1, 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-14, 18, 0, -2, 0, 14, -5, 2, -7, 1, -10, -2, 2], [6, 6, 6, 10, 4, 4, 15, 14, -10, 4, 6, 16, -4, 11, -7, 8, 0, -2, 3, 0], [-1, 6, -2, -7, -1, -6, 1, -5, 25, -7, -8, 0, 5, -3, 7, 5, -1, -6, 6, 0], [3, 15, -1, 6, 3, 7, 1, 3, 17, 4, 1, -2, -4, 4, -7, 2, 1, 8, 0, 0], [-3, -4, 3, 9, -7, 5, 5, 0, 4, -2, -15, 14, 1, 17, -9, 1, 5, 4, -5, -2], [0, 13, 4, 0, 0, -6, 5, 4, -1, -6, 6, 10, 0, -4, 8, 0, -7, -15, 4, -5], [-5, -6, -3, -5, -8, -8, -10, -12, 5, -1, -4, -14, 2, 4, -6, -4, 1, 1, 0, 7], [2, 4, 0, 10, -4, 2, 10, 6, -14, 0, 4, 8, 0, 14, -10, 4, 10, 0, -6, 2], [11, -1, 3, 4, 5, 2, 17, 7, -4, -3, -1, 2, -4, -1, 6, 4, 3, 1, 4, -6], [5, 7, -1, -16, 8, -9, 0, -8, 22, -1, -7, -12, -2, -16, 16, -2, -9, -7, 9, -5], [2, -4, 3, 6, -4, 2, -9, 0, -2, 2, 2, 2, 0, 7, -2, 9, 3, 0, -8, 4], [1, 7, 3, 1, 5, 1, 17, 4, -8, 2, 1, 5, 0, 1, 3, 8, -2, 0, 2, -4], [25, 11, 1, 2, 0, 9, 8, -6, 13, 6, -1, 1, 0, 2, -5, 0, 3, 4, -3, 3], [1, -4, 0, 7, 1, -1, -6, 3, -9, 0, -1, -3, -1, -4, -7, -1, 3, 4, 1, 5], [-16, -17, -2, -4, -9, -9, -27, -8, 4, -5, -7, -13, 2, -1, -1, -4, 1, 0, 5, 4], [-22, -14, 8, 6, 2, 0, 1, 4, -22, -2, -10, -2, 2, 5, -9, 0, 8, 6, 1, 2], [-4, -1, 2, 3, -1, -1, -2, 8, -3, -4, -4, 3, -1, -1, 2, 2, -4, -1, 6, -3], [-15, 2, 7, -3, 3, -17, 23, 13, -12, -14, -15, 4, 1, 3, 3, 1, -1, -2, 17, -8], [-1, -7, -2, 14, -5, 4, -1, 7, -5, -1, 0, 10, 0, 6, -14, 0, 7, 7, -4, 2], [-3, 12, -7, -15, 3, 3, -8, -16, 15, 4, -3, -11, 8, -1, -7, -16, 3, -1, -2, 1], [-8, -3, -4, -3, 9, 9, -16, -3, 3, 3, 5, 1, -1, -4, 5, 2, -1, 5, 0, -6], [-4, -6, 4, 6, -2, -4, -12, 4, 0, 0, 0, 0, 0, 12, -4, 10, 2, 0, 2, 6], [2, 4, 0, 0, -14, 2, -8, -6, 8, 2, -4, 14, 8, 2, -6, 0, 4, 0, -8, 0], [3, 1, -13, -4, 5, 0, -9, -15, 10, 5, -1, -14, -2, 1, 4, -2, -3, -1, 0, 6], [2, -2, -6, -1, -3, 2, 17, -4, 3, 0, 5, -2, 0, 7, -4, -2, 5, 0, -5, 1], [-14, -2, -2, -3, -7, -7, -32, -12, 3, 6, 0, -11, 1, 3, -4, -2, -2, 1, -4, 13], [5, 3, -8, -1, 3, 15, -2, -16, 8, 8, 5, -1, 6, 2, -16, -3, -3, 4, -4, 4], [-1, 0, -6, -3, 0, 1, 10, -3, -1, 1, -4, 6, -3, -4, 3, -3, -3, 0, -1, -9], [4, 0, -4, 0, 6, -4, 0, 2, -9, 2, 2, -2, 0, -2, 0, 0, 0, 0, 4, -4], [-8, -11, 9, -5, -5, -11, 3, 7, -27, -7, -8, 5, 4, 2, 8, 0, 4, -5, 3, -4], [-2, 0, 7, 2, -3, -1, -1, 2, 2, -8, -8, 3, 9, 8, -5, 0, 9, 2, -1, 7], [6, -3, 3, 12, -1, -1, -7, 7, 0, -2, -6, 9, 6, 22, -12, 6, 9, 3, 1, 1], [-2, 10, 4, 3, 3, 3, -1, 