
// Make newform 8.17.d.b in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8_d();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_8_d_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_8_17_d_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_8_17_d_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 := [279841437428593117864520581120, -2811006993630615015868334080, 21723325027733376807731200, -122098039773726666915840, 64434406660761845760, 5355071973862932480, -697940891942912, 465478371454976, -652293490688, 11331786624, -135772320, 219192, 7894, -7, 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], [-1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4476, 42, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-176481310109098931717428953956766187520, 1513638432009977863658379407964241920, 741381185833276749197284453908480, 70452696231227959291828369489920, 715300597594788165511777812480, -2693005054430854357422981120, 8384552064063068792651776, -20269713654432500382720, 514365470864709861120, 12941406522678329952, 338450263655874432, 2567640267290346, 5986305819397, 58320936057], [270101432507374827453346061180382761451520, -607477185539139873028601405720399708160, 8975155651649775233886645322084515840, 4366867283294468571413400132648960, -183813749390261554716393891102720, 1729543258117384764998431948800, 25240273199306757761974435840, 445367533666365059689552896, 2711837486550076197460224, 17516388906524481238176, 13059367493115071616, -134304160947187674, 3679768792675075, -59559682613073], [13680408558541930348351581163360270417920, 75695509955635579329771774691948625920, -473410272226725214191675938785198080, -13822283514080509977104087012474880, -114076526505930585119890224906240, -878686711322623677776799252480, 5530983882330275337754804224, 36977882278288483605302272, -21657438899412178858752, 642447840602638989600, -32581393512709134720, -582007274862497634, -4052879338989057, -11214439470053], [1057810030778773363076297235168973815808, -7980980499461337222692955919365439488, 53674354918537191358353350200393728, 70777026487837759674608820289536, -1639743776687142447551323373568, 81797756945076138688364544, -197632392274712785729126400, 330062848935416240440320, -5112633309255982039296, 72440214758722847328, 285673832524316544, -953736685017366, 14223951977221, -375239388039], [-322209802111205245917055032357473610629120, 4982396811329695285770436994328313200640, -21774355382132346478128392138328637440, -116870868096182953733431300752015360, -560944245809642659568346380697600, -36907461707714430355325396336640, -119123179786183557735667761152, 596764021078698023431742464, 5606724662346279236318976, -60863620998736426826400, -963298369771195712640, -8735973951543936198, -53794823890515539, 22798506203329], [-551679602029196350940807242550260331970560, 6011052032619844281886301526957993492480, 263004655702424731611774721279918080, 1241725971346736615918569702311198720, 1145214983786675275384713152102400, -1885728452825311439592137932800, 85469617510151187745823555584, -308208502237179693644301312, 1665254284266544386461952, -32686436336515324766304, 25526624903855638656, 1691500331582104182, -4870955965165397, 218134071226359], [18177411131067093194996903043799061626880, -400332714841088082495775252295209451520, -37875980785742335857103888733070950400, -100272256112897076060289698526003200, -1646824685553866520545900916572160, -2222732640607341472268550389760, 102758743819068287844839358464, 137915000797290506345659392, -6556701619342514477559552, -80588539711877262741600, -479709212226828720000, -347060958724085514, 26908102121867243, 238078010965047], [3795165327056209117152118129046015589744640, -43983203169215878242860042808914419384320, 461863725615516519923961233747906396160, -2296697739545688153720844107965399040, -17593305208907891447070576807444480, -162474436447823333694130623528960, -1360506502701944376368809213952, -962106828521238672684880896, 