
// Make newform 4.17.b.b in Magma, downloaded from the LMFDB on 28 December 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_4_b();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_4_b_Hecke();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_4_17_b_b();".
// 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_4_17_b_b();".
// 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 := [64957563630, 402444531, 17329473, 242526, 5152, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [424169950, 19281661, 278884, 5194, 6, 1], [262341750258, -346364613, -20309508, 275366, 1930, -361], [-1037716791858, -47656971675, -113266044, -12663398, -161482, -1655], [313280271198, 6308187453, 121467492, -1050422, 34694, -191], [-104406897222, -332488665, -47309076, -52930, -9038, -13]];
    Rf_basisdens := [1, 4194304, 37748736, 37748736, 9437184, 2359296];
    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_4_b();"
function MakeCharacter_4_b()
    N := 4;
    order := 2;
    char_gens := [3];
    v := [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_4_b_Hecke();"
function MakeCharacter_4_b_Hecke( : Kf := false)
    N := 4;
    order := 2;
    char_gens := [3];
    char_values := [[-1, 0, 0, 0, 0, 0]];
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    values := ConvertToHeckeField(char_values : pass_field := ISA(Type(Kf), Fld), 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]];
    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 := 17;
    raw_aps := [[-27, -1, 0, 0, 0, 0], [1, -3, 1, 0, 0, 0], [-84595, 405, 0, -5, 0, -5], [-930, 2774, 110, 32, 48, -48], [118279, -355957, 615, 192, -736, -1312], [423970625, 314977, 0, -6929, 1664, -5265], [258536360, 13972442, 0, 50502, -122048, -71546], [17440989, -52522935, 155133, 74304, -51360, -274272], [-4226710, 12882130, 546906, -211488, -220976, 413488], [-193037842387, -97353099, 0, -3891941, 2787840, -1104101], [-530953896, 1595365240, 61695448, 3115264, 8734080, -611712], [1429769192945, 1389745457, 0, -11217121, -3251072, -14468193], [303737018702, 8825429300, 0, -60927732, -26285696, -87213428], [-1787936097, 5335200995, -1310087713, 42358400, 56109504, -70965696], [-14462248124, 43541688980, 2811268836, -15857856, 123228896, 170802464], [21809258860025, -93719455703, 0, -489308761, 901036928, 411728167], [106964991803, -321783877937, -2049477957, -15669504, -920241536, -873233024], [-71726648131903, 433066704865, 0, -652168337, -2569196416, -3221364753], [55541042769, -166593687827, 27991909489, -334531520, -639622560, 363972000], [-277283981490, 836230063302, -71805071202, -3486811488, -2595504144, 7864930320], [-190824319116040, -320118172918, 0, 3635570966, 173222464, 3808793430], [-1057454359524, 3175576005260, -80628767428, 6323241536, 15859409760, -3110314848], [1622534505325, -4870668840007, 63602050413, -12774497280, -28614318592, 9709173248], [3404794399636808, -989023478854, 0, 5503737702, 3670410304, 9174148006], [697157780806640, -236073751918, 0, 25742619662, -12493773248, 13248846414], [-6293080174768903, -6696553852375, 0, 32350407591, 27541694848, 59892102439], [-12924550749018, 38907000342910, 659823943990, -27427364576, 78493366704, 160775460432], [-4281421657809, 12878598930387, -1569708687921, -15512858304, 3308240352, 49846815264], [-10272055132372387, -23285522322619, 0, -233216223925, 284973219328, 51756995403], [12347171484788210, 50291784302352, 0, -225101969936, -216611653632, -441713623568], [-50050167171552, 150721038936672, -2283267610272, -228689553792, 113158314432, 799226975808], [1928129623553, -5839463663843, 11389035531489, 173386622400, 291698451616, -228461415584], [56232850343096510, 37610801444292, 0, 1959854130556, -1326749905536, 633104225020], [-218469504353145, 657036906020011, -816345175481, 221694741376, 2071782443328, 1406698219200], [-116710891715480827, 281951813654301, 0, -1916980815629, -855921402624, -2772902218253], [-130300579814454, 391845064649138, -11949295355206, 