
// Make newform 285.10.a.h in Magma, downloaded from the LMFDB on 21 December 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_285_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_285_10_a_h();".
// 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_285_10_a_h();".
// 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 := [15712212684310961400, -21881601450607548510, 844341253042208334, 617735239298795077, -1105301955330540, -4369460380063800, -17762605232062, 13077899446663, 51117957936, -19804799606, -49616078, 15858707, 18436, -6356, -2, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-848, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5458, -1350, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [834694077651700571827264074362048568333456412299255361113912, -536561870250324440894758009127393539246979321397182842125414, 6665131630638766904132830570585134067595219778226318828756, 8857244262202496053357921551348950140764928528392786138057, -53358374840580713955589387036701597116419558367590684173, -44199543335674331404557074292902757171385883365999400323, -84886533047277227648010423688007535858087246160475075, 93584099421780640742072304924188223200373634586057706, 605350320553237584151968317510600445169613301977494, -95424525931746082073808108210335623431150191870348, -886618413315732887500787737477113893224558132402, 46178351442019059587642291674663362096653769949, 522233461150711741445077601234785948190370415, -8481072638572798912870037531335366489078043, -109269391109411765462867267268577662347663], [-8160136114164901538205474852239074616480935338191048996940216, 1104720108347678604461751551377620536059975579304788202044678, 228719084915295812395264533224604007083365073994090287590156, -9656813266013102034405934158627077537206007985309319566297, -1762508697957174027139538983101251790952503859879371519187, 45041333091654569864436215644218710352192373331578458707, 5904979568766696050807641613387609402677890158558216867, -112214070822507500359793593049202086672689797258304778, -9825957843349941961282784383345078397217251030100054, 137322415287775038889793503989667931791245461063500, 8549876966983392254871120070958374875329757973202, -77546144168342301718263075715016608055492713389, -3730067306145169502061617225066575089971080527, 16084878625159501184574508375757550395733483, 641523333236704848165786975972824100518831], [2866973740910835456549013921464000250366690652123518026650904, 757940431260321944173861870845360190534321796211073899694530, 156347559414140225027696552605072967219320226929870669268452, 31703511918122554488381091229331454847069659395653599607565, -40119313418138620597631123542683778179525772198905404865, -254289044089078504896618062487880554775867383971165534767, -5407559134718993028912004295496698899593979306659138767, 640937156058515112475718535715246539025644400666779090, 16496069202860939527247910278443741602951751316797678, -721792669811817793585499764341816404648778787380284, -19293085736431257717601237327673751178551365019322, 375613748560321262917958749250100754066562610673, 10001540852269959583025078619095904718989599659, -73121029502303205401387897689394021615075879, -1914544484452034365991393167175397861369419], [-3278778764779784385527239244508124546400566147044271258546632, 1489641213406996244293096864823408623293230236957364435708058, -30990039471694659958014770789862548588568707184228160616732, -39784890308869625368152741134473579835397821735814836225415, -690761279088154380365537784139025708393070115979678550837, 223352274958561363470654677312586919155319515480665339069, 6287004769989053479499134906914007889773544844242630245, -481227084630431123225428893711891286323490049404550646, -15274232048366514736179544756573706881363424571634106, 488946405345320306211717379115061228754718966385844, 16007940968147688994386426669372078381199494436334, -236395932148005416919371066645022186024286141043, -7681270859944493997115872878095272928514037017, 43645452895126486803639060920031465452360677, 1382974704077930858352928025296020511584409], [-3832124370571414507358025898657677308389230457674276193726248, 