15359708300982390039618816, 585128904208779297783840, -4157265813116128890240, -21960089176649252178, -320633945769169529, -4186634072503101], [-4628522820869557735066896221439839940116480, 124857911880152686291094996342290492948480, -122247022119048274622513657726191534080, 3670021536411728944401198060217958400, -2414605791274134937888865244610560, -185338972362262178255694258094080, 325306134897063931254293954560, 287578160767890582529088512, 211455767470386056182249728, 1405653423925877946171552, 12224144162338428796032, 40109149264408807782, 229383117872071075, 4994608270611919], [-12365866495923744547152099580355678012702720, 4807123178791455698851154304238564147200, -639545684755019567276063937602802155520, 1124665942085803264011735225078251520, 23920337102188935774732225351843840, -85150724912387887699323095531520, 40177498144879219065499844608, -28168883036313927292802749440, -171477744490864343215614720, -1474984638296136506548704, -1943541086894356116864, 23737172275955491278, 275912899806284311, 3532537240168851], [-4304384418588685625869253151553186451947520, 128434611235071249437177721649156231004160, -216678429748838589614150887684775608320, 14203836602766104161246265900215173120, 116453463217412575234282771510394880, 412503246278464397842506368532480, 4450982558133706602982411829248, -2807143998932373401198484480, 118070268701451279959996160, 2854910424521539609539936, 29094314084099191798656, 259734533691930798138, 2461547649861093421, 16391956323533121]];
    Rf_basisdens := [1, 1, 1, 35830037999228392691985026415329280, 465790493989969104995805343399280640, 35830037999228392691985026415329280, 1023715371406525505485286469009408, 35830037999228392691985026415329280, 155263497996656368331935114466426880, 116447623497492276248951335849820160, 465790493989969104995805343399280640, 232895246994984552497902671699640320, 116447623497492276248951335849820160, 465790493989969104995805343399280640];
    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_8_d();"
function MakeCharacter_8_d()
    N := 8;
    order := 2;
    char_gens := [7, 5];
    v := [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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_8_d_Hecke();"
function MakeCharacter_8_d_Hecke(Kf)
    N := 8;
    order := 2;
    char_gens := [7, 5];
    char_values := [[-1, 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]];
    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 := 17;
    raw_aps := [[-25, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [855, -6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 95, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-10, -2937, 0, -24, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0], [-3507114, 55855, -119, 6787, 10, 32, 30, -2, 0, 0, 1, -3, 0, -1], [-2452, -568320, 1539, -5026, 61, 110, 151, -4, 19, 0, -7, 1, 8, 2], [-713187718, -872749, -21257, 76217, -36, -1096, -401, -69, -208, 0, -35, 8, 0, 72], [4494158110, -11440793, -1327, -651613, 410, 2400, -4194, 142, -608, 0, -23, -155, 0, 151], [44320, 23158935, 155148, 121650, 5389, -37836, -10491, 808, -1150, 123, -1146, -362, 432, -244], [66403, 282855581, 3105493, 1248499, 28197, 40560, -60424, -544, -12776, 4224, -17592, 4232, 2112, -3824], [-375262, 382719546, 5751268, 1174638, 71524, 65756, -79502, -520, -7898, -76, -25998, 1186, -5104, -796], [3083532, 2636571336, 21036053, 13739258, 703803, -1216590, -759687, 24132, 69693, -65024, -81673, -42897, -11400, 24798], [622884039810, -5578871598, -37204638, 114258798, 808952, 1288176, -1347726, -21790, -62800, 0, -96906, -99256, 0, -12152], [1194102016621, 9335286124, -53465446, 170355189, 893284, 775104, 2795596, 109996, 3136, 0, -230902, 6946, 0, 1270], [-32569502, -17417875156, -82636724, -114233270, -4690134, -5681676, 3131336, 154280, -484382, 11742, 329382, -53578, -120144, -62132], [437680658, 103403274458, -294609203, 