
// Make newform 384.6.c.a in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_384_c();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_384_c_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_384_6_c_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_384_6_c_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 := [2870280625, 0, 28497132750, 0, 79355888475, 0, 74958811500, 0, 18093172325, 0, 1774000974, 0, 88368509, 0, 2442168, 0, 37827, 0, 306, 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, 43540949605520342404406877136411693907578250, 0, -98694134946189134883430019200976312334579525, 0, -78995769934523043208374840086012045763245150, 0, -17350894303583371221619898228006582318529605, 0, -1630867407655517482108380785495308722325151, 0, -79518401422094523042277315092170024939671, 0, -2171869530692738508045271019117295249037, 0, -33412654397875138212725105610853638778, 0, -269205113828240445632357121202158969, 0, -877630987274709872248495160216654], [6117376549920223125527749348657921593109602500, -4370055467179721344160893110895653590722004500, 30500202457632135302900452907641614175298835250, -584900833642064158270808968625883379992004850, 36991164201275960618669344485084172768695446000, 652058055074909713841617223298446766365917400, 9388640712122762203303327148174784081191980300, 197657689962522156719372747078666728957751230, 937673123597763607916436922060052046914106810, 20568070425325550321020180724426182152405366, 47161535267410856356398959264184401196572010, 1051261047790030824201269801028815786880486, 1311355918101363992885450924295924888889720, 29462821452820452763742525500886320705042, 20398817312776091609057282520673136046680, 460320081285501684920837806025648223848, 165535732833230955377646427604766476890, 3745229006620921328799155084873047054, 542242648158324217265528033074724990, 12288103926572895410995779943228064], [1341596904113089647056239598536072152337478125, -6772566373714727159301714422096992369624510750, 18992470069256714618876232098479434582437853875, -29386905863089041723011114776871102909645576975, 32121606488581784769012711483608513044355885500, -32732936646341436089893949714163816009457307350, 8514057634797048550657274968985432149625965400, -8150966009791279669416616617295932230126083595, 860693710126092250394203632903524417745099255, -807426980071764012166909002404529840615133869, 43477452574733832675926711119914604955754855, -40406514319058355671144866777899867986372349, 1210780796114610321866152245423741994499810, -1119431893418397567686082596759255107035803, 18841451611904064019797597367624640108140, -17364187325365027254825570980952581634382, 152879138261640033862819312717529149595, -140595451277343024735190672506828363911, 500626779656902543447258376068941895, -459738277028909019906119559793272526], [150158889722822227351826759038639176336918701875, -6772566373714727159301714422096992369624510750, 943480562469180288049917732969540788382163905125, -29386905863089041723011114776871102909645576975, 1227022363309880371621588656281782352444798057500, -32732936646341436089893949714163816009457307350, 314033221223308452313519870862794562524590219800, -8150966009791279669416616617295932230126083595, 31395674890293626350996881378647017860526111305, -807426980071764012166909002404529840615133869, 1577829992094647404448876885456817351537913305, -40406514319058355671144866777899867986372349, 43813150578552073869110747293970982354364310, -1119431893418397567686082596759255107035803, 680542993340150289908370598224831677034940, -17364187325365027254825570980952581634382, 5515034860562242482374702121885596468045, -140595451277343024735190672506828363911, 18044070660698168885105992794880404745, -459738277028909019906119559793272526], [-119330807572219291782744404742579423777059298125, 6772566373714727159301714422096992369624510750, -1734146772326009211715185644046020089558775417875, 29386905863089041723011114776871102909645576975, -3116851220361138421132626235104774797429463513500, 32732936646341436089893949714163816009457307350, -834356548054714940883239690890139490009928379800, 8150966009791279669416616617295932230126083595, -84646411677551811354579659554744569062559796215, 807426980071764012166909002404529840615133869, -4283783168123404807717472095133844191295264615, 40406514319058355671144866777899867986372349, -119438934976458710289947945499277988816284930, 1119431893418397567686082596759255107035803, -1860247038672090886211942203246286901252620, 17364187325365027254825570980952581634382, -15104118524338860134629311720148330107835, 140595451277343024735190672506828363911, -49486911998447377443301242341276979335, 459738277028909019906119559793272526], [0, -3176129755312840129066859484500, 0, 9161439551900211568500471993900, 0, 27347879925353439655251820064900, 