45257360864, 1033839927504, 898067844912], [-237438269900206855, -322581231328343, 0, 4425952643623, -242709005440, 4183243638183], [-484395118701351, 1457171004919989, 7319082608025, 101620371840, 4188889559616, 3884028444096], [-1523820403690, 4278402922606, -11786437127322, 270940173984, 248822059504, -563998462448], [326353681005760745, -1561370645231943, 0, -2954928047081, 12167025790848, 9212097743767], [359640144971733, -1077694621854399, 68230719707925, -4728309737856, -8230806414912, 5954122798656], [-283054074884867203, -350149038550875, 0, -1049714944533, 2940378034176, 1890663089643], [945440831000656, -2849921579927728, 84806666061840, 8439304871808, 3279522817856, -22038391797568], [-151204114065739840, -231191369316158, 0, -610282775330, 1896109960256, 1285827184926], [254807076567732005, 4195436265328637, 0, -11188038545901, -22224359075072, -33412397620973], [66509658120942, -204189083977434, -324300240198402, 1860896398368, -938316817872, -6521006012976], [-1675222180796403, 5038754705561497, 316543093053517, 4388145483904, 21864454140096, 8700017688384], [4558226337106536, -13689433345533112, 404687287599080, -25465210856704, -65684755926912, 10710876643200], [-706043907633143, 2096069516435429, -100216596725751, 35218863366144, 48375520268288, -57281069830144], [5878103920382637173, 5424136381303981, 0, 108480174297187, -96020476347136, 12459697950051], [-2338456366551553720, -5480844118134598, 0, 52996915149414, 8027662101568, 61024577250982], [2467608772225940, -7417843487938844, 747349463456244, 1041058213056, -12935054834912, -16058229474080], [-3714248794577478808, 15837161215399450, 0, -77433785129210, -64628544729280, -142062329858490], [-17401374443161077, 52321639840758879, 34092598062987, 34580313729792, 186677138735232, 82936197545856], [-5365071181576725790, -7744658292849888, 0, 6479517687520, 48782549730816, 55262067418336], [-10210318947759650, 30801406231770902, 114868641790254, -110743961483616, -51038534475280, 281193349975568], [4948403126699030213, -28699302896916259, 0, -248820518048973, 330093005803264, 81272487754291], [4984975435347948, -15035236885068324, -2651904671059380, 22373117801664, -35564343421152, -102683696826144], [-1028931324973460215, 32396313132812057, 0, 417572252877239, -447430173080192, -29857920202953], [11555587699803174032, -3315291079340430, 0, -25868227493330, 36558226393920, 10689998900590], [34547211338986467, -103965957943837001, 3910675973392771, 92544728888128, -139234469101344, -416868655765728], [-13645491991459702555, -2156333551826883, 0, -518788272645677, 298501240784640, -220287031861037], [-21610285674667947, 65217767743636833, -11778362090378763, -397680360121536, -408450000610080, 784591079754528], [-51856069543729342, 156245659568377930, 10760300016983346, -208120363863072, 261210209463760, 885571301052976], [5215175519402298830, -26347853933266508, 0, 352348928629900, -14813576255104, 337535352374796], [-86440636445084341795, 148104700965092037, 0, 823542498448843, -1451430022563840, -627887524114997], [-105660593579432841, 318039630126303995, -5297241345131497, -297165846390976, 463517695223520, 1355015234396448], [106502133165102598490, -61501687875548248, 0, 784331416945880, -13710519574784, 770620897371096], [194824445836393907, -585771611359402457, -1909036147171725, -426261786095232, -2150797422411200, -872012064125504], [54780227405921458613, -423310841254782739, 0, -1859834503790557, 3878090784201472, 2018256280410915], [-75412990919470663270, 356662621651358312, 0, -1603012935814632, -1532557931421440, -3135570867236072], [-21575442699199386, 63960356120168766, -900449389465098, 1218898952459040, 1671825927488688, -1984870929888432], [38956638782026932, -116677887759081148, 2093721618697556, -646219098820288, -1100409610640928, 838247685819936], [86881718969900512865, 364659451915397057, 0, 397904306057615, -2681687166932864, -2283782860875249], [132407685059048235, -399066533722791873, -25685612902778517, 