
// Make newform 8034.2.a.bd in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8034_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_8034_2_a_bd();".
// 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_8034_2_a_bd();".
// 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 := [-66432, 94528, 185524, -296326, -122680, 270913, 19731, -113788, 6763, 25368, -3150, -3101, 498, 196, -36, -5, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2641861718989240104, 2608177483732148142, 8434099748549824528, -8015723884984487975, -8218562721686531825, 7057641060272104164, 3770017974633780087, -2812402864763475044, -933492931001692430, 584806300906520047, 126845466474286622, -65847084572606208, -8779176678679124, 3828384374947411, 240231261271053, -90586583806696], [-14690943728166969488, 15822903042704832740, 47716865559993728766, -48815686138384895136, -47249773825946922341, 43039314676128770737, 21958491635614630188, -17153609961115061407, -5491103861096290984, 3564165190681044406, 751279156738320473, -400715718523472458, -52222785574841876, 23250750972171732, 1432628181298625, -548861320433565], [55874993881846012448, -49887972149323407140, -178441043110187005830, 155576241533390408220, 174248716157357704813, -137710113475680299789, -79839053134054770160, 55060744838113792651, 19666961745324013104, -11487640535802356658, -2653626772894102149, 1298746915725286210, 182455633738698884, -75869762801105224, -4966726230624225, 1804326041550225], [50159255507717243952, -52289606909934558532, -162139203272019169390, 161726537131518925220, 160045111057739017785, -142761745839245510897, -74248219122217515688, 56965202389909391415, 18546698540088649616, -11852110311085567842, -2535841645574667481, 1334671116861721130, 176229450470376708, -77588508853292304, -4835063132536829, 1835427375702341], [-17193626618790198144, 16815865184121493238, 55327722525776352088, -52163888681140811825, -54416371328603985543, 46062057857375063812, 25116251602804037253, -18376977040077066764, -6233456803346647046, 3824729425828204465, 846763531102328270, -431159357317343856, -58527974832066220, 25105417772097457, 1599200104156899, -595029787973500], [-78040356907095709104, 75872710426262168508, 250609270874405645338, -235238717548900685604, -245983134707975915715, 207587078710285962883, 113376045704201381856, -82787094387047921925, -28110032331446166560, 17225700209520332286, 3815774167702393179, -1941458087986298718, -263611332890321948, 113027570175626792, 7200273222605183, -2678489495580815], [-47772605674210336512, 45943002513497625888, 153429764577484876258, -142627782445967128474, -150709788164175297649, 126120647536918697015, 69503600178868582750, -50388167884484641945, -17239844280702946500, 10500262821630922156, 2341043276285811571, -1185014847148291254, -161784188747179548, 69072367077303942, 4420432159038421, -1638703541012891], [-100871910618813386288, 