2455738409421256848342223536789890585430360239985658467185586, 122522515375222715315023161776695630438338055679612902451420, -72548063208247989837796539093694199571924105561781555669395, -3147053164079960725375198339425491228625385381942298140341, 439342322034617610147326745458983873882174074655219611049, 18229947483631515879319447526525772520867028419923779045, -1002092370329423842498139615123573787211370427794563854, -39864315847374815916148573667571265861468714565625082, 1066826805435928920958874590626857373171243089461892, 40432219754554228610282351842117127347826689958662, -536269013569090993659338207261956970600732281039, -19238025224209446450721022251602369568154841145, 102188166773690132732920074060433840779897233, 3466954949200265636321945454266853537085769], [-6895467770324649882030977123302861228871024795261455216218456, 5489267928738608339370906494038141153498739925033044855468046, -129661614203956104110697216729287138363410738724250449997220, -131512581575628084723424196829822402960957674650925798112357, -1014205264105897585078504827890068697956379754674080206135, 758038908226695726483875155001242682405276911727367110551, 12680803850015754936902118776155643106627789263759114951, -1696416734860230778179803656830343524797001074084665410, -33667813746420602295752002304867091465629140193435998, 1779748155502205429615863176582449511162659037308252, 37686611975209029666510231900499399400306859482986, -880471802348282111613266428977990507576168792745, -19194944451489345666954357149996762115646589059, 165034741367536343171446419446983579688469071, 3648522253942494160644460269203475207918563], [-12757491364001838754112363176683061937805968246898518016333912, 3518147769862128263457029742311771718117464781880679156976590, 330093351899151158427269456134032803606790386387211977613340, -82665508404813634578929471330414003498249425419814540340805, -5175345913255932240524753839583763069923286549656354753207, 477609757931215488954368538298106745252104266650774509815, 27322244242496877334721590358060529538479666524661537991, -1074603037207460690175767441193308415702274769738496514, -58664390997511416961601920271141224290456188496063582, 1147988778960525027117554158221279311989405826434268, 59384046635407890597314999453165976075823859642410, -586797662754870718124715136233509257302386913033, -28251511512716677518005471877657404761749102339, 114400236095221209374880382819854975039548847, 5083166803857521142500836788298264748556643], [4153410451276799225104168135770941560121186182833652796653320, 9597493527515861426010753404162621180612625237252306054428118, -582617304324650579700798022504921935329810812786569638486788, -358211330938798152979177590664190506527603042205322971057569, -8786394376928383340480535651135315305423987831475938770947, 2304712508754556166692066450308148237669371180879401811451, 80495023030454822091101705279686200774481556989128394067, -5441477328165975415390743886904230441200876687565814298, -201321926966543997636001464652011001469652407431740982, 5953949514426166989745901651426924907237869890570796, 218669063400000117821822118564172958825284656159586, -3065924728229384915758005526150725789371189423317, -108619078563617087929411911005540297829259192447, 596402454288237708915218664981352127115409043, 20163446355769010366530108451717437881788927], [20206087779062552390978556484466995317040803231458596277943768, -11322249438838297846253590538777295666312742676172686159630766, -1081538636734544400447819590153589603924689176776542829126556, 401830248744938236992751100039518780816748501825020106285013, 25937758983432585105233196711030796665268803056395680886791, -2561957511524098134169041612909965575269641861432388982631, -145613973082270374160429977639113398099997023792775769751, 6078470674543497166829674070079328779797798012424437154, 316442814926856682227665532351991547839298674054451198, -6720470775258312012579095123253197415079677849936028, -321293140048215521605686435474240875936922106106954, 3503271353703919052014461753706495792679027851481, 153257478502190012163536669923957941655288043411, -689408089205545232051157854337069529199973535, -27679808038616091444545503875600116409003763], [-435444515508234007904132478786565049590454174900822331196296, 