933759652, -3942233, 16431822, -23038201, -338244, -430077, -4045440, 1281225, 440913, 65160, -187230], [24787242511287, 298913196986, 397987376, 2490999473, -1802976, 18062656, 89879280, 2490048, -1591520, 0, 282128, -82832, 0, 502896], [1340436696, 335200927092, -630972305, 2874611994, -21354055, -31266274, -73743825, 565340, 3738187, 19220608, 3811233, -1603607, -556216, 1179602], [-43880676271546, 881540186367, -242334279, -11986490493, -20116374, -99783264, 210323358, -9452706, -933696, 0, 3247857, 1393389, 0, 775695], [-5187867064, -1222100553323, 2645884692, -10594581538, 557284943, 75226284, 276252239, -872296, -7185746, 240873, -9323766, 1621370, -3971376, -967148], [-38777824511494, -1636448971167, -4513796811, -1651350613, 53209828, -34717752, -471370723, 4763577, 6871296, 0, -18469561, 5410560, 0, -486912], [-6486169308, -1825831736826, 3518515056, -16087399144, -1749211570, -362986096, 409109082, 7789088, -14967320, 1613138, -30343240, -2218760, 5366720, -3623056], [525867047257663, 1431278972818, -6203603128, -48878600639, 142947088, 281414848, 321409376, 22345552, -22279072, 0, -28715992, -9200536, 0, 4359512], [-29199620227590, -1216159596695, 6741379453, -108892541021, -186048572, -289206904, -557863515, 7110145, -72550464, 0, 19765087, 12561696, 0, 28370720], [1312259460143930, 4117687417539, 57395487495, -64862652183, -621669156, 728810424, 1284584319, 61852971, -63465360, 0, 171156621, -22557336, 0, 13636008], [-27041548646, -13125433910462, -57904629135, -86743923820, -1165108013, -2872155930, 2485179347, 69058924, -302624449, -124355328, 192526461, 22495141, 46327080, -74289334], [37917456616, 13275111122073, -10029291996, 113020907382, 25395631771, 2564057244, -3287463781, -57216648, -61795194, 41309693, 140084370, 81525186, 49743120, -38612700], [-3483703578299008, -24187204403459, 61274702223, 6970924207, -1201580186, -1908876576, -6631384526, -157568174, 236726272, 0, 258052695, 70111483, 0, -55538263], [-108454203925, -32365239664155, -10780271983, -255175722189, 1037813241, 491204152, 7212300316, -7110416, 246424460, -962873088, 149761956, -87433276, -129972704, 92766088], [2057192502147586, 29765664822564, -68444108156, 416404520988, -92966800, -3894940960, 8187808292, -10178620, -143269664, 0, -257811668, 220435792, 0, 121235152], [69252420890, 27047868632814, 189984590212, 146317109246, -84501224760, 4724000572, -3013347458, -169970504, 1409218838, 206008336, -1089723838, -170648590, 89235088, 298126468], [-16554350388908492, 28515262734329, -181391349381, 369616299143, 221049054, -12499112352, 7124913434, -1481814726, 2068800768, 0, -59163933, 298887255, 0, -589971171], [2804070793960578, -37883727783930, 385869014262, -13579564025862, -2753393368, 8779297872, -29935453914, 1426644278, 1779116048, 0, 533361234, 387005528, 0, -464036840], [-2207187386732499, 125764719049196, -47674340678, 2172431201685, -2834877916, -11654200512, 36504885740, 1102459436, -1164079360, 0, -808418966, 1134107330, 0, 766062230], [1283194897879, 306687973607393, -781311203017, 2713659898075, -8452732981, -10660860228, -71712313506, 135710136, -939728682, 1414404480, 2967602946, 415800978, 1232388240, -517583580], [-1747328087152, -593503646615049, -848420989012, -4485184566046, -137678132611, 4188520596, 141439923205, -540117528, 11067065970, -3113522485, 5334402134, -2307262746, -187425744, 2712350892], [726962444598, 201285801591102, -205186663261, 1688016630708, -3710450663, 48552851746, -30728046351, -1761353180, 13425799637, 15281992832, 2768224959, -1336223881, 1475829688, 2657238766], [67403514915176293, 424971830857492, -659659463998, 2625635616165, 18243781876, 48502814016, 122743087516, 2311908124, -7819052672, 0, -2535791950, -2852853398, 0, 1655399758], [-453569550730, -170542939969861, 701813165328, -1670117750528, -868427260933, 32367445488, 61511348125, -283929376, -13806523688, 8199752037, -10451288952, 4147328840, 