101341860589668676780, 325396081581932857258, -313893272371210960748, -320980123683727999659, 277001407604204710851, 148581497019745053416, -110474820709431665877, -36974698692332377376, 22983893465451743718, 5034026218476398539, -2589606301822829662, -348541387262623900, 150690531878100656, 9534940311240535, -3569097596475919], [127255514637495805936, -128593948008476186420, -410559868342291139342, 398014867364435051884, 405296071724458119681, -351310754565662542289, -187791522521265099936, 140160717342289010247, 46778612431374204912, -29168492201670204122, -6374316318038130041, 3287022861871681850, 441626866537395316, -191288673559836344, -12086915535739717, 4530672367783573], [-18225241076803877394, 18677578787028375660, 58840600922971927372, -57709904926601002470, -58121177129369561431, 50875551644113476007, 26951008155860129116, -20278331057027016475, -6719299055051450480, 4216832882426115422, 916354503792581425, -474890744134306278, -63529149729873054, 27620987107450456, 1739613880476431, -653898814567821], [-18213479751581720838, 18677578787028375660, 58838640702101567946, -57709904926601002470, -58121177129369561431, 50875551644113476007, 26951008155860129116, -20278331057027016475, -6719299055051450480, 4216832882426115422, 916354503792581425, -474890744134306278, -63529149729873054, 27620987107450456, 1739613880476431, -653898814567821], [88599863268713580968, -88113331148205643228, -285212960447565670230, 272973521847255931684, 280741064934462981181, -240890934966007223645, -129712942536712800344, 96059841589747052611, 32228305300709613072, -19980925687065254106, -4382238950785207301, 2250734259315229658, 303115201650576348, -130935794410224976, -8285924509613657, 3100242079114577], [363101975930316935296, -353504367066187383884, -1167474063125882771310, 1096868025231990569216, 1147728394339846755949, -968407126713045024321, -529515818232642909092, 386326816150958387783, 131346321914925220744, -80401614076340790046, -17832062238083640769, 9063391346572318730, 1231914240821691860, -527725179776986492, -33646326659730001, 12507240909772965], [106042702582046298700, -104837318910714038052, -341269633737372277150, 324775010444080001192, 335808992886363284979, -286655332333952125587, -155097830554963060684, 114339342138814438977, 38519889889014706292, -23790467262191524218, -5235830759322990715, 2680768089249478598, 362058147223910800, -156009228278353240, -9895392816158751, 3695268078821707]];
    Rf_basisdens := [1, 1, 3920441740718852, 7840883481437704, 15681766962875408, 15681766962875408, 3920441740718852, 15681766962875408, 7840883481437704, 15681766962875408, 15681766962875408, 1960220870359426, 1960220870359426, 7840883481437704, 15681766962875408, 3920441740718852];
    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_8034_a();"
function MakeCharacter_8034_a()
    N := 8034;
    order := 1;
    char_gens := [5357, 1237, 5773];