698576409263232, -446325727120704, -2542054954910400], [312833281267153184, -940741156953173600, 42306556305636384, 7227595654656, -2226857960404736, -2248540747368704], [683871013459097726993, -12047855925455599, 0, 272807542148415, -67902398571392, 204905143577023], [-143523732710145062515, 1597311527653838357, 0, -688128339907717, -10416034676495360, -11104163016403077], [-264705319776755442568, -630782520960067830, 0, 2088600055126294, 3118958895235392, 5207558950361686], [-556218713551412678722, 51093002277316, 0, 7542347350249852, -4128251543057536, 3414095807192316], [-74003243470488775, 227291589836864053, -50909165284581543, -6623773250400192, -7965687075402656, 11905632675797920], [556897801806143069837, -1123551039333789035, 0, 1275731025583867, 6893356934199296, 8169087959783163], [-1207258501459793244, 3632400819455345076, 88254307364724996, 105910587448512, 10837136250862368, 10519404488516832], [1023084085331497129880, -538553183395401238, 0, 12694164378813494, -3308608995192512, 9385555383620982], [1524519896392331682, -4588198689000927958, -59037896855303278, 2018937477938144, -10601124868056624, -16657937301871056], [319913097744748027, -966281658008046673, -37858063696150437, 4665107270851776, 2787849767900960, -11207472044654368], [374789772576712496288, 2774802383257317346, 0, 1540338415652798, -19591687803548608, -18051349387895810], [32453879592085074590, 3225144494975674852, 0, -10401505988078756, -16098800742846592, -26500306730925348], [-1650437628011513231563, -3771698850978627475, 0, 3370605005330595, 23639728686127360, 27010333691457955], [909359248264342332, -2731002462310037972, -96561520990885028, -7011074727923648, -16946866972858272, 4086357210912672], [-455192758163162067, 1363704071748202905, 41715533345695245, 7781578744130496, 13688954746977696, -9655781485413792], [-766722074314948568, 2301763848746968328, 48789821992831656, 6690313701623040, 14978253205368704, -5092687899500416], [2190781300202636550, -6592879505769244770, 392169224141951574, 7378453209256608, -5778698742821904, -27914058370591728], [-3477975902438610577, 10450947131401620403, 55420376855699823, 15849956611977216, 48719337309743104, 1169467473811456], [1888022532940889157, -5686721823423975119, -366671794747705787, 5230826334082048, -12192571933143552, -27885050935389696], [3391606320519056658, -10180286951746212582, 102190021698196674, -28255800924158112, -61979592037358832, 22787810735115504], [-3098785885336265324647, 458816202820097801, 0, -6647596378934073, 538102053199744, -6109494325734329], [-2031592566062518012978, -171252213358491980, 0, 8582559576487820, -3540102110385280, 5042457466102540], [-4613645376446678841, 13864659946213158027, 98629258468536807, 19803148314704448, 63330113502530400, 3920668558417056], [-7788724035849409058383, -2857208013124153615, 0, 46173547889353055, -5965198418334080, 40208349471018975], [-6544713997235750631, 19711134481353473429, -318115378590244807, -33220350844594624, 10551787957032288, 110212840490816160], [137046420843534193745, 2215254615899353937, 0, -66308286214343937, 21322409239611520, -44985876974732417], [6252161542845109013, -18813918571825659359, 306700371454887861, 10796193190752576, -35841556908827168, -68230136481084896], [-8843888869918249991122, 11616726221840132436, 0, 567124528568044, -78801779112528000, -78234654583959956], [4361970403620410715, -13123077018202504433, 1057526926118019643, 12823862481629632, -11518082378013024, -49989669822901920], [-3744703399257193099270, 21991435471127967752, 0, -108035571468290440, -89463203933759744, -197498775402050184], [-599539695947958665, 1782992673905415995, 543037176222264279, 32616913534665408, 49607413130870816, -48243327473125408], [-3933448842945758494030, -289734531169924528, 0, -11350853254035792, 8169957059100160, -3180896194935632], [-4742246209456336294, 14228639375584287298, -1861181256595469046, 28506177847442784, 58913102910163984, -26605430632164368], [-4667951117782057483768, -28397476674892838150, 