1718056512, -3934381808], [1271241098274, 534218422505682, 2176653584407, 3452350518624, -34425925939, -214425002142, -132279448367, 5945647780, -22049479819, 74880704256, -12431503713, -1107749033, -4184296776, -3351486802], [-95226659826393519, -167829426569000, -10245114803738, 42831337161181, 119857383388, -90558050944, -11255212668, 6111555700, 19315794912, 0, -39730198826, 11130130398, 0, -2728554838], [-2363393136347, -506637309590469, 2266725642011, -4895259621851, 302508322203, -413697381376, 31378164416, 8041656320, 9103187968, -95699019136, -10309095680, -8938191872, 3506631680, 2906949632], [2263181205666, 1486627334438222, 6648976055412, 9978915408838, 2068877261568, 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[-8917344467022898760902, -29720815949612236581, 112891320225198687, 1604020118489742673, -4533667996789636, -13437956498706696, -6554491104385385, -644620617468669, 746919977881008, 0, 545155530895957, 610926969669960, 0, -45331002737016], [-356610232562917624, -59861776208595552420, 434110276892774157, -617883299112657714, 64509617355496811, 4268277656848986, 13801941988026189, -69118811090668, -176553001894175, 2445094471993344, -1707174323167773, 75607759281083, -133317506359848, -23768650963082], [-973258626349950530161, -107399346309404578782, -166254450881460664, 1708845855363138513, 3153741589536848, 5443442878006528, -27055968186390032, 926534912844272, -893598395414016, 0, -950613019926520, 11352477119976, 0, 301650290844664], [-1742538462467198860083, 62336167016226057260, 262844029772588170, -7136347677680950811, -4634692840099580, -7068164469078528, 6268821097927932, -91749451006612, 2209566845267936, 0, 742839373184858, 672081409472594, 0, -512495145265114], [-212817545762415208, -58142499967833781196, 20614020681268047, -473218162173388390, 32643753940915289, -14237430460389282, 9691955160434639, 352778166323420, -1513800078007829, -1907111883695232, -290531855456127, 81943328533961, 136891359840840, -346526953276526], [108482043680477616, 9016807649475717492, -372196602238830955, 201145029481631254, 92926839105568787, -19241929394539078, -8671294838181891, 342627725570516, 899545211245393, -6772891876839936, 2183713874668339, -479133002022005, 267867174046808, 222162207844118], [252903220426001072, 47814725050309883354, -243483764680558424, 465005432211447676, -55119371956577906, 12621256218816216, -9402583280799250, -285352433753040, -75313195561188, -3750563934650910, 800447333015892, 333392933468724, 188186911739808, -119378608153944], [-292633501943677674, -72300009111213169023, 158035146641064520, -624884713226303340, -19006055045415619, 23869726153390904, 19575300336334383, -541182579403024, 1797622133117452, -3745714659979277, 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-308928232091024, -43918595033236, -8094044457959274, -53912902116796, 335193642534308, 138375104762656, -103497468466040], [551664403538163743, 192911801331749959065, 525787779583694831, 1361603297093115939, -101323602315559293, 1636902489977788, -41836259435238050, -63508065554504, -554578078277290, -1421213050180992, -3280838106878334, 321039968408594, 491426549527696, -273408919242716], [-16822369290929356024958, -50232861481890008670, -289306888253964110, 5868690490376782494, 1522808153422520, -15976554250177168, -5017020530162878, -476679233697742, 5156083512821296, 0, -1160177826256922, 1404705462889864, 0, -1250459349977144], [-7711692408605422697414, -132521788367308937381, 124733285047948127, -5015037470910358703, -1590708823067268, 1996448053098744, -44476294216178281, 1279327054193539, -535849635300176, 0, -214186106043051, 447904319365576, 0, 327917984888584], [-150487768106353668, -5177046618021280840, 289855081544687165, -129447739659282374, 105599653363768051, 14218132837551714, 6081337363644369, -372082869485404, 6202381724917, 16863949919170560, -1049001041186529, 510144957951959, 651471452962488, -231082805837906], [-41314159284095130791931, 