    v := [1, 1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_8034_a_Hecke(Kf)
    return MakeCharacter_8034_a();
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..(prec+1)]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 2;
    raw_aps := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -1, 0, 0, 0, 0, 0, 0], [1, 0, 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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0], [2, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], [1, -1, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, 0, 0, 1, 0], [0, 0, -1, 1, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0], [3, -1, 0, -1, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, -1, 0, 1, -1, 1, 0, 0, -1, 0, 0, -1], [2, 0, 0, -1, 1, -1, 0, 0, 0, 1, 1, 1, -2, 0, 0, 0], [1, -1, 0, 0, -1, 1, 1, 0, -1, 1, 1, 1, -1, 0, 0, 0], [2, -1, 0, 2, -1, 1, -1, -1, 1, 0, 1, 1, 0, 0, 0, 0], [1, -1, 1, 0, 0, 0, 0, -1, -1, 0, -1, 0, 1, 0, 0, 0], [3, 0, -1, 0, 0, 0, -1, 1, -1, 1, -1, -1, 0, -1, 1, 0], [2, 0, -1, 0, 1, -1, 0, 1, 1, -1, -2, 0, -1, 0, 0, 0], [2, 1, -1, 0, 0, 0, 0, 1, 1, 2, 1, 1, -1, 0, 0, 0], [0, 0, 0, 0, -2, 1, 0, -2, 0, 0, 2, 1, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 1, 1, -1, 3, 0, -1, 0, 1, 1, 1, 1, -1, 1, 0], [1, 1, 0, 0, 0, 1, 0, -1, 0, 0, -1, -1, 2, 0, 0, 0], [1, -1, 0, -2, 2, -1, 0, 0, -1, 0, -1, -1, 1, 1, -1, -1], [1, 1, 0, 2, 0, 2, -1, 2, 1, 2, 1, 1, 0, -1, 1, 1], [2, 1, 0, -1, 2, -2, -2, 2, 1, 0, -1, -1, -1, 0, -1, -1], [1, -3, 2, 2, 0, 3, 0, -1, 1, 1, 1, 3, 0, -1, 0, 0], [-1, 1, -1, 0, 1, -1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0], [3, 0, -1, -1, 1, -1, 0, 0, 1, 1, 0, 2, -1, 2, -1, -1], [1, 0, -1, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, -1, 0, 0], [-1, -2, 2, -1, 0, 2, -1, -1, -1, 1, 0, 1, -1, -1, 0, 0], [2, -2, 2, 1, -1, 2, 0, 0, -1, 1, 2, 0, 0, 1, 1, 1], [-2, -1, 0, -1, -1, -1, 1, -1, -1, -2, 1, -2, 1, 0, 0, 0], [3, 0, -1, 1, 0, 1, -1, 1, 0, 1, 0, 0, 0, 0, 0, 1], [-1, -2, 1, -2, -1, -2, -1, -2, 0, -2, 0, 0, -1, -1, 0, 0], [1, -3, 2, -2, 0, 0, 0, -1, -2, 0, -1, -1, 1, 1, 0, -2], [0, 0, -1, 0, 2, 0, 1, 0, 1, -1, 0, -1, 0, 1, -1, -1], [3, -1, -1, -2, 0, 0, 0, 0, 0, -1, 1, 2, -3, 1, 1, 0], [-1, -2, 0, 0, 1, -1, 0, 0, 1, 1, 0, 1, -1, -1, 1, 0], [1, 0, 1, -3, 2, -3, -2, 0, 2, -1, -2, 0, 0, 0, 0, 0], [2, -2, 2, 1, 1, -1, 0, 0, 0, 1, 0, 0, -1, -1, -1, -1], [-2, -2, 0, 2, 0, 1, -1, 0, 2, -1, 0, -1, 1, 0, 1, -1], [6, -1, -1, 0, 1, -3, 0, -1, 0, -1, -1, -1, -1, -1, -1, -1], [-2, 0, -2, -1, 2, -2, 2, 2, 1, 1, -2, 1, -2, -1, -1, -1], [3, -2, -3, -2, 0, -3, 1, 1, -1, -2, -2, -3, 0, 1, 1, 0], [-1, 1, 1, -1, 0, 0, 2, 0, -2, 0, -1, -1, 1, 1, -1, -1], [-1, 1, -1, 2, -3, 0, 1, -1, 1, -1, -1, 0, 2, -1, -1, 0], [2, -3, 4, 0, 0, 2, 0, -2, -2, 0, 0, 0, 1, 1, 0, 0], [-1, 1, 0, 3, 0, 1, -1, 1, 4, 0, 1, 1, 0, -2, 1, 1], [1, 0, -2, -4, 2, -2, 1, 2, 0, -3, -2, -1, 0, 2, -1, -3], [-2, -1, 