0, 7618122809732203136442633426880, 0, 781627306482316294778866975016, 0, 39741797741560917372468840536, 0, 1110616425664310628186808492, 0, 17319054432688388812793948, 0, 140717748754952081668404, 0, 461227691633996115064], [324682403679033959591862551975992690340751228125, 20317699121144181477905143266290977108873532250, 1602404612350367501053237824057550544780993939875, 88160717589267125169033344330613308728936730925, 2085931966998108908068389252183502435750041411500, 98198809939024308269681849142491448028371922050, 534531228249288295890000712970218085725103193400, 24452898029373839008249849851887796690378250785, 53457170782969006421056120694959481781120489495, 2422280940215292036500727007213589521845401607, 2686582002542732832242891906174039317455922695, 121219542957175067013434600333699603959117047, 74593943583627811645448489726157452804067490, 3358295680255192703058247790277765321107409, 1158516438640957735039266017862368850989660, 52092561976095081764476712942857744903146, 9387360400717884849228189374848180454155, 421786353832029074205572017520485091733, 30710333501854084538220306234567919655, 1379214831086727059718358679379817578], [316429201811621432767945236085299180620024984375, -231999065512259402790233025171387779144116467000, 1574844198841391992964920151359464832010610615625, -478399917615331736580495145712121909700970808975, 1971727898083774248738425984330328000211922790500, -11080598851498638099775581907201693330898592600, 501798089495423871108750252726042882751527124600, 22780775653615317359950348345694532161443875555, 50075891074709100240798603965889191181514547925, 3117217597174926598731539586739378039689338781, 2514764612946085546085067395520614097557739525, 175856177107668054700624862515000693505473701, 69809694592109911923626538093138627798404950, 5171721095721457193343750572385320582115897, 1084256838002803281777836135978040299778500, 83025749154460969091741021324706700287468, 8786834804202697271936053754051307379825, 686866831958377725833598112317559878189, 28750364715451812186803511234964339925, 2278038552145837694211659191227700974], [0, -731189776330120113372100961942491460879570525, 0, -2719932393311839702194392158113783588895884880, 0, -4022569530728140015634171216848892386890886925, 0, -1053781776487993880508333989567705250047887753, 0, -106214770819440972221956369823521409285532219, 0, -5359587049502738028873899912165472091125927, 0, -149188799136137433448634317033730801444326, 0, -2321157422527040584832220386415447831875, 0, -18832730626206506540622198288695288626, 0, -61670906658713728331779538678697554], [-1352148503102952725863931421232425650150033125, -6772566373714727159301714422096992369624510750, -18992470069256714618876232098479434582437853875, -29386905863089041723011114776871102909645576975, -32121606488581784769012711483608513044355885500, -32732936646341436089893949714163816009457307350, -8514057634797048550657274968985432149625965400, -8150966009791279669416616617295932230126083595, -860693710126092250394203632903524417745099255, -807426980071764012166909002404529840615133869, -43477452574733832675926711119914604955754855, -40406514319058355671144866777899867986372349, -1210780796114610321866152245423741994499810, -1119431893418397567686082596759255107035803, -18841451611904064019797597367624640108140, -17364187325365027254825570980952581634382, -152879138261640033862819312717529149595, -140595451277343024735190672506828363911, -500626779656902543447258376068941895, -459738277028909019906119559793272526], [76640598697321299549429926789576415000957375, -407469304307576730357060284831221209425585125, 485486477331264894891213019727056604277799275, -1808717367317335446355254020995454094016034975, 495997842565408052002512716305820470451423850, -2084546989431128777693809812700006122359936125, 121120964176053592519631413616354604885867630, -523002418766536066325803921594659514282412570, 11915699307607621221462839285225340587597601, -51950721800433409047782229808621831422546174, 594359381162898669557181898490078791459521, -2603365389232905213869272721215295260305954, 16436400821581938501205566573602386205262, -72183157490921698433843623570876427437013, 254671750956916632871614013668361533678, -1120280191281962803640489636171490851047, 2060547460577599133223161561813762919, -9074179715415279108911641639931744381, 6734542918909049369302897908637179, -29680063568700606905866091121373096], [42102330036073854075990932411979423144466174375, 180110128007424477144489367666771991874734543875, 419085123380285477403323297947535906706892059875, 973859114970725762711395583019633391216545163850, 566205603558511498993814502271814768703109776250, 1152147713237681387195711712702259203278224671475, 145551994552926190070931020862658988674779063950, 290235524548897331761787889140831896040904869945, 