171140704753233185108, -1325651343891652814, -14337233414225413931, 21279888368680852, 18027302280189312, 19981002904171212, -7245050434852, -3657666867468256, 0, -4077456414558334, -1587537276162790, 0, 690043197101822], [282921453636528918, 150020996045475076702, 734118762312699075, 964430502215789204, 91474760165310009, -24700824254367198, -45275010810116623, 549214576960548, -828563861561259, -19570324608216192, -3363183272859585, -280504357493001, 108973372068792, -131406575227410], [-6366581140611220397950, -82095697997617195662, 1839390062907549698, 7042590097766047182, -26687552250406024, -6587871069923600, -7123084853639918, -2725011700036990, -2704005990608976, 0, 7724779163970134, -1288764656974392, 0, 471747111211528], [86160667138549709918650, -50675438762768874821, 73953831140094437, 9926762315543330267, -2124283858205086, -3917724073888992, 1938876984131718, -290838980121146, -692620671836480, 0, 400630058570941, 12860680577929, 0, 235160450804803], [-378978143178755684, -202323862621162649688, -1014672124460632303, -1305120450914159310, -56768278322169601, -32522642879141238, 48280450059237797, 589369717007988, 1396632769238361, 16926642198789504, 4638202406627403, -800242269940125, 405800128257816, 358214982184134], [367580793154333522, 22947624971396224065, -619902015659486320, 369420554287172816, -323685665999913359, 37213376487487344, 10151662715560679, -1113190039478304, 3722104019699352, 7925885392082415, 1480267184668616, 496207023515784, 1532469465718848, 338685506092944], [99393443528494214057196, 20880831263316494209, -421942261217727341, -1542498205853222777, 11059766639943310, 15266526187325600, 5888926847191482, 491108343058090, 5579420539684896, 0, -1821999397700453, -11176147718193, 0, -1863532229134363], [-631041547716037094, 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-6170875587253854, 2748769840428888, 0, 1020122807558424], [204473431636633540692665, -376333944709790978736, 1832033074258152798, -20939337278666700435, -22733954179086708, 10099440280187904, -130765416322838028, 5370528829545924, 1579464561041568, 0, 3320003092988622, 2251482467391414, 0, 224005968783282], [575060413933918458, 107742895999219248234, -897484956807631500, 1200331567572205542, 86395322706582396, 71488684695941196, -21508566957531726, -1750702836732456, 7085242562325438, -18664694011040772, 6180706271545914, -298833555853014, -675227298833328, 1611860683402356], [-2061518703057111315, -349593162436636891557, 2777040738712961029, -3727036295224233367, 147887692939729009, -3116950103012924, 86987572140248610, 190968772496200, 3516420635593322, 25438976582651904, -10643417086839874, -1702709556888274, -2578284695099024, 1559482977516124], [-37691829826182217682622, -27027615408807980732, 494248818080784004, 11421268295576717404, -17898514974179792, -42466697956833184, 5454978459772836, -5228804186808092, -5551055631360480, 0, 4312587467510572, -654115425022032, 0, 1632313402112816], [-267466107047631441822240, -215555230289725315267, -2135523658900615745, -5583824956496156065, 28406783681089158, -3788617802607072, -74508736180631390, 3001103106915602, 3987669212901920, 0, -9045516338811033, 2235798817733483, 0, -583956798389479], [382026139650392886, 156129226313165018837, 718831786082074264, 962217692099437324, -59804775219352711, -107332269042958872, -44052063896562325, 2850900846549328, -12792207806931772, 25638180610996887, -5825268691090356, 471549651543148, -215131026199200, -2609725286455144], [278469650287133743029863, -282152806002420419286, -3885150884472140208, 3936253112918456193, 56434491392613024, 6502970548873344, -81517526641332480, -4240278403231584, 5562622272495168, 0, -11045064213069168, -1831247076858480, 0, -2464623116451216], [-2039316876120482882, -693484621248827215924, -901790390718428972, -5312437457046897434, -252818006907615138, -25623494863356180, 181259437969167200, 344182349701400, 4640211109676110, 