0, 4, -1, 3, -1, 0, -1, 2, 2, -1, 2, -1, 0, 1], [-1, 0, -1, 0, -1, 1, 2, 2, -2, 1, 0, -1, -2, 0, 1, 2], [-1, 2, 0, 3, -1, 2, 1, 0, -1, 3, 2, -1, 0, 1, 0, 0], [0, -2, 0, 1, -1, 1, 2, 0, -1, 1, 0, -1, 1, 0, 1, 0], [-2, -1, 1, 3, -1, 1, 1, 0, 2, -2, -1, 0, 1, -1, -1, 1], [4, 0, 2, 0, 1, -1, -2, 0, 0, 2, 0, -2, 1, 1, 0, -1], [1, -1, 0, -2, 0, -2, 1, -2, 0, -2, -1, 1, -2, 0, -1, 1], [0, 0, -2, -1, 1, -4, 1, 1, 1, -2, -1, -1, 2, -1, 0, -1], [-2, 1, 1, -2, -2, 1, -2, -1, -2, 3, 1, -2, 0, 0, 0, 1], [3, 3, -4, 1, -1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 0], [2, -1, 0, 1, -2, 0, 0, 1, -2, 2, -1, -1, 2, -1, 0, 0], [3, 1, -1, 3, 0, 0, 0, -2, 2, -1, 1, 1, -1, -1, 0, 3], [-2, -2, 1, 2, -1, 4, 0, 1, 1, -1, 0, 1, 2, -1, 0, 1], [-4, -1, -3, 2, 0, 0, -1, 1, 3, -1, 1, 1, 0, -3, 1, 1], [4, 0, 1, 3, 0, 4, -3, -2, 1, 1, 2, 2, 0, -1, -1, 0], [-1, -4, 2, 0, 0, 4, 0, -1, 1, 2, 2, 2, -1, 0, 1, 1], [-5, -2, 3, -2, -1, 1, 1, -2, -2, 0, 0, -3, 3, 1, 0, 1], [-8, 2, -1, 1, -2, 0, 2, -2, 0, -2, 2, 0, 2, 0, 0, 1], [0, -3, 0, -2, 0, 1, 0, 0, -3, 3, -1, -1, -3, 2, 1, 1], [3, -2, 2, 2, -1, 2, 0, -1, 1, 0, 2, 1, 0, 1, 0, 1], [-1, -2, 0, -1, -1, 0, 0, -1, -2, -3, 2, -1, -1, -1, 0, 1], [-4, 1, -1, -5, 2, -4, 0, 2, 0, 0, -3, -2, 0, 2, -1, -3], [5, -1, 0, 1, 0, 1, -1, 0, 0, -2, -1, 1, 2, 0, -2, -1], [-8, 1, -2, 2, 0, 2, 2, 2, 1, 2, 1, 0, 2, -1, 1, 2], [-1, -3, 1, 3, 0, 1, 0, 2, 2, 2, 1, 3, -1, -1, 1, -1], [-3, 3, 2, -3, 3, -1, -2, 0, 0, 1, -1, 1, -1, 0, 0, -2], [1, 1, -3, -1, -3, -3, 0, 0, 1, -3, 1, 2, -2, 1, 0, 1], [-2, 5, -4, 4, -2, 2, 1, 3, 2, 1, -1, -2, 3, -1, 1, 1], [0, -1, 1, -3, 1, -2, -1, -2, -2, -3, -3, -2, 1, 3, -3, -1], [-1, 2, -1, -1, 1, -3, 1, 2, 2, -4, -2, 2, -3, 0, 0, -1], [7, -2, 1, 2, -1, -1, 1, -1, 1, 0, 2, 1, -1, 0, -1, 1], [2, 0, 0, -1, 4, -3, -1, 2, 2, 1, -2, -1, 1, 2, -1, -1], [1, 2, 3, -1, 1, 1, -1, 1, 0, 2, 0, -2, 2, 0, -1, 2], [-6, -3, 0, -5, 1, -3, -1, -1, -3, -4, -3, -1, 0, 3, 0, -1], [5, -3, 2, 2, -4, 1, 0, -1, -4, 2, -1, -4, 1, -1, 2, 1], [0, -2, 0, 0, 2, -1, 1, 1, 0, 0, 2, 1, -1, -1, -2, 0], [2, -1, 0, 3, 1, 1, 0, 0, 0, -1, -3, 0, -1, -1, 0, 3], [5, 3, 0, 2, -3, 1, -2, 0, -2, 1, -1, -4, 3, 1, 0, 2], [1, 4, -3, -3, -2, 0, 0, 0, -4, 3, 0, -3, -1, 1, 1, 1], [-3, 2, -2, 5, 0, 3, 1, 1, 2, -1, 3, -1, 1, 1, 1, 1], [-2, -3, 2, -2, -2, 0, -2, -2, 0, 2, 3, 1, -3, -1, 1, 3], [-8, 2, -1, 0, -2, -2, 1, -2, 1, -6, 0, 1, 0, -1, -1, 1], [1, -2, 1, 0, 1, -1, 2, 0, 0, 1, -2, 0, -2, 1, -1, -2], [2, -1, -1, 4, -2, 4, -2, -1, 0, 2, 2, 3, 0, -2, 1, 4], [-6, -2, -2, 2, 1, -1, 1, 2, 0, -2, 1, 1, 0, 0, 1, 1], [8, -5, 1, -1, 3, -1, -1, -2, -1, 0, -1, 2, -1, 0, -1, -3], [0, 1, -2, -3, -1, -3, 2, 0, -1, -3, 0, 3, -3, -2, 1, 0], [2, 6, -4, 2, -1, 1, 1, 3, 4, 3, 2, -1, 0, 0, 1, 3], [2, 1, 2, -2, -1, -1, 0, -3, -1, -1, 3, 0, -1, -1, 1, 0], [1, 3, -1, 1, 0, -1, 2, 0, 3, 2, 2, 4, -3, 0, -2, -2], [-2, 4, -6, 0, -2, -4, 1, 0, 2, -5, 0, -1, 3, 0, 1, 1], [2, 3, 0, 