829315800795099516720743166568513158033331949666911140525258, -30932952281047778993647964715993317523186602628829928724092, -24854096209256867088782216354630977981629097585766581956879, -548889666470800843211569906260411243941649245401862849901, 150159941255976141514492411383452810462236095118219770389, 4913894432072223995199955986745939591735872063731682013, -344007181409942733669497767455434509201486220811526086, -12235378371655897746121904103495062409415279349984426, 369493851816084629570391355375410875105729448611476, 13259604427163126298552423569723899539018143305598, -187954393971542622021335995904804846667747188123, -6574101283187982402947325841198493366010714545, 36265466424885048675054807771624953711358205, 1218222943732218489097452694614575351663473], [29651616631702704157898641815733236580982478346241555599688184, -19822855154400999138255777291913549953234736844712705232037334, -966292524297748307412409889161380489189592871867737335993932, 544526567214436822826896683802837163351453942289182769634737, 28819457120806453028432714360334192921425040367858071620043, -3285212361438012390341383954542304478738494838231222705083, -170339174794745258103754072968288010822886477265129883163, 7570293540295495932509451814766020517598063984305462394, 376696007589900578002495626878774667159243304085195974, -8202640297019879150789144630944804035344211978869612, -385265438160641851804317924277142327912551781022082, 4216934681270170983322713692938559835263105527525, 184272550749613731733916389450835602093048831015, -822308698205564147102505378872977450231008275, -33293978906070450193311391074820302875909831]];
    Rf_basisdens := [1, 1, 1, 1, 111603398439321864521484664212157576838892065057261223936, 37201132813107288173828221404052525612964021685753741312, 55801699219660932260742332106078788419446032528630611968, 37201132813107288173828221404052525612964021685753741312, 55801699219660932260742332106078788419446032528630611968, 55801699219660932260742332106078788419446032528630611968, 37201132813107288173828221404052525612964021685753741312, 111603398439321864521484664212157576838892065057261223936, 111603398439321864521484664212157576838892065057261223936, 4292438401512379404672487085082983724572771732971585536, 111603398439321864521484664212157576838892065057261223936];
    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_285_a();"
function MakeCharacter_285_a()
    N := 285;
    order := 1;
    char_gens := [191, 172, 211];
    v := [1, 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_285_a_Hecke(Kf)
    return MakeCharacter_285_a();
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]];
    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 := 10;
    raw_aps := [[-1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [84, 45, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9209, 81, 26, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-11685, -732, -4, 0, 3, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0], [-17853, -3681, -1, -10, 14, -2, -1, 0, 3, 0, -2, 0, 1, 0, -3], [-130321, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [112989, 8865, -459, -34, 46, -7, -11, -4, 4, -6, 8, 2, 9, -15, -12], [119176, -16463, 643, -61, 20, -7, -6, 11, 5, 6, 3, 23, 17, -15, -34], [562696, 2285, 1264, -43, -42, -1, -42, 13, -2, -10, -28, 15, 28, -39, -37], [211630, -105688, 5221, -337, 90, -78, -25, 22, -89, 59, -11, -51, -33, 40, 18], [-2594385, 188566, 4765, 123, -374, -21, -126, -144, 49, -52, -29, 46, 135, -91, -136], [3375380, 68856, 12311, 41, 1560, 18, 171, 96, -17, -89, 11, -61, -23, 28, -40], [-2737822, 408057, 576, -36, 213, 44, 25, -191, 306, 2, -155, -35, -12, 24, -180], [4348303, 177973, 20203, 992, -300, -67, -247, -398, 8, -6, 406, 8, 35, -307, 330], [11831340, -984487, 24505, -112, -8254, -196, 48, -6, -552, 441, 240, -595, -647, 276, 126], [10010051, 588850, 46614, 1185, 1049, 522, -78, 218, 378, -291, -577, -321, 0, 10, -533], [2624517, 273176, -12127, 2525, 13056, -65, -137, 709, 353, 272, -354, -263, 959, 215, 130], [6205418, -2698374, 52434, -985, -821, -282, -307, 948, 1627, 