14556596998780970990078412113768730124992068745, 28867109845417088634018633773693154767228468919, 731131446518570285852421499588240010192888745, 1447462911039464465898030158726793841409159499, 20285790705083937286326353496208384412479790, 40147033417853117241781914425470017115075628, 314845811952708184109636342935824066263710, 623210429888605837144743520702945493070757, 2549653424359578668838034297520427646655, 5048655236186143969518615011700557830736, 8336922456072879441190480475183613955, 16514858264395033338150375217081151326], [-131678759674138133677335545591054968840482811250, 44712098883739605102583291473992664528457269875, -645563548434644474022077578232378926793058225250, 628228914886455763440792979005588677646117894025, -872728806662832446010764811514915299240795807500, 1058303618385784622154604805450690215216040146775, -224947012806043655848362062475106725844340100100, 280805815447476335779893835635367179235839213130, -22542557082702808470014303743965523805956957710, 28402117023508044890911542065642215455932154666, -1134275779256346873605049535148962832499043710, 1435143723834760485817885078396858809459766686, -31521602965924525751008478696423738265399820, 39974211003119893514470731105866717344695667, -489910065157964314118482596077420752025180, 622141520179017142112385803492392357589273, -3972001738130185058668042149712109025490, 5048598516851899627341567117537862066879, -13000277568493633197991771373286024890, 16533909350525160948727523116856424164], [-74804055178977822887330947441589958138237761875, -203765618250134923576489356403009336682697904000, -376363935612480247574148004659246685323418837625, -731166918711726684874909609670271134504444539575, -393003652744971470923296580789117826492551213000, -821322528119654060687141170619302652678989602200, -96804128821251853057111043588820272106146321900, -205322360503715404153838071453179275798716701365, -9566426588370804388519391799007725951240621105, -20372145386921657700366602683503714311631701003, -478660083068615833950712481164862123374524705, -1020372374025216860751231820290361278032719363, -13268701276884036992955321621801103747670510, -28283705872592916640944843723711600352095511, -205988166539694027632994933393172166183440, -438884492717722643401607577868896030263284, -1669261957506191203389746491792911904745, -3554507958978621992073574100128642774107, -5462532584670415361810579320759474045, -11625219114154205296794731749476066962], [34070078706116601395362963165614836159469580625, -529302045137749192995077697256457359919862900750, 398467325355975289234064686048056696459294751375, -2674806766532498638703443807506688829646892341975, 789195647823474451250451430992234897369426066500, -3143840018944951636411649964544975670716748617350, 213650417991309118532091294513208475270813899600, -791239588670855506104769572259092421461231416595, 21741044035417390575361482007212403272539623755, -78675220515277840445234792473884719549523717789, 1101324116622795700446648356467691401140618555, -3944442402887896948078923914928263440378719069, 30713075293819528703335219208050655941434010, -109395524327190060836821393500849947008197243, 478304238155750463884339476916737958710340, -1698088134659507934183511012256078415859542, 3882690164186174347796065703897810381095, -13755838013782987061488637080027555934391, 12717995370463202631936016933789270595, -44996224380604785019459262908794183606], [-180065752760661606648820819100639875601954633125, -220872270838783528357985062200154532752883881000, -734090377083806610996711382965386122777244859875, -2402057071571372687166177350043017364171146761925, -675341063149453351913169639708459955945102739500, -3518353243405970237436808871358764492133556550800, -159122540242509937186491357948482529796897505000, -915798043290185033508928715693263378579060011935, -15383460091871343187453680422873654233514517495, -92052542462849703825579351299124889495288674537, -758918205130180689285243592325164697464232295, -4637962994242098912621693902086188242729150577, -20820964193736047580501724562727598863593090, -128977813570819254892337374066842224954534069, -320651132675073462347897067046266395891260, -2005360978491465633483671858051139296430436, -2582056746260855171161968872017009914155, -16262530579197180589017193427758426379153, -8407650101704533887137126513231075255, -53234841437436517424464065506807254798], [-86619842811946339722985864510066618214773311250, -170942881208498066117502957639429710946021689750, -198331706490397056313452487909655379287999542250, -1573107906290071597185365518734716954007021994675, -39351145885860721835487819984820956924081431500, -2352732102322844086025861662845995644427272965050, -101001141210686862874049659846539388458676700, -614477596781863873165938252159297014717059038535, 