2, -1, 1, 1, 1, 1, 4, 1, -2, 3, 2, -2, 0], [-8, 6, -3, 1, -3, -1, -1, -2, 0, 0, 0, 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[15, 0, -6, 1, 1, -1, 3, 4, 3, -2, 0, 4, -6, -1, 0, 1], [-2, -5, 2, -5, -1, 1, -1, 0, -3, 3, -1, -2, -2, 1, 2, -2], [-10, -6, 2, 2, -3, 7, -2, -6, -5, 1, 0, 0, 3, -2, 1, -1], [6, -3, -3, 1, 2, -5, 1, 2, 1, 2, 1, 6, -6, -1, -3, -2], [-2, -5, 2, -3, 4, -2, 0, -2, -3, 2, -1, -4, -5, 0, 1, -2], [2, 2, -6, -2, -3, -1, 3, -3, 3, -6, 0, -2, 3, -2, -1, 2], [3, 1, 1, -1, 0, 0, -4, 2, -3, 4, -2, -1, -4, 1, 0, 1], [-13, -1, -2, 2, -3, 4, 4, 4, -2, 3, 1, 1, 0, 3, 0, 2], [3, -6, 1, 3, -2, 2, 2, 0, -3, 4, 0, 1, 0, 1, 0, 1], [-3, -4, 0, -5, 4, -4, -2, 3, 3, 2, -4, 2, -5, 0, -1, -3], [7, 0, -2, -2, 3, 1, -1, 0, 2, 2, 1, 3, -2, 0, -3, -4], [20, -7, 1, 5, -3, 6, -1, -4, 1, -1, -1, 4, 0, -1, -1, 1], [-8, 0, 4, -1, -1, 4, -4, -2, 4, -1, -1, -1, 3, 1, 0, 4], [-14, 0, 4, 1, -1, 8, -5, 3, -3, 7, 2, 0, 0, -1, 4, 4], [-1, 4, -4, -4, 3, -5, 2, 1, -5, 2, 0, -2, -1, 2, -3, -4], [-3, -1, -1, 6, -6, 6, 4, -1, 3, -4, 3, 4, 0, 0, 4, 3], [-12, -4, -2, 1, 0, 4, 3, -1, 0, -8, 4, 0, 1, 1, 1, -1], [8, -9, 4, -4, 5, 0, -5, -3, -1, 3, -1, -2, -4, 1, 0, -4], [-8, 0, 6, 1, -5, 1, -1, -7, -4, 4, 6, 1, -2, 1, 1, 2], [10, -5, 3, 3, 1, 0, 3, -1, -4, 0, 3, 0, 0, -1, -4, -2], [-6, -6, 0, -1, -1, 5, -1, -5, -3, 4, 3, -2, 0, 3, -2, 0], [11, 2, 2, 0, 3, 1, -3, 2, -1, 11, 2, 3, -2, 1, -1, -4], [-15, -1, -6, 2, -2, 1, 2, -3, 2, -2, 3, 5, 4, -2, 0, 2], [5, -1, -3, -5, -2, -6, 6, -2, -5, -1, 3, -2, -3, 0, 0, 2], [-4, -3, -2, 7, -5, 1, -1, -3, 6, -4, 6, 6, -2, -2, -3, 4], [-8, 3, -12, -5, 1, -5, 4, 0, 0, -5, -1, 2, 0, 2, -2, 3], [-8, 5, -2, -1, -6, -2, -1, -4, -1, -5, 1, 0, 2, 2, 0, 4], [-7, -1, -5, -1, -2, -4, -2, 2, 4, -12, -1, 2, -1, -5, 1, 0], [-23, -4, -1, -1, 1, -3, 2, 0, 4, -7, -1, 4, 0, 4, -2, -3], [-4, -3, -3, -3, -1, -6, -2, -1, 2, 0, -1, 0, 1, -3, -3, 0], [15, -5, 0, 2, -4, 7, -3, -6, 1, 0, 5, 2, 0, -1, 2, 4], [1, 3, 0, 2, 0, 4, -3, 0, 0, 2, 3, -2, 1, -1, 1, 4], [-2, 2, -2, -6, 2, -6, -3, -3, 3, -1, -2, -3, -2, 1, -2, 2], [10, 5, -6, -1, 1, -3, 0, 4, 5, 1, 0, -1, -1, 4, 3, 4], [18, -1, -4, -4, 5, -8, 3, -1, 1, -6, -7, 0, -4, 5, -4, -2], [-11, 3, -4, 2, 1, -4, 5, 2, 4, -8, 1, 1, -1, 1, -3, 2], [-15, 7, 1, -1, -1, 5, -2, 2, -2, 2, 3, 3, 3, 1, 1, 0], [1, -1, -6, 7, 2, -2, 2, 6, 4, -4, -3, 5, -7, -4, 3, 3], [6, 0, 2, 0, 3, 1, 4, 0, 0, -1, -1, -3, 5, 5, -4, -4], [9, -2, 3, 7, -1, 5, -1, 2, 3, 9, 6, 5, -5, 0, 3, -1], [-5, -3, -5, -6, 4, -8, 4, 4, -2, -4, -3, 2, -3, 2, -1, -5], [15, -4, -3, 7, 0, 4, 0, -2, 6, -8, 4, 6, 3, -3, 0, 2], [-2, -7, 1, 0, 4, -4, 0, 0, -1, -6, 1, 0, -1, 0, -1, -5], [-9, -4, 1, -1, 2, 0, -3, 2, -1, 1, -2, 1, 1, 2, 1, 0], [5, -4, 5, 2, -2, 3, 0, -3, 0, -3, 0, -3, 1, -7, 5, 1], [-13, -2, 4, 6, 1, 5, -2, 1, 0, -3, 2, 7, 0, -2, 0, 1], [5, 4, 2, 4, 0, 0, 3, 0, 2, 3, 4, 3, 2, 0, -3, -1], [1, -1, 2, 4, 2, 5, 3, 2, 3, -1, -1, -2, 4, -1, -2, -4], [4, -5, 