694, -267, 1032, 964, 582, 138], [-23705734, -2544212, 24218, 2639, 16077, 1008, 159, 1316, 1921, -342, -951, 168, 542, 1266, -510], [14151366, -3031333, 168633, 7776, -10530, -2616, -1066, -2278, -5674, 1487, 1642, -1541, -2001, -502, 374], [-3604996, -4532512, 85663, -10402, -11987, 788, -2527, -4181, 562, -1437, -1921, -1354, 2527, -1972, -2060], [-25303085, -824778, 20005, -3994, 16058, 2372, 2033, 3482, 2984, 2027, -223, -883, 1349, -2464, -1238], [-261117100, 425792, -228005, 9470, 32981, -1186, -2440, 2134, -2172, -931, 3500, 1725, -1839, -2578, -364], [-16612181, -3265724, 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-158427712, -8434883925, -7191854730, 3160357086], [25008351208824, 22043344514560, -389153287870, -66275182422, 95973145412, -323963354, -1225237206, 7290667770, 12381814826, -5478683720, 977089276, 6007359778, 1880575854, 3032743158, -1612787436], [-148606355327782, 7600650090300, 651473777462, 10858617667, -93073282513, -1232026320, 7244049649, -2361871886, -39163277999, 15694825922, 471335417, -7602916382, -10572658328, 1014723804, 12552080432], [83342898831941, 22571056539462, 1713266477760, 739681193, -19277948272, -15031041652, -3021719827, -4546040795, 6562713627, 2008536356, 4229490507, 1980636983, 2555465672, -9693450330, -965640010], [100950800021600, -23415641087661, 1034790171115, -9248675037, 56123216746, -15636341687, 10407883966, -1423991409, -7595296539, 2167024498, 955150183, -5236104629, -3939259591, 2844017869, -3160390778], [-605905762034907, 20650230246381, -255520844019, 558471604, -20710938616, 10478629516, -9694433753, 5857844548, 4473773085, -8225313936, -6863882960, 6551356616, 20698119395, -6864407242, -14766246647], [78905707733792, 954297956541, 1576023204250, -106954169694, 54365755247, 6082172544, -8937209144, -3686323946, 11037528414, 1575617620, 10329866472, -4416996802, -5576588020, 1538525428, 10752293876], [1381338201829856, 17499778868423, 269926364507, 17049800724, 29534792622, 384626600, -1501757342, 17537768578, 7297160638, -5197162467, -8672287082, -3777323487, 510648379, 1960352040, 2838923860], [91960447673701, -249865653538, 1140178756844, -63939027931, 174264271099, 9696434772, -2090158836, 10569257416, 3229851748, -5684363109, 8257161519, -3704818169, 5116592170, 463146944, 2227287633], [243987346773096, 28428963298718, -407912097651, -16531912048, 42375838439, -6734077379, 3741453641, 860767675, 493718929, 12616023287, 1925292451, 2823358550, -12840613595, -1264594007, -7921158979], [-247984253104415, -23374977593668, -1393007312859, -32718549256, 93528756973, 7587850389, -1232900498, 8455705469, 9029896266, -442281326, -1539020983, 18004654957, 10461980355, 6804043507, -1101901600], [316631591914164, -26641922544569, 2501745736261, 3315428099, 142745677909, 1849612502, -257157279, -6088091466, -3359207243, -8810476057, 10566493029, 11000868601, -2782615529, -4133770738, 6381055254], [246608365454082, 12573152047624, -2035728227715, 10446227835, 37137847310, -11151292406, -3853974217, 15891578868, -24556682851, 8440772885, -509306721, -1042706583, -12194668285, -3418476108, 7554536440], [629454803541155, -7496155492264, -1073353317522, 37361436024, 38420510812, -3515977464, 2087435161, 14952097392, 5424587117, 2906881885, -10636929202, 17037517147, 11345281248, 5076958278, -16602383057], [764981522028874, 47897081569744, 1757523738378, 86461347714, 141917620858, -2228019028, -18709067718, -23665967508, 3159734972, 5309475904, -13492889040, -10288681684, 4897898938, -4246082016, -19560927590], [171258012997687, 15783199331059, -704774268391, 5241470412, -158993054066, 6870295341, 13472968845, -10247557526, 18246306516, 6875945452, 10104980268, -4174050090, -19173455661, 16069396979, 22255461096], [240252640443215, -24978688041617, 1229336408302, -46814338857, 18207618099, -3603018502, -4918602358, 2798425618, 7787242455, 14032236510, -7344422692, 1536466772, 5787263336, 8117713706, -2979880], [-55736749291838, -32579919771948, 425113231125, 16586959121, -93003088392, 23742894, 3962002909, 1375447564, 25006714527, -3557732135, -17037214995, 232722877, 13292768763, -3552899684, -15898484672], [250672793948232, -16529892488180, -687207917550, -24875958292, 