63341012241113946, 4118294943952362, -1474398619862182, 33300441607632, 1216261857586132], [1162156082739004444, 91162680680336711643, -2001568598919783900, 1369845672892830758, -803023295293356435, 132599931042464924, 10562976366580169, -2420286693373576, -5128533490470266, -1564744427779541, 5722749481198226, 3121682674006978, -1717877894593264, -1306467653976796], [-120549340313735978543174, -924856056372545186509, 5702121288782429367, 39027652822530961721, -101024631653628516, -108832519017578184, -183287214175461457, -4686155293019877, 6995190773019504, 0, 20199777130408221, 5333353638716136, 0, -553945711434456], [-55706057322438492114950, 347131457691958011529, -1544270568574197475, -62030103677638651389, -1073082256795580, -106059620327512440, -19943171009613755, -4530847642300895, 12706817140573120, 0, -4557523602911425, 5951654591890720, 0, -2251720849560800], [1826342610083043759, 444665486483117798353, -1831335424018414551, 4309975078893926783, 366469526627148345, 286700228623044912, -75879357733701352, -6552534275084448, 15065876871653112, -20513228888881920, 14076548397050088, 1933388093109288, -1772574287476416, 2981012613204048], [-250818348401680779639846, 693236045554554429243, 143351404463061, -16885629176595274101, -9830174314264318, -24058461341512608, 157175835708896502, 3663765483736838, -10421103371853856, 0, -1651022080012659, 2032898654231225, 0, 4151334008695027], [-137369934163593508115326, -260820304875951204074, 5227309611617241606, -41421972884933813654, -56697597235561496, 48648289653791184, -118323768854231882, -6212811091553594, 1061217426342544, 0, 21367918929267714, -6014271470845928, 0, -2358496299062824], [2254735707200535470, 720831640725087286311, 1494211577247937680, 5189023818251499872, -456895134956256377, -107524684027226512, -161605344214902191, 2490386397105632, -18728979954897896, 37238284023509721, -14816920196844472, 3744231905090824, 5586896654611520, -5612021702920048], [523139303398090865938287, 190797088160086615170, 4100950558639497480, -31195153121954334351, -28964289206369200, 135415735023841152, 24424945923885072, 12028554197686448, -17678561733375424, 0, 9730176328984968, -4659026556818776, 0, 4339845058852216], [-80660865786014080407558, -639844921883219110341, -4293034210606625697, 63491491275020090385, 43320836510583740, -70340646149141640, -91072153313533161, -3632376860587165, 8037692955677552, 0, -13672876137435051, 3584813573487464, 0, -1484293127396696], [-2989228624270701246, -728903102214527629307, -208904839882370560, -5618340533959229896, 1391703154761764845, 33587008780058112, 136466362058271763, -1729940901102592, 14420034467996416, -27124197667225581, 8365823504430336, -1039181790426880, 3776028927154176, 2336637466253824], [4323780345061877256, 1449623489729068190292, 1610094346956355328, 11076358173837826400, 573927467221968756, -138934236101379840, -357645042582577908, 2589108582130176, 18494562724773504, -5592154580501876, -292753573637248, -8038079612354688, -3948598541657088, 6096248175757056], [-5584748357807425916, -1570557183742070874192, 2077254342974645845, -13361515852028773246, -1122015394299798325, 96107309069622946, 409987953651281009, -2047251807556316, -12410917595348587, 48436483020613376, -19041691369185025, 6268796022232247, 4987072215244216, -4733357166565010]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_8_d_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_8_17_d_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_8_17_d_b(:prec:=14)
    chi := MakeCharacter_8_d();
    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_8_17_d_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_8_17_d_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,17,sign)));
    Vf := Kernel([<3,R![42252278198540030770423680, -48076904850839036094528, -23234376480743090592, 6277143698064432, 713806378344, -154370700, -5982, 1]>],Snew);
    return Vf;
end function;