0, -207174996011490266, 305261157782591552, 98086161771101286], [-21489953480758011192, 64693274641478849128, 1273579756643231752, -45909514692273536, 131595169820268480, 269323713897089088], [5973644001594326601485, 19833061534363239957, 0, 202466171852956539, -244816361178734592, -42350189325778053], [-20402593746975346176400, -28377416797514633838, 0, 34726740259216654, 172733451598095168, 207460191857311822], [898044806008677999, -2649985948259760685, -1535315451805688497, -83605646231542336, -123062822696811360, 127754115997815648], [14836204972601136498, -44680167407778519558, -3646366791788688606, 24465371210736480, -122621747553637104, -196017861185846544], [13211435002652244859472, 30374952518793848370, 0, 177966981403994734, -302637013598090688, -124670032194095954], [12941593161727248705, -39040303983823729379, 1948407125358440545, 162207293540980288, 108890088439977312, -377731792182963552], [1300105893262963710, -3870634513942925898, 1880225635868388942, -32382186287702880, -35081206729440528, 62065352133668112], [-2306534907820575255115, -15942229238748470803, 0, 319127869504667427, -66940055345470208, 252187814159197219], [-15177869391635135267, 45776535252458461673, 2391821750224665693, -127145002602795264, -11362927652534656, 370072080155851136], [8107889537059471940717, 65364727061975595445, 0, 105066730982836699, -499156299132333568, -394089568149496869], [28521220355583576113120, -38114389817261718878, 0, 153141664592967934, 173715641792103488, 326857306385071422], [-879459633817438690495, -127178916291798945823, 0, -72100356541383825, 898777332240885376, 826676975699501551], [-11342123774503806657, 34115732929099996227, 1894095404717551935, 26058762397888512, 141479130384353280, 63302843190687744], [18600070514313918549, -55726678778214582079, 5685481870859048597, -234538206187557760, -395543647647941952, 308070970914731328], [11319643002175100898257, -65535024960179710255, 0, -201397338465288321, 553028441728838272, 351631103263549951], [4673465437194560440913, 5684036946352528081, 0, -712473533828013185, 351529184417003648, -360944349411009537], [-55846353283429710468, 167964466548696929004, -3964788659095049700, 4380151795603776, 434167001999005152, 421026546612193824], [-39894337883047579974, 119924355900301272866, -5927293597244323990, 51232601028180320, 343807453214893584, 190109650130352624], [-28320844969917366596515, -71454040949476567483, 0, -1066297691842657717, 1066379418842782720, 81727000125003], [-14948409917366123895, 44520674507133679461, -3164993844231027831, 548974201224331776, 773393157483971328, -873529446189024000], [-38304077579718133306, 115623356658931678558, 14620333465834029846, -356146056424715616, -1168193072152592, 1067269976201994256], [31343493428979912084, -94272536816985877148, -8602918816417142924, -114597549567892544, -471251629181925984, -127458980478248352], [-56521285350814353169915, -245193540932980485603, 0, 1570166957771488755, 797364982118174976, 2367531939889663731], [-45828017307024066427378, -18054952844708170380, 0, -225291311372235572, 245294250444994944, 20002939072759372], [-50013655363479045366592, -107840178723408448574, 0, -373535360651120162, 933084749568575552, 559549388917455390], [39973827850208696862785, -14990418383973388063, 0, 649778178767055471, -254335230379446656, 395442948387608815], [-24624050821245722499, 73921586610721691593, -10251265383181310147, 90228533902548352, 229891214789620800, -40794386918024256], [52419109500192412656905, 207477145363061677977, 0, 1108255779805626679, -2008417996806198912, -900162217000572233], [12481569073968796608878, 141175547785078492436, 0, -392287069090502868, -739191183707755136, -1131478252798258004], [-52715348042873606721, 158826637886995332963, 22620223051061368095, -75443802896570688, 529706152581371424, 756037561271083488], [87262729554829640684417, 207240176272680707745, 0, -2070466723232077649, -267110619532989312, -2337577342765066961], [-1404968754865500222, 