157469662270, -3947772378, 3479640652, -3827478256, 2088022626, -4595666654, 977388720, -284371146, -6144742106, 430881734, -14011052278], [800404414570244, 48274111292092, 450958722711, 53008409087, -133454442517, -7867518317, -7733711777, -8066273994, 172233695, 8615527238, 10052823298, -6538551784, 5970015089, -10342703741, -3934878266], [609092846904636, 24192659597803, 753498798626, 33648305507, -112680526452, -3040362001, 7362469980, 13768687565, 5180037856, -309677592, -12155968770, 11886886441, 4870036682, 6186186729, -14399722977], [-1217316420825703, -36243723376592, -1709163013507, -7467193202, -5116537988, 9267104058, 16808306671, 1888609938, 1456907228, 1078400173, 1615246993, -16066885825, -9958100803, 4931610322, 9705234230], [437954158846045, -30285388004846, 482361140934, -75520530671, -54770257979, -7286862554, -13278083134, -10933982698, 401390322, -15833256855, 26025673385, 11635937595, 1390163364, -12591333390, -982879757], [611933081484171, -10796957130742, -860530925395, 35376553020, -54160664343, 17095478421, -2005150930, 12601922293, 29387521312, -4786627928, 4020501439, 2926844059, 1091012299, 12038516355, 5653601198], [-211339811509172, -29130061572479, -995840442191, 40447207730, -30663251308, -7148574816, 595490302, -6957484980, 13338081742, -7626583247, -13010011016, -286395385, 3077210039, -4182690938, -3498956332], [-35882706793255, -34891709119647, -703697579251, -25691140956, -154875850264, -4709147988, -5907735077, -10315065148, 10830711373, -9858416640, 1451954520, 5637478112, 11521520739, 7745106294, -4245229759], [250419281017076, -35293742595990, 2390174173200, 22646967255, -94224089889, -1889963762, -11673472933, 146831216, 7866704399, 12425520976, 821707489, 9743043794, 3944003414, 3894242242, -13255480570], [904283279036296, -11353316950363, -1873878985226, -99912616138, 253859299453, 9349505220, -11373821741, -26757484171, 10761053746, -6062943390, 10524877683, -10584143323, 5322706248, -150691474, 2972994180], [16816350411996, 13160464624047, -1098047803413, -81615084301, 192057762754, -6844028999, -4340989752, -1112803119, -12283395559, 8829915226, 14945744681, -8998774055, -7996552011, 3433569773, 20284307198], [1421455532115116, 6556717237964, 917089446594, -32987039430, -74331313048, 14764399694, 2548760204, 8573231750, 11432136362, 1072478856, -21495816848, -2094010402, 6697664968, 10871944992, 10149278242], [-240056034830950, -14053058165399, 508269108439, 90443225156, 225540987320, -804285744, 6805461112, 1305222802, 7202108906, 20967992385, 3102546426, -11536864299, -19783578807, 5916296666, 6073382110], [1116419547777269, -25858503046880, -740333678749, -31941667935, 27354628378, 90074739, 8786815946, 8210045292, -16434745061, -9540226602, 8051726203, 13131214844, 8063698697, -10711758159, 11253255488], [883498184002889, 10458900218640, 1476150189185, 22580531428, -89225690859, 21195078459, -9602631702, -13847307675, -17162453088, -9544135266, -6636073903, 10382976361, 3689655795, 2027436117, 7386397494], [-104743916332555, 1550701221521, -1184683590794, -23149203365, 739321033, 7330369616, 4525355754, -6446500556, 33017370511, -18076224908, -1046844034, 18281887780, 16383010660, -16312395540, -7448092620], [303063763598926, -4456875001886, 690467442649, -12567809792, -275342995023, 8491330686, 13246346424, -1463119902, -25563313478, -10733911745, 17333889876, -24260331261, -14146201921, 1933156590, 26916788928], [89342131677310, 7985459031776, -1634219167631, 50568846878, 29027798389, 13239463745, -11736953429, -6681058465, -14159060819, 1485015061, -13690371005, -4948013056, -7353058331, 11850462425, 10538930971], [-256858606828608, 33993274465100, -549954891728, 59566475652, -17145487416, 5155979624, 11175290124, 3212262572, 14297060584, -7839405060, 23565446364, 14288340928, 10134646464, -7897466760, -6588158460], [-200808534747112, 75734146271690, -2372280772876, -2797936790, -37216828950, 23838772416, 14084822754, 16199068556, -19458400868, 3233084070, 5165821392, 9544235822, -13272547760, 13045350376, 27272340906], [1731504721919392, -41530051265536, 1067392414640, 