329518672285481290643819835749087661437073210, -61838651948608784209276907285473074709129735317, 24341186918560336609648873690280789899582410, -3117546863116958851380171606569331516627167157, 789959281074403573044197238758477631680020, -86728374281376892437529853730010152410862379, 13290156216785409670714894187770500399380, -1348803601725818371208973675208534621858226, 112740317687089134756967175143786675990, -10940175985898742324264981924755474293723, 379308387458930818635991553714361590, -35817215362375642738986282536705090618], [-22705955673633143856338904804241110662697179875, 68397710548777747886685122032534106133283112250, -249067595946300533044042009638904117699937597825, 650554285614781851524264061181985657047510408425, -364680275727447841052969656627897073663752086400, 1021469049554273101757886360817335657008574913050, -94793723043385129086982025949014977258389414980, 268608043325065080714968162264655944422393735005, -9523594192895026467738082951812808207483175313, 27090034704156757203754445617252441514070111987, -479798515116698158013707099628605660569257313, 1367022819402391514903631762853770087697411347, -13344568094816703238282707139761950788589246, 38048643200851393678439787230906774742172989, -207531525812259542431357905383193908187304, 591902033432476835240208205375891574054106, -1683441831095777994462866918276044579697, 4801756153558807106402650357885073551353, -5512171258299816817814863655859173317, 15722245351811026453246419399218200218], [-131678759674138133677335545591054968840482811250, 574966563390416991953358460530383062624939272875, -645563548434644474022077578232378926793058225250, 2925293520522838270226270502001946229813421565425, -872728806662832446010764811514915299240795807500, 3572288100780127245537258704923074851551312405175, -224947012806043655848362062475106725844340100100, 904755602979272931662156555094519132533097625810, -22542557082702808470014303743965523805956957710, 90144593186537986486143206891581506809302888122, -1134275779256346873605049535148962832499043710, 4523644379619139365612480571083422821127680062, -31521602965924525751008478696423738265399820, 125523519380753871902342300344303322635460539, -489910065157964314118482596077420752025180, 1949058626828732792593055898969052538376641, -3972001738130185058668042149712109025490, 15792292149603533981943239644122917018143, -13000277568493633197991771373286024890, 51665361485259560946026339227324118588]];
    Rf_basisdens := [1, 1217492191138047554733671849579249747602500, 11870548863595963658653300533397685039124375, 94964390908767709269226404267181480312995000, 94964390908767709269226404267181480312995000, 94964390908767709269226404267181480312995000, 50585658082792434405556854375, 94964390908767709269226404267181480312995000, 94964390908767709269226404267181480312995000, 1899287818175354185384528085343629606259900, 10551598989863078807691822696353497812555000, 243498438227609510946734369915849949520500, 47482195454383854634613202133590740156497500, 47482195454383854634613202133590740156497500, 31654796969589236423075468089060493437665000, 94964390908767709269226404267181480312995000, 94964390908767709269226404267181480312995000, 47482195454383854634613202133590740156497500, 18992878181753541853845280853436296062599000, 47482195454383854634613202133590740156497500];
    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_384_c();"
function MakeCharacter_384_c()
    N := 384;
    order := 2;
    char_gens := [127, 133, 257];
    v := [1, 2, 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_384_c_Hecke();"
function MakeCharacter_384_c_Hecke(Kf)
    N := 384;
    order := 2;
    char_gens := [127, 133, 257];
    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]];
    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 := 6;
    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, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-47, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1], [-1, -6, 0, -4, 0, 0, 5, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 1], [-15, 3, 0, 20, -2, 1, 1, 2, 0, 1, -1, -5, 1, -1, 1, 1, 1, 0, 1, 0], [-4, -7, 0, -44, 0, 2, 12, -1, 2, -12, -6, -1, 0, 0, 1, 1, 1, 1, -2, -1], [-3, 24, 3, -23, 0, 1, -20, 1, 2, 0, -1, 8, 0, 1, 3, 2, 2, -1, -1, 1], [-753, -9, 0, 6, 12, 0, -4, -2, 0, -4, -2, 4, -7, 2, -3, -4, -5, -1, -4, -1], [8, -14, -3, 91, 0, 4, 14, 2, 4, 46, 9, -6, 3, -1, 3, 3, 6, -2, -4, 3], [2, -77, 6, -21, 0, 2, 27, 4, -5, 14, 1, -19, 9, -2, 2, -3, 6, -4, -2, -1], [-1851, 2, -15, -130, 6, 4, -10, -3, 0, -6, 12, -26, -2, 4, 2, 4, -7, -1, -6, -1], [-45, 30, -6, -365, 0, 0, -36, 10, -8, -56, -34, -3, 9, 2, 2, 1, 10, -10, 0, 0], [-3185, -20, -42, -225, 8, 4, -28, 10, 0, -12, 21, 16, -12, 8, 0, -12, -14, -2, -12, -2], [-3595, -7, -12, 648, -28, -12, -4, -4, 0, 4, -70, 