5, -2, 1, 0, -2, -3, -4, -1, -3, 3, 3, -3, 1, -5], [-2, 3, -4, 4, -5, -1, 0, 4, -1, 0, -1, -1, 2, -1, 1, 6], [6, -6, -1, 4, -4, 6, 4, -4, -6, 4, 4, -2, 0, 1, 2, 2], [1, -5, 5, -5, 4, 2, -3, 1, 2, -1, -3, 1, -1, 3, -3, 0], [1, 4, -2, 0, 0, -6, 5, 0, -2, -7, -2, -4, 0, 2, -5, -2], [-8, 0, -2, 1, 2, 0, 0, -2, 2, -4, 4, 1, 2, -6, 0, -5], [-9, 5, 0, -3, -5, 1, 0, 1, -1, 1, 1, -3, 0, 3, -1, 3], [8, 0, -8, 1, 3, -1, -1, 4, 3, -2, 6, 2, -2, 1, -2, -2], [2, 9, -6, -4, 4, -6, -2, 6, 2, -6, -7, -4, 5, -1, -1, 0], [13, -9, 2, 4, 0, 4, 2, 0, -1, 0, 1, 3, 0, 0, -1, -5], [-9, 0, -1, 5, -5, -1, 4, -2, 4, -9, 2, 4, 0, -4, -1, 1], [-3, -3, -2, -6, -2, -8, 2, 1, -8, -2, -1, -1, -5, -1, 4, 2], [-7, -2, 7, 3, -1, 2, -4, -1, -4, 6, 2, 1, 0, -2, 2, 0], [-19, -3, -1, -1, 0, 1, 3, -1, 0, 0, -3, 2, -1, -5, -2, -1], [8, 2, 2, -4, 1, -1, 1, 7, -5, -1, -4, -5, -3, 0, 2, -1], [-11, -1, -5, 4, 3, -6, 3, -1, 8, 1, 5, 8, -4, -2, -2, -2], [6, -7, 2, -1, 0, 0, -1, -5, -2, 5, -1, -2, 2, -4, 1, 3], [-1, -4, 1, -3, 0, 1, -2, 2, -1, -2, -2, 2, -1, 2, 4, 4], [-18, 6, -2, -5, -2, -1, 6, -6, -3, -8, 5, 1, 0, 1, -1, 3], [-8, 3, 6, -1, 0, -2, 4, -2, -3, 2, -1, -8, 4, 1, -1, -2], [-2, -3, 10, 2, -4, 8, -2, -2, -1, 2, -1, -2, 6, 3, 1, -2], [-11, 2, 1, -1, 0, -2, 0, 4, -2, -4, -3, 0, -4, -2, 3, 6], [-20, 6, -4, 1, 1, 0, -3, 5, 2, -4, -4, -1, 3, -1, 3, -1], [7, -13, 6, -4, -2, 6, -3, -3, -10, -1, -1, -1, 4, 3, 3, -4], [14, 7, -4, 3, 1, -2, -8, 3, 1, 6, -1, 2, -3, -4, 1, -1], [27, 3, -2, -3, 5, -1, -3, -4, 3, 0, -1, 1, 5, 0, -1, 2], [-1, 0, 5, -9, 0, -4, 0, -1, -7, 5, -2, -2, -3, 4, -2, -2], [0, 7, -4, 2, 0, -7, -1, 2, 5, -2, -1, -8, 6, -3, -2, -1], [-9, -6, 7, 3, 1, 1, 0, 1, -1, -1, 2, -4, -1, -4, -2, -3], [-9, -3, -2, 1, -1, 3, 0, 4, 2, -3, -1, -4, 5, 0, 4, -3], [0, -5, 0, 3, 1, 3, -8, 1, 6, -3, 3, 5, -1, -4, 5, 3], [20, 0, 0, 2, -1, 1, -2, 4, -3, -1, -2, -5, 2, -1, 3, 0], [-25, -1, -2, -2, -1, 5, 8, 2, 1, 1, 1, 3, 0, 1, 2, -1], [11, 6, 2, -7, 4, -1, -4, -1, 7, -4, -2, 6, -2, 1, 1, 3], [-1, -7, -3, 3, 0, 0, -4, 0, 4, -6, -3, 6, -1, -1, 1, 4], [14, -7, 11, 3, 4, 6, -7, -4, 2, 3, -3, 4, -1, -3, 2, 2], [-15, -3, 2, 2, -7, 11, 1, -7, 3, 2, 11, 8, -1, 3, 0, 6], [15, 3, 1, -7, 0, 0, 1, -2, 4, -3, -7, -3, 3, 1, 0, 2], [-20, 14, -7, 2, -1, 1, 3, 1, 4, -4, 6, 1, -4, 3, -1, 3], [12, -6, 0, 2, -2, 5, -3, -1, -1, 8, 2, 3, 4, -3, 2, 6], [-6, 4, 4, -1, 1, 1, -2, 5, -4, 5, -4, -2, 0, -1, 0, -8], [1, -2, 5, -1, -2, 3, 0, -3, -6, -2, -4, -5, 2, 2, -3, 5], [1, 11, 2, 4, -2, -2, -1, 0, -4, 7, 3, -4, -3, -1, 2, -2], [-2, -4, -1, 1, -1, 5, 1, 6, 2, 4, 4, 11, -8, -2, 2, 2], [10, -5, 0, -3, -2, 0, 0, -2, 2, 1, 5, 7, -6, 2, 0, -3], [4, 9, -10, 3, -2, -6, 0, -1, 5, 2, 1, 6, -3, -6, -2, 0], [-7, -1, -1, 1, -4, -2, 5, 1, -3, -3, -1, -5, 6, -3, -1, 4], [8, -4, -1, -2, 4, 0, 5, 6, 3, -3, 0, 1, -2, -1, -1, -1], [-3, -3, 5, 7, -2, 8, 1, -1, 5, 1, 3, 12, -2, -3, 1, 3], [6, -3, 6, -8, -5, -5, 1, -3, -7, -2, -1, -3, -4, 