101649584627, -33172588549, -14766324910, -702470077, 1486634678, 6018059553, 6022058674, -9158949801, -11201130050, 3021478076, 7099995820, -6050858178], [-456289254686347, -3126078437852, -730125223521, 131872669375, 216362944346, -11357748661, 10266082473, -19041723345, -30460958887, 4729658756, -3611080600, -7088945657, -15376012721, -4904443407, 3210933294], [3011707582954, 6571161051742, -1740580898016, 18736484415, -235799164613, -23243673858, -3357863415, -7665199148, 5046012781, 3476464242, 15888691671, -14481689968, -16000262886, 8227427814, -2986758260], [225674166572906, 31079184383382, 1869319253984, 144282439502, -120303228052, -2627073266, -3841429776, 32726057396, 15006316068, 4919723436, -8371301044, 12606074108, 19265064302, 1062541832, -14263157816], [389412516021540, -91278103235461, -1861597028371, 9538906052, 27356090600, -12905283308, 3909958820, 27222548152, -338529742, 15124793271, -758952100, 14666431609, 4240017685, 3718026556, -3846113336], [1219685249375945, 25638145667324, 1354093766087, -26843950982, -30487647113, 3061455707, 20269924062, 23802968775, -2105322820, -15689089850, -26064921379, 4209334103, 7828244461, 313466689, -20751116752], [17483957302898, -8300449078943, 839289008947, -47133149494, 86839255898, -5210356350, -4772338795, 3829920679, 11597026064, -19552552819, 15237756373, 2409614460, -1128104173, -5951654928, 8073596688], [1561116957960784, -655290730710, 1809587472623, -47644337661, 198007790030, 990123152, -2372778345, 7150528608, -8932571585, -3816333665, 27083983959, 6026839939, 1164939729, -1569331398, 32377264574], [2835492112080330, -49625265662239, -1447896930682, 39108408150, 108254813303, 19606136952, 16409388701, 2264822987, 460864154, -14020717842, 3423680923, 1246252135, -67355478, 838092132, 23228128386], [-1039301570546896, 10650381103257, 126990734253, 56381200501, -214834548331, -6429718732, -10160950479, -2418411882, 28609088559, 1422694713, 741582117, 5402579927, -7497494825, -17505771444, -7599238834], [-1549613199138448, -30280885320218, -2165774858107, -61667089746, 191610507823, 13493262756, -2314904026, -20840688892, 28643285372, 290134289, -3260296536, 23244115963, 5935068047, 4937424200, 380319736], [800775105742905, -60294904713995, -265673127993, 11810542670, -50112506616, -4249941107, -49753220785, -38805998292, 12241578232, -6185015032, -6764908036, -23585274588, 18553431033, -17940792581, -16000004898], [-1491056405742066, -17662536185110, -1419328136874, 53571135952, 264957056916, -2712297092, 7912102420, 10621405522, 13291404352, -4618635394, 11910326680, -843082264, -12222700536, 6143105358, 30573375118], [-103507231654084, -54130041033044, -129444854822, 79909985854, -269174041570, -28635390472, -11349547242, 1356209082, -17236573658, 5980032122, -16541638342, 10819680084, -2893359038, 1672820248, -12994941240], [1441192237242789, 41651784644228, -367846972021, -116149006728, 9803212383, -40047378259, 6018239004, 9406510451, -39825614042, 22998983772, 315384335, -10466316595, -14084826295, 618297979, 59514004], [1051762335382710, -15901265946315, -740340875857, -55815425279, 285513436433, 30259577080, 2180642236, 15026218069, 63771628259, -1255876415, -11679071736, 13545403140, 18583723985, 8344940378, 20810768054]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_285_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_285_10_a_h();".
// 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_285_10_a_h(:prec:=15)
    chi := MakeCharacter_285_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 10));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 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_285_10_a_h();".
// 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_285_10_a_h( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_285_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,10,sign)));
    Vf := Kernel([<2,R![-37823653537439285248, -21734306798463614976, 972340606580015104, 579270304260685824, -20023892408597504, -3993587063486464, 106230713537856, 11967144805120, -224529037776, -18445001392, 221032268, 15143800, -100427, -6223, 17, 1]>],Snew);
    return Vf;
end function;