4, -17, -10, 3, -20, 1, -3, 4, -3], [12, -315, 54, -30, 0, -14, 20, -12, 4, -50, 3, 35, -15, 14, 2, -11, -26, 12, 14, -8], [-1788, 3, -75, 24, 20, 17, -17, -25, 0, 11, -29, 55, 13, 3, 23, -17, 18, 7, 11, 7], [2549, -22, 33, -969, 12, -15, 22, 15, 0, 8, 118, 28, -24, -2, 0, -24, 11, 3, 8, 3], [10, 341, 75, -314, 0, 17, 219, -9, 4, 28, -29, -57, 21, 13, 19, -13, 8, 9, -17, -35], [11202, 77, -108, 266, -29, 8, -10, 30, 0, 18, -36, -107, 49, 10, 56, 31, 32, 14, 18, 14], [238, 72, -51, 2469, 0, -24, 75, 8, -8, -64, 269, 14, -15, 12, -23, -1, -16, -8, 24, 12], [106, 94, -99, -2545, 40, 54, -13, -54, 0, 48, 243, 30, 69, -60, 31, 3, 42, -6, 48, -6], [-363, -104, -90, -2891, 0, -6, 460, -23, 34, 204, -364, 18, -45, -26, -29, 16, -29, 23, 6, 43], [15, 197, 174, -273, 0, -14, 551, -24, 46, -45, -30, -73, -3, 14, 22, -35, -38, 24, 14, 22], [-6318, 21, -246, -662, -18, -36, -110, -64, 0, 14, 25, -31, -47, -70, 40, -89, -14, -28, 14, -28], [8809, -73, -174, 3344, 156, -38, -68, -2, 0, -12, -438, 202, -3, 50, 31, -54, 7, 19, -12, 19], [378, -10, 150, 3376, 0, -12, 856, -26, 100, -464, 362, 24, -36, 68, 36, -2, -38, 26, 12, 18], [31, -472, 273, -317, 0, -5, -488, 75, -42, 54, 85, 40, 96, -69, 97, -26, 70, -75, 5, 107], [36156, 43, -372, -1754, 94, -80, -190, -174, 0, -26, 35, 99, 87, -2, 32, 9, -40, -14, -26, -14], [636, -130, -303, 6003, 0, 32, 1502, -24, -64, -510, 609, -20, -21, -55, -79, 29, 8, 24, -32, -65], [-53, 746, 276, -793, 0, -68, -372, 16, 16, 164, -39, -74, 18, 180, 28, -70, -52, -16, 68, -80], [-624, -189, -432, -4512, 0, 24, 2332, -36, 24, 464, -648, -228, -48, 136, -124, 36, -12, 36, -24, -172], [-31, -1515, 300, -1615, 0, 28, 23, 18, -70, 81, -40, 327, 45, 56, 116, 1, 46, -18, -28, -136], [-34664, 208, -552, 2715, -128, -56, -240, 1, 0, -32, -352, -616, 16, -32, 136, 40, -64, -32, -32, -32], [-68, 2673, 174, -999, 0, 42, 1205, 128, -53, -522, -19, -361, 207, 14, 90, -37, 170, -128, -42, 19], [-147729, -121, -234, -3158, 158, -33, -161, 72, 0, -65, 365, -217, -231, -19, 19, -159, -107, -42, -65, -42], [-353, -204, 546, -4769, 0, 72, 5664, 102, 32, 376, -434, -715, 285, -110, 166, -111, 174, -102, -72, 172], [117255, 98, -174, -457, -48, 140, -176, 394, 0, -56, 131, 158, 210, -28, -80, 150, -98, -42, -56, -42], [45598, -220, 834, 137, 416, -102, 192, -27, 0, -120, 36, 262, -16, 72, -306, 158, -144, -24, -120, -24], [-161013, 308, 177, 1646, -822, 82, 244, -87, 0, 88, -82, -600, 180, 70, 144, 234, 167, 79, 88, 79], [-17203, -14, -1155, -3597, 772, -111, -546, -383, 0, -64, -38, 230, 28, 2, 158, -170, -95, -31, -64, -31], [408, 699, -864, 5688, 0, 30, 4292, 105, -258, -2468, 630, 381, -12, -336, -145, 147, 135, -105, -30, 153], [153, -3195, -204, 2429, 0, 132, 2285, 98, 110, 257, 232, -225, 117, -64, 84, 113, 230, -98, -132, 140], [25, -2096, -408, 87, 0, 152, 3842, -208, 150, 2200, -235, -48, -156, 72, -88, 100, -56, 208, -152, -282], [214, -1939, -633, 3542, 0, -75, -1503, -365, 288, -304, -105, -457, -411, 305, -377, -29, -440, 365, 75, -307], [315394, 217, 924, 802, -349, -48, 358, -34, 0, 18, 192, -1119, -163, -182, -144, 179, -64, -82, 18, -82], [65470, -452, 1818, -6919, -592, -126, 968, 193, 0, -8, 1316, -894, -648, 352, -46, -54, 164, 172, -8, 172], [-1870, -2160, -1329, -10721, 0, -168, 9831, 56, 72, 3332, -1521, -206, -237, 54, -397, 125, -112, -56, 168, 242], [-288011, -36, 999, 7692, 1122, 68, 406, 711, 0, 186, -648, 1240, 232, -272, -330, 22, 143, -43, 186, -43], [18429, 146, -1767, 16319, 676, -287, -566, 153, 0, 160, -2218, 670, 168, -78, 434, -366, 201, 41, 160, 41], [536294, 211, 1536, 3498, 97, 464, 690, 574, 0, -106, 124, -1341, 127, 310, -152, 673, -4, 102, -106, 102], [-2300, -8156, 1608, -25516, 0, -172, 17464, -542, 500, -1804, -2892, 654, -492, 426, 150, -222, -714, 542, 172, -296], [-383958, -501, 1527, -9164, 688, -315, 607, 209, 0, -45, 1167, 959, -59, 231, -361, 91, 48, 93, -45, 93], [3442, 607, 1332, 24858, 0, -248, 23932, -208, -232, -2864, 2756, -2126, 270, 60, -192, -726, -456, 208, 248, -252], [-1154, 2717, -1521, -3354, 0, 45, -11251, 635, -296, 560, -337, -745, 453, -215, -129, 227, 680, -635, -45, 509], [78791, -293, 1908, -20298, -484, -396, 844, -246, 0, 348, 2478, 1688, -115, -502, -491, -304, 271, -77, 348, -77], [-2842, 5464, -1527, -22735, 0, 32, 17621, 132, -528, -4644, -2575, 338, -3, -470, -343, 167, 164, -132, -32, 42], [56, -13787, -1482, 3380, 0, 178, -12222, 156, -358, -1954, 299, 243, 69, -194, -206, 265, 334, -156, -178, -186], [1990, -1143, -1452, 27638, 0, -22, 17372, 103, 698, 4324, 2670, 897, -474, 580, -87, 555, 81, -103, 22, 243], [-218, 443, -1614, 6166, 0, -282, 10470, 636, -526, 8010, 763, -547, 291, -838, -378, 63, 354, -636, 282, 1230], [-564506, 243, 2379, 33950, -1172, -525, 1489, 437, 0, 77, -3059, -2321, -119, 621, 173, 691, 426, 349, 77, 