7, -3, -5, 3, 11, 1, 6, -7, -2, 10, -5, 3, -8], [0, -2, -5, 4, -2, 0, -9, -1, -2, 3, -4, -1, 0, 3, -6, -5, 9, 0, -5, 5], [14, -5, 4, 11, -14, 13, -13, 4, -7, -1, -1, 21, 1, 5, -11, 1, 6, 5, -13, -1], [24, 1, -2, -3, -6, 14, -10, -2, -1, 4, 17, 6, 7, -1, -2, 0, 1, -3, -10, 10], [15, 3, 2, 8, 5, 0, 17, 13, -3, -5, 2, 4, -8, -1, 10, 8, 3, 7, -6, -2], [-4, -2, 5, 0, -6, -4, 33, 7, 2, -13, -1, 3, 0, -3, 4, 5, -5, 0, 11, -3], [-27, 10, 10, -9, 0, -14, 7, 2, 11, -6, -13, 0, 5, -4, 9, 0, 3, -9, 7, -8], [11, 1, -4, -4, 5, 5, 8, -4, 4, 6, 1, -3, 0, 2, -2, 0, 9, 4, -14, 1], [-4, -25, 4, 0, -4, -4, -5, 8, 0, -2, -8, 4, 4, 8, -12, -8, 12, -8, 3, 2], [7, 6, -9, -5, 5, 5, 11, -18, 11, 0, -1, -10, 5, -1, -3, -5, -7, 6, 3, -4], [-6, -7, 4, 10, -8, -8, 0, 16, -4, -14, -6, 8, -2, 6, -12, 0, 6, 10, 0, 6], [9, -5, -4, 11, 5, -1, 10, 9, -12, -1, 7, 2, -18, 2, 11, 9, -11, 4, 5, -5], [-2, -1, 5, 9, 5, 5, -8, 13, -9, -5, 6, 15, -4, -1, 5, 8, 2, -1, -4, -10], [-3, 1, 13, 6, -4, 1, 6, 9, -14, -3, -5, 14, 8, 8, -6, 8, 7, -1, -1, -3], [8, -3, -11, 16, 1, 8, 1, 2, 1, 5, 5, -2, -12, 10, -12, 6, -7, 20, -2, 2], [2, 7, 1, -1, 0, 2, -20, 6, -6, -7, 6, 8, 0, 10, 0, 9, -2, 0, 5, -9], [12, -9, 11, 10, -10, 14, -12, 2, -8, 5, -5, 10, -1, 5, -14, 0, 10, 10, -12, 9], [-6, -2, 3, 3, 1, -6, 2, 4, -1, 0, 6, -2, 0, 12, -5, 5, 0, 0, 7, 5], [1, -10, 0, 3, 2, 1, 7, 1, 7, 4, 10, 2, 0, 5, -1, 6, 3, 0, -3, 1], [-2, 0, -6, -8, 2, 4, -8, -13, 6, 2, 10, 4, 8, -2, -4, -8, -8, -4, -12, 6]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2736_dc_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2736_2_dc_e();".
// 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_2736_2_dc_e(:prec:=20)
    chi := MakeCharacter_2736_dc();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(1999) - 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_2736_2_dc_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_2736_2_dc_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2736_dc();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![64, 3840, 74208, -155520, -140400, 478656, 378496, -1205184, 522512, 370848, -217160, -88896, 66892, 6096, -8096, -336, 708, 0, -32, 0, 1]>,<17,R![2064793600, 11690803200, 29369630720, 41362391040, 34264899584, 15318417408, 1866555392, -1310423040, -401001728, 138484224, 85142144, 6802944, -3689088, -594432, 135360, 37344, -348, -744, -14, 12, 1]>],Snew);
    return Vf;
end function;