4143947968396830154, -15641077878634252622, -60754357888264736, -192467011976199984, -10203938311405776], [-116298497409889313061, 349508617219582954575, 5871968827311498747, 515939166209504832, 1645003322334025056, 97185823705510560], [56273831819081030688473, 115400743789460478921, 0, 1558013299015347207, -1632431223038537856, -74417924023190649], [-1327208705753565362, 4825770362303679110, 27461243472284035806, -788741951313584352, -733339657584185680, 1632886196356567376], [-16251399469123328692375, -422063826868385706823, 0, 1041243131424923159, 2281913062317344128, 3323156193742267287], [47121650063402289859790, 268363792284808100532, 0, -3798651579242142836, 265722875904091008, -3532928703338051828], [-270943513226578082637, 814637433182448214183, -14220831935958444557, 409554488841179776, 2626002480396325824, 1397339013872786496], [187161358995144543432, -563535372190863002712, 26893648658051687112, 945580747525389312, -160133710378593792, -2996875952954761728], [282318954958630183859525, 329640242018477461597, 0, 343756680826764211, -2415436034901657856, -2071679354074893645], [-96942758629092456464998, -755239379732348272280, 0, 1023243275124906776, 4542950503021829888, 5566193778146736664], [51056430034282948869, -154338843190333828335, -20967708723308746011, 747223492775173056, 324893898065364384, -1916776580260154784], [-208789025245064672782, 628810311887939997754, 15791592100846811106, -763988786412387360, 915258579921204688, 3207224939158366768], [432096488364697301127, -1301353100625953778325, -52376814470358283897, 1378780607744422400, -2306074316373030144, -6442416139606297344], [-565354932383538879668, 1700246548420626678332, 867337356067364652, 647638344821413824, 5477027959652866976, 3534112925188625504], [394725537944722539402, -1186745760641477358606, -9819577128602674950, -1007294100955340064, -4583735009220420528, -1561852706354400336], [-397100166609996455816512, -356929317102556798014, 0, 3890697062688485854, 282316588005334080, 4173013650693819934], [759889247232110911482920, -130124789703373637158, 0, 945339934893685574, 361839560655304768, 1307179495548990342], [285064027292154631364717, -1207399144928144246475, 0, -1458686705408472485, 8956437622069125120, 7497750916660652635], [673248248740149376309, -2026137809753407977151, 694515556454202453, 1086096282843510336, -4220870967272827552, -7479159815803358560], [-139092112040423656705090, 732257499238758835652, 0, 4444446629047801212, -7380119433727234688, -2935672804679433476], [652700355451532599470, -1964706091699386526874, 14896434936418946878, 1735528453809919264, -3133968437168889936, -8340553798598647728], [-664956255577526034441, 2001270719692110398619, 46618026234515864439, -678086304208234752, 5045780351115825792, 7080039263740530048], [-307081224167161606763800, 532632797692044387482, 0, 3620068594428240006, -5580124012437377216, -1960055418009137210], [680581891167230130682, -2048634490040362095646, 15395215122709883946, 1810323926180170848, -3268168686311361904, -8699140464851874448], [-148356044763334373016, 449311686919301102856, -74584302680310673368, -4727936839376691840, -5212321049455399872, 8971489468674675648], [-92298322741118725106815, -743697188269555703903, 0, 5763488292039952303, 1870639436583240320, 7634127728623192623]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_4_b_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_4_17_b_b();".
// 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_4_17_b_b(:prec:=6)
    chi := MakeCharacter_4_b();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 17));
    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_4_17_b_b();".
// 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_4_17_b_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_4_b();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,17,sign)));
    Vf := Kernel([<3,R![68111840207423731138560, 0, 9656364500582400, 0, 197927424, 0, 1]>],Snew);
    return Vf;
end function;