349], [34253, -772, 1524, 20920, 2212, 267, 227, -987, 0, -232, -2621, 1134, -365, -38, -703, -107, -367, -135, -232, -135], [3716, 3621, 1824, 27068, 0, 100, 17944, 630, -892, 7320, 4484, 3714, 492, -720, 1010, 238, 730, -630, -100, 358], [-36, -3355, -1782, 26, 0, 510, -10746, -376, 164, 4594, -917, -2853, 129, -230, -546, 5, 134, 376, -510, -492], [-254223, 8, -1434, 17222, 1132, 427, -775, -669, 0, 288, -2307, 800, -551, -1098, 1, -1091, -117, -405, 288, -405], [919844, 529, 852, -2732, -919, -824, -130, -394, 0, 106, 272, 841, 549, -990, -776, 315, -336, -442, 106, -442], [-104084, 406, -354, -16877, -2152, 70, 0, 1339, 0, -560, 2912, -6074, -938, 908, 740, 574, -386, 174, -560, 174], [-2574, -22534, 564, -17350, 0, 64, 32276, 908, 432, -7704, -1556, -1090, 798, 472, 628, 174, 972, -908, -64, 804], [-855190, 3707, 807, -33712, 400, 1161, 963, -935, 0, 1047, 3507, -2793, 2669, -1373, 235, 2099, 884, -163, 1047, -163], [-1849, -10494, -237, -20909, 0, 481, -22430, -787, 550, 928, -2937, 54, -486, -231, -61, 180, -306, 787, -481, -487], [-170700, -2060, -48, 5267, -2384, 992, -336, 1001, 0, -592, 88, 2120, -1124, 968, -220, -872, -404, 188, -592, 188], [-2344, 14453, 210, -12421, 0, 70, -29127, -60, 1889, -5926, -2119, -1173, -345, 2122, 310, 355, 10, 60, -70, -363], [-1316371, 130, -783, -16628, -2190, -506, -212, 2221, 0, 216, 2814, -642, -526, -482, 276, -628, 83, -133, 216, -133], [185, -448, 750, -11943, 0, 60, 40440, -1064, -796, 7120, -1226, 2281, -717, 414, -276, -287, -1004, 1064, -60, -2334], [239647, 601, 678, 31902, -796, -994, 292, 1428, 0, 364, -3514, 3998, 2051, -210, -535, 926, 441, 77, 364, 77], [2928, 35832, -1020, 25996, 0, 128, 31617, 160, -768, -1162, 3140, 1072, 108, 475, -124, 180, 288, -160, -128, -1211], [-29384, 16, -1206, -19574, -2232, -1194, 416, 2098, 0, 656, 3088, -1300, -1152, -204, 1156, -1344, 882, 226, 656, 226], [1019279, -1252, -2664, -12001, -1983, -400, -1080, 880, 0, -904, 1564, -2564, -1396, 1736, 992, -508, -488, 416, -904, 416], [-205752, 334, -2430, 25475, -1336, -438, -1272, -941, 0, -944, -3448, -3498, 310, 1380, 612, 1102, -726, 218, -944, 218], [-1281727, -152, -3249, 45184, -750, 3108, -610, 1463, 0, -238, -4784, -940, 228, 1752, 1510, 90, 519, 757, -238, 757], [557502, 1754, 3165, -57877, 1792, 1774, 1535, -628, 0, -120, 6219, -964, 2929, 1080, -455, 3289, 360, 480, -120, 480], [-9649, -26729, 2976, -102253, 0, 536, 61659, 882, -1254, -1171, -10180, -4027, 2295, -2452, 880, -877, 1418, -882, -536, 1544], [1257429, 1564, -4692, -16399, 2667, -480, -1400, -4740, 0, 696, -624, -2236, -148, -1168, 1432, -1036, 460, -236, 696, -236], [8446, -46614, -3066, 86620, 0, -840, 27975, -336, -568, 20198, 9142, 2606, -1368, 127, -1286, 192, -1176, 336, 840, -191], [377812, 4228, -4410, -64726, -976, 1358, -272, -1952, 0, 1080, 5556, -2386, 3920, 224, 2134, 2318, 1732, 652, 1080, 652], [-10702, 4907, -4548, -70302, 0, -238, 37196, 1339, 322, 6036, -8594, -3439, 570, 204, -795, 531, 1101, -1339, 238, 1695], [-6567, 23402, 4761, -65199, 0, -1069, -51652, -825, 1598, -5682, -7491, -1754, -726, 3019, 177, -1168, -1894, 825, 1069, -1177], [372533, 2930, -5328, -27643, 805, 3240, -2652, -1660, 0, -356, 2384, -8110, 266, -1044, 1080, 806, -1056, -700, -356, -700], [-944024, 1206, -7182, -67746, 4140, -956, -2820, -1666, 0, 780, 4248, 8462, 3438, -728, 736, -258, 806, 26, 780, 26], [14772, -49382, 4182, 122924, 0, 450, 83874, 734, 584, 4839, 14230, -5586, 2010, 2746, 1238, -826, 1184, -734, -450, -1878], [962425, 1000, -5604, 27939, -492, 792, -600, 7316, 0, 1448, -1847, 3808, 1336, -48, 2256, -1304, 2148, 700, 1448, 700], [-4147, -48936, 5436, -35853, 0, 484, 67100, 1204, 2406, 18620, -2471, 3456, 732, 2036, 3012, 956, 1688, -1204, -484, 1090], [-1184322, 661, -7791, 147908, 616, 2259, -4095, 3455, 0, -899, -16855, 1481, 1819, 553, 673, 541, -1072, -173, -899, -173], [-6353, 6816, -6678, -57241, 0, -356, 20992, -932, -3212, 10640, -7398, -605, -819, -3078, -2968, -469, -1288, 932, 356, -710], [9542, -19528, 7497, 66513, 0, -88, 6266, 2296, -1928, 21898, 11113, 1334, 3021, 417, 2693, -813, 2208, -2296, 88, 39], [207, 31710, 6048, -22510, 0, 64, -76121, -2656, 2271, 4656, -3113, 2426, -1992, -224, 752, -600, -2592, 2656, -64, -225], [400071, -5129, 9864, 59778, -3204, -1320, 2116, 4926, 0, -2932, -3218, 448, -2119, 3818, -3143, 1832, -2489, 443, -2932, 443], [-1517, -1822, 3612, -17934, 0, 1412, 112325, -604, 3627, -15364, -2569, 78, -156, 1268, 2116, 964, 808, 604, -1412, 343], [-3797, -8348, -7710, -27773, 0, 94, -14752, -1293, -2058, -24300, -4196, 5626, -2187, -886, -2311, 988, -1199, 1293, -94, -2559], [-355201, 3364, -5580, 4747, -3459, -2848, -2424, 2228, 0, 440, -1028, -372, 3124, -1280, 712, 1372, 20, -420, 440, -420], [5958, 33284, 8127, 22683, 0, -672, 