1, 0, -1], [2, 5, -7, 1, -7, 2, 3, -5, -2, -1, 3, 1, 1, -1, -2, 0], [-1, -1, 2, 0, 2, -3, 1, -3, -2, 2, 5, -1, -3, 3, -5, 1], [7, 6, 3, -10, 6, 0, -4, 0, 1, 6, -1, 1, 1, 4, 1, -5], [-2, 3, -1, -1, 4, -4, -2, 3, 5, 0, -2, -1, 2, 3, -3, -2], [11, 5, -4, 1, 2, 0, 2, 7, 1, 0, 3, -3, 0, 3, 0, 2], [7, 7, 3, 2, -5, -3, -3, -6, 5, -4, 1, -2, 3, -3, -3, 5], [-6, 5, -6, -1, 0, -8, 8, -1, 1, -5, 1, -2, -6, 1, 1, 2], [11, -4, 1, -3, -8, 2, 0, -4, -3, 5, 4, -4, 5, 0, 0, 2], [7, 2, 0, 4, 0, 2, -5, 0, 1, -1, 4, -1, -1, -2, 3, 5], [6, -3, -1, -7, 6, 1, 1, 0, 1, -6, -1, 2, -1, 4, 1, 2], [-10, 3, -4, -3, -1, -3, 3, -3, -2, 5, 7, 6, -2, 0, -1, -4], [5, 0, 6, 2, 4, -2, -3, 3, 0, 7, -5, 4, -2, -2, 1, -4], [1, -3, 4, -3, -1, 1, 6, -4, -4, -1, -1, -1, 7, 2, -4, 0], [-9, 0, -4, 4, 1, 7, 4, 3, -4, 3, 4, 4, 0, 4, 0, -4], [-5, -8, -3, 0, 0, 3, 4, -2, -3, -2, 0, 2, 4, -1, 0, 2], [-5, 1, -5, 9, -6, 0, -1, 1, 7, -1, 3, 6, -3, -2, -3, 1], [-2, 8, 2, -1, 7, -1, -1, 5, 0, 4, -2, 5, -1, 1, -1, -5], [-9, 2, -5, 4, 3, -5, 2, 2, 4, -1, 0, 4, -4, 1, -5, -4], [-1, -5, 6, 4, -3, 11, -4, -3, -2, 7, 8, 6, -5, 1, 2, 0], [0, 6, -6, -7, 2, -8, 2, 1, -3, -10, -8, -7, 0, -1, -1, -1], [-13, 0, -5, -5, 2, -6, 3, 3, -6, -3, -2, -7, -2, 2, 2, 0], [18, 1, 5, -2, 3, -1, -8, 3, 0, 7, -3, -1, 1, -1, 1, -3], [-7, 6, -5, 2, -4, 5, 4, 2, -5, 1, -2, -2, 5, 0, 4, 2], [6, 5, 0, 0, -1, 5, 0, -4, 3, 1, -2, -3, 6, 1, -1, 0], [1, 2, 0, 0, 1, -1, 7, -5, 2, -8, 2, -5, 5, 1, -1, 0], [8, 2, 8, 1, -1, -1, 0, -4, -4, -1, -7, -8, 7, -1, -2, 3], [5, 6, -4, 1, 0, -2, 3, 4, 6, 3, 2, 8, -7, -1, -3, 0], [19, 3, 4, -4, 4, -2, -3, 0, -3, 2, -3, -2, 0, 3, 1, -4], [2, 7, 0, -3, -2, -2, 6, -3, 2, -6, 5, 3, -1, 5, -2, 1], [3, -1, -1, -11, 2, -8, 0, -1, 0, 5, -3, 0, -5, -1, 3, 0], [21, -5, 0, -1, 5, -9, -1, -1, 1, -2, -1, 2, -7, 1, -2, -4], [0, -8, 10, 3, -6, 10, -2, -5, -1, 6, 6, 6, 1, -1, 3, 5], [16, 3, 3, -2, 5, -5, -2, -3, 7, 0, 3, 4, 0, -1, 2, 0], [5, -5, -7, 2, -1, -9, 0, 0, 4, -8, 1, 1, -6, -2, -3, 0], [-5, -11, 7, 2, -1, 9, -3, -1, -1, 6, 2, 3, 5, 4, 3, 3], [5, 1, 3, 1, 5, 2, -6, 0, 7, 1, -1, 1, 0, -3, 0, 0], [-3, 4, -7, 0, 1, -5, 0, 6, 2, 3, -7, -2, -2, -2, 6, 1], [6, -2, -2, 3, -9, 4, 2, -5, -2, 0, 2, 3, -1, 3, 0, 4], [10, 2, 0, -2, 3, 2, -3, -3, 6, -6, -2, 3, 0, 2, -5, -1], [24, -3, 2, -5, 2, -10, -1, 1, 4, -9, -3, -1, -2, -4, -5, -4], [5, -8, -2, 6, 3, -1, 3, 5, 2, 4, -2, -2, 0, 3, 1, 0], [-3, 4, 2, -1, -6, 2, -4, -2, 2, 4, 6, 1, 1, -3, 6, 4], [-8, -4, 5, -2, 3, 5, -4, -2, 0, 5, 0, 1, 2, 1, 3, -2], [10, 7, 1, 3, -2, 3, -5, -2, 7, -2, 1, 7, 0, 3, 3, 3], [9, 0, 0, -2, 5, -1, -5, 6, -1, 0, -4, -6, 1, -4, 4, -1], [11, -1, -1, 1, 3, 1, 0, -2, 5, -7, -3, 5, 3, -2, 0, -2], [19, 5, -3, 9, 2, 5, 0, 0, 11, -4, -2, 2, 6, -5, 0, 8], [4, 7, -2, -6, 0, -1, 3, 1, -3, -4, -7, -2, -1, -2, 5, -1], [6, -5, 6, 3, 2, 1, 3, 3, 4, 0, -1, 7, -4, 0, -1, -2], [4, 9, -4, 10, -3, 5, 2, 1, -1, 3, 1, 3, -2, 1, -1, 4], [-16, 5, -3, 