27670, -780, -336, -30946, 3399, -4782, 999, 3707, 591, -2451, -1452, 780, 672, -4151], [-370, -105553, 258, -1818, 0, -522, -80270, -956, 1634, -2406, -2705, -12839, 423, 1210, -1674, -1901, -1478, 956, 522, -10], [873293, 5896, 11814, 9062, 5164, 519, 6333, 1243, 0, 2352, 1401, -9588, 2005, -3322, -1015, 3589, 1867, -485, 2352, -485], [-395814, -6085, -420, 29584, -4006, -1584, 402, -782, 0, -170, -2803, 5027, -5689, 1422, 768, -5431, 456, 626, -170, 626], [-1020, 72232, -8862, 27866, 0, 768, -31244, -2632, 5216, -3676, -1646, 3084, -4638, 6330, -1726, 2774, -1864, 2632, -768, -4514], [1065671, -2735, 492, 298890, 5038, -3283, 889, -6142, 0, 913, -35113, 145, -5089, -1457, 645, -4837, 641, -272, 913, -272], [-1367899, 194, -11535, -37665, 2460, 4409, -7146, 3339, 0, -3272, 4334, -11688, -1912, 1622, 1340, 476, -4097, -825, -3272, -825], [14603, 122692, -1455, 132475, 0, 75, -123850, -1189, 906, 7414, 13245, -1772, -1020, 1275, -919, -94, -1114, 1189, -75, -1633], [-2411001, -987, -11886, -43702, -15084, -1766, -6876, -4356, 0, -1588, 2662, 3194, 111, 6, 513, -1494, -2379, -791, -1588, -791], [-4812, -31878, 8451, -60151, 0, -272, -57343, 3824, -2736, -200, -2045, -2212, 4881, -2908, 3115, -1329, 3552, -3824, 272, 4268], [558, -11781, -2202, 19516, 0, 850, -159050, 2776, -1000, 3454, 3575, -667, 2535, -106, 1202, 1091, 3626, -2776, -850, 1032], [-38550, -18748, -2646, -350442, 0, -354, 137486, -5874, 3384, -28149, -41862, 18852, -8436, 2734, -1486, 2208, -6228, 5874, 354, -4870], [-14364, -88984, -8190, -109286, 0, 3304, -65191, 2908, -1336, -15822, -10870, 5984, 2322, -1823, 1934, 3890, 6212, -2908, -3304, 91], [1417, -138864, -3252, 9832, 0, -2268, 151351, -1224, -3433, -1844, 439, -1288, -1470, 924, -3596, -2022, -3492, 1224, 2268, -3313], [3210161, -1507, 6222, -365004, 1654, 3375, 2483, 6012, 0, -581, 42281, 9885, 4135, 3033, -1901, 3427, 645, 1226, -581, 1226], [8300, 23445, -5880, 95324, 0, 138, -116764, -1461, 1354, 9204, 9674, 14731, -4296, 1224, -419, 2973, -1323, 1461, -138, -1469], [430819, 3996, 9852, 30593, 1160, -1808, 6824, 732, 0, 1592, -2405, -4460, 4268, 1712, 552, 5156, 3244, 1652, 1592, 1652], [-459593, -6531, -9510, -194102, 3012, 658, -5156, -3760, 0, -740, 20102, 1502, -9545, -1778, 1197, -9506, -1999, -1259, -740, -1259], [446710, -7734, 6105, 106759, 4928, -7690, 835, -116, 0, -88, -12833, 19988, -2939, -904, -3851, -4787, -584, -496, -88, -496], [22541, 11880, 5670, 178525, 0, -2338, -25868, -4009, 1286, -26764, 17832, -3136, -3309, 262, -2251, -3038, -6347, 4009, 2338, -647], [-3401274, 315, 6756, -127098, 11385, -1344, -1278, -11734, 0, -2554, 10144, -4301, 423, -1490, -4736, 3561, -4576, -2022, -2554, -2022], [-3914, 5943, -12246, 14833, 0, -1378, 192347, -360, 1021, -13422, -2531, -6879, -2103, -3942, -4418, 365, -1738, 360, 1378, 5981], [28687, 3236, -7950, 251439, 0, 2682, -72344, -19, -1742, -3140, 24488, -22960, 4161, -3702, -2761, -1498, 2663, 19, -2682, -741], [681679, -3717, -5076, -198434, 23228, -6756, 460, 8578, 0, 1884, 19278, 19224, 1549, 2138, 2101, -3680, 3895, 2011, 1884, 2011], [2138608, -7046, 12318, 207940, -9688, -2342, -178, -7582, 0, 726, -22218, 21866, -5682, -9506, -9010, -7542, -3664, -4390, 726, -4390], [-65451, -21193, -16518, -526855, 0, -1930, 212723, 2576, -2642, 37823, -62498, -21467, 2199, 2186, -6326, -1553, 646, -2576, 1930, -322], [1312102, -13300, -30, -87355, -7088, -3430, 1864, 10021, 0, 1208, 12004, 34082, -4344, 3696, 98, -9702, 3660, 2452, 1208, 2452], [635, 86874, -11280, 80143, 0, -2944, 161906, 908, 1808, 26192, 7233, 11342, -4782, 1976, -2608, 2746, -2036, -908, 2944, 3684], [6051981, 7907, 11724, -525342, -5662, 2643, 6879, -10322, 0, 6263, 57073, 10419, 6629, -9303, -2709, 1313, 4743, -1520, 6263, -1520], [-31598, 80959, -17955, -234954, 0, 4775, -188571, 1001, 2580, 30350, -30331, -4155, 735, -9893, -699, 5041, 5776, -1001, -4775, 8699], [4450720, 8466, 7350, -162637, -10712, 6110, 9504, 9595, 0, 1280, 23848, -22090, 6762, 7812, 5832, 10446, 5826, 4546, 1280, 4546], [-33840, 47406, -4713, -289671, 0, -412, -160790, 2082, -1756, 41474, -34269, -24590, 4593, 2553, -2963, -2923, 1670, -2082, 412, -1815], [-761447, -366, -627, 311555, -23644, 5933, 4898, -3423, 0, 48, -30522, -25030, -7096, 6242, 7230, -1354, 3193, 3145, 48, 3145], [22937, -34220, -5154, 202297, 0, -2718, -156524, -4483, -1110, -10948, 18084, -7430, -4113, -3602, -6177, -3088, -7201, 4483, 2718, 727], [-1832, -75479, -9630, 38939, 0, 2262, 122293, 652, 4425, -46454, 4725, 30599, -5253, 1546, 3206, 8167, 2914, -652, -2262, 1269], [30745, -11090, 6966, 262081, 0, -3642, -177556, -1317, 14, -70764, 27376, -19360, 735, -74, -3127, -5694, -4959, 1317, 3642, 2413], [-21868, -9794, -9843, -160321, 0, -1284, -217634, 198, -740, -39786, -20143, -3206, -1329, -1669, -3481, 243, -1086, -198, 1284, 2411], [9635, 112318, -17604, 130634, 0, -3004, -195687, -2484, -1749, -4612, 7019, -22078, -2352, 8324, -9788, -3136, -5488, 2484, 3004, -9553], [31537, -58944, -9666, 284129, 0, 4550, -134744, -1133, 398, -32796, 29832, 6000, -561, -4634, 569, 3978, 3417, 1133, -4550, -651], [-83322, 44596, -2418, -760010, 0, 1850, 199100, 754, -2220, -47425, -83338, 2524, 1524, -8086, 782, 1080, 2604, -754, -1850, 4770], [-3400746, 25337, 15942, 118818, 8350, 7628, 12682, 20172, 0, 4534, -5995, -28067, 22437, 474, 2384, 23427, 7038, 2504, 4534, 2504], [3035744, -1344, -19440, -180189, 9136, -3520, -7224, -8747, 0, 496, 8864, 30292, 9744, 3624, 2436, -156, 2556, 2060, 496, 2060], [4639760, -14011, 11367, -797522, -6104, 241, 4695, 12237, 0, -5725, 95887, -4687, -9553, 13183, 19, -847, -1996, 3729, -5725, 3729], [3446702, 10094, 21888, 44829, -17448, -6256, 7848, -7833, 0, 2488, -916, -20472, 1250, -9436, -5206, 5864, -986, -3474, 2488, -3474], [-2460, 27770, -13797, 11329, 0, -3920, -212142, -608, -7408, 55030, 3515, 32636, -7191, -6221, -4333, 2663, -4528, 608, 3920, 2125], [5898, -24705, -2958, 19901, 0, 1686, -195161, -304, -5611, 36890, 3721, 2505, 1569, -9422, -650, -187, 1382, 304, -1686, 1821], [6601631, -15552, -1599, -280986, -8526, -7570, 1984, 9825, 0, 3076, 36962, 16212, -19160, -2982, 2444, -20978, 3123, 47, 3076, 47], [-1602106, -8616, -23178, -153555, 3664, -11922, -6176, -8203, 0, -2552, 10868, -14238, -12908, 8832, 10238, -10022, 588, 3140, -2552, 3140], [-5608, 2660, 13998, -183398, 0, 12004, -149444, -2254, 1636, -44016, -20646, -26238, 10530, -11664, 7396, -780, 9750, 2254, -12004, -958], [-2445, 52186, 5820, -95996, 0, 2148, 325479, -9524, 4669, -90516, -17965, -17850, -3528, 5188, -3084, -3848, -7376, 9524, -2148, -12191], [7714120, -1261, -3111, 877562, 1648, 4639, -7727, 17899, 0, -3947, -92815, 8719, 3609, -1287, -5779, 3231, -6564, -2617, -3947, -2617], [-11682, 94211, 5706, -90677, 0, -8418, -237695, -8, -3593, -63710, -7939, 5493, -3759, 58, -4018, -4667, -8426, 8, 8418, 4759], [4550577, 21942, 5649, 388334, 17366, 1072, 8570, -24083, 0, 5198, -48032, -60110, 362, -7072, 7230, 7640, 4261, -937, 5198, -937], [-113688, -58738, 4614, -1009036, 0, -62, 221668, 5822, -1164, 76079, -108578, -9934, 6534, -2422, 2942, -774, 5760, -5822, 62, 7142], [18702, -21910, 21630, 105044, 0, 1832, 64141, -6712, 13240, -32678, 4414, -37130, 864, 3385, 1754, -5744, -4880, 6712, -1832, 1311], [3385904, -21570, 36777, -58941, 11768, -8092, 15673, 26466, 0, -4856, 19661, 8792, -13025, 14164, -5229, -2177, -202, 4654, -4856, 4654], [-8826, -112017, 25764, -201978, 0, 1854, -312164, -1443, -3762, 26668, -14526, 13791, 2814, 9092, 7123, -2403, 411, 1443, -1854, -16151], [-5086288, 8613, -10398, 7204, -11174, 6532, -9590, 5416, 0, -5082, 2883, -33695, 1201, -1358, -480, 7735, -8302, -3220, -5082, -3220], [51414, -37740, -34065, 536859, 0, 1048, -214314, 4560, -8600, -110090, 52383, -46930, 8151, 791, -11181, -2543, 5608, -4560, -1048, -5879], [125798, 108468, 11790, 1013502, 0, 9946, 205160, -2654, 156, -3817, 113926, -7956, 6564, -7990, 6846, 728, 7292, 2654, -9946, -4454], [-5932118, 10887, -18660, 208778, -20147, -16992, -7686, 4698, 0, 1966, -29740, 28511, 23043, -250, 464, 10173, 2824, 858, 1966, 858], [44706, -102222, 34488, 274694, 0, -2112, -299849, -7588, 2480, 64234, 36304, 30558, -6774, 5961, 6312, -2926, -9700, 7588, 2112, -8957], [-2183772, 887, -50151, 950522, 13504, -501, -25195, -16261, 0, 2473, -122875, 39851, 4789, -12203, 2153, -13469, -2392, -4865, 2473, -4865], [55368, 98489, 20625, 458956, 0, -3053, -305669, 4417, -5920, 51026, 64961, 47651, -759, -2753, 8745, 2123, 1364, -4417, 3053, 4303], [-3770639, -10199, 45792, 609256, -8572, -5184, 30444, -8280, 0, 6676, -61198, 3416, -10841, 6646, 1759, -5312, 13337, 6661, 6676, 6661]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_384_c_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_384_6_c_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_384_6_c_a(:prec:=20)
    chi := MakeCharacter_384_c();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 6));
    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_384_6_c_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_384_6_c_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_384_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,6,sign)));
    Vf := Kernel([<11,R![1135278813973092926473216, 30019229162747732359680, -143524334927313786112, -3498937761828271872, -1325356220305088, 76348018199520, 129628916560, -368139504, -742804, 474, 1]>,<13,R![307278719962112441561082880, 3354990236182319367782400, 888635632386592666880, -87956968548008116224, -207239138890801280, 377750230069248, 1179051645856, -389121024, -1985572, 0, 1]>],Snew);
    return Vf;
end function;