9, -10, 6, 3, -4, -2, 3, 5, -2, 5, -3, 2, 4], [11, -14, 7, -10, 5, -1, -3, 1, -6, 4, -4, 0, -6, 0, 1, -8], [5, 0, -4, 0, 2, -8, 2, 0, -3, -9, 2, -10, -3, 2, 1, 3], [-8, 3, -5, 1, -8, 4, 4, 0, 2, 3, -1, -2, 7, 1, 0, 1], [27, -7, 7, 2, -1, 12, -4, 0, -3, 4, -1, -4, 2, 1, 0, -3], [0, -1, -9, 3, 2, -4, -2, 3, 7, -4, 3, 6, -3, -2, 2, 1], [9, 6, -4, -7, -1, -8, 3, -1, 3, -11, -2, 0, -2, 5, 1, -1], [-9, 5, -7, 1, -1, 1, 2, 0, -3, -3, -5, -1, 6, -3, -2, 4], [-9, 11, -4, 3, -3, 1, 6, -1, 3, 5, 1, 4, 3, 0, -3, 0], [-19, 16, -9, 5, 0, -7, 4, 4, 3, 1, 6, 1, -6, -1, -2, -5], [10, 10, -4, 1, 5, -2, -3, 5, 2, 2, 0, 2, 1, -5, 3, 2], [-15, 10, 5, 0, 5, -1, -6, 3, 1, 1, -2, 6, -4, -1, 0, -1], [-3, -1, -3, 6, -2, -2, 4, 1, -3, -2, 1, -5, 2, -2, -2, -2], [-5, 2, 5, 1, -5, 7, -3, 2, 4, 6, 4, 2, -1, 2, 4, 5], [-5, -2, 2, -3, 2, -5, 5, -2, -1, -1, -3, -3, -4, 7, -4, -5], [-10, 14, 3, 3, 3, 5, 1, 6, 4, 2, -2, -2, 2, 0, 2, -3], [3, 3, 0, 0, -6, -2, -2, -5, 4, -4, -1, 2, 1, -5, 2, 3], [12, 11, -2, 1, 2, -8, -4, -4, 13, -6, -3, 0, -1, -2, -3, 6], [8, 1, 0, 3, 3, 3, -6, 0, 6, -1, -1, 6, -4, -4, 2, 5], [8, -3, -1, -4, 2, -6, 1, 0, 0, -1, 4, 4, -8, -4, 1, 4], [1, -2, 1, 7, -2, 6, 5, -2, -4, -1, 1, -7, 8, 2, 0, 2], [16, 2, -1, -1, 6, -10, -3, 0, 5, -9, -1, -2, 1, 4, -8, -6], [7, -2, 8, 4, -4, 8, 4, -8, -4, 0, 4, -1, 8, -1, -4, 3], [-10, -4, -7, -6, -4, -4, -2, -6, 4, -4, 6, 1, -3, -2, 2, 1], [10, -4, 8, -2, 4, 2, 1, 3, -5, -1, 2, -6, 0, 5, -2, -5], [-4, -2, 2, 4, 2, 0, -3, -1, 0, -4, 4, 6, -4, -8, -1, -1], [10, -9, 5, 1, 5, -6, 4, 1, 2, -8, -1, 6, 0, -8, -3, -4], [-3, 9, 3, -2, -1, -8, -5, -2, 3, -3, -3, 1, 3, -4, -1, 3], [-9, 6, 2, 4, -3, 8, -3, 0, -5, 2, 6, 5, -2, -5, 6, 6], [17, -2, 3, -4, 6, 2, -2, 6, 5, 0, 0, 3, 2, 1, 2, -3], [-9, -6, 13, -8, 2, -2, -5, -3, 0, 5, -4, 3, -6, -2, 2, 2], [-1, -4, -3, -1, -1, -1, 1, 0, 3, -4, -3, 5, -1, 4, 3, 7], [17, 12, -4, 1, -2, 0, 6, -1, 5, -4, 0, 4, 0, -1, -1, -1], [-7, -2, 8, -11, 3, 1, -6, -1, -6, 7, 0, -4, -1, 3, 2, -2], [-25, 4, 3, 3, 0, -1, -4, 4, 4, -2, -5, 0, 0, -2, -3, -4], [11, 3, 1, -5, 4, -4, 1, 6, 1, -1, -2, -4, -4, 3, 1, 5], [0, 12, -11, -7, 5, -15, 5, 2, 2, 0, 0, 1, -4, 0, -6, -6], [20, 0, 1, -8, -3, 5, -2, -3, -8, 3, -2, 0, 1, 7, 2, 2], [-21, 10, 6, -1, -3, 7, 2, 0, -5, 9, 6, -8, 5, 4, -1, 4], [-4, 0, -4, 3, 3, 2, -1, 3, 4, -8, -4, -3, -1, -1, -1, 1], [2, 5, 4, -6, 10, -2, 0, 6, 3, -6, -3, -3, 3, 6, -1, -7], [10, 4, -3, 9, 2, 6, 4, 1, -2, 0, -2, 6, 3, -3, -3, -1], [27, -6, 7, -5, 3, 5, -4, 2, -1, 5, 0, -3, 3, -2, 3, -4], [-8, -1, -2, 0, -2, 0, 2, -1, -8, -2, -1, -4, 2, -5, 0, 3], [0, -7, -7, 5, 2, 0, 1, 0, 4, -5, -1, 3, 7, -1, -2, 5], [5, -9, 4, 9, 1, 5, -1, 2, 0, 2, 5, 6, -3, -1, 1, -5], [-26, -2, 6, -4, 0, -4, 0, 2, -3, -7, -4, -7, 4, 5, -1, -3], [-7, 6, 1, -1, 5, -1, -4, -1, 7, -5, -2, 0, 4, 2, -4, 0], [15, 4, -11, -10, -2, -14, 5, -2, -4, -12, -4, -5, 1, 3, 0, 0], [3, -7, 3, -5, 1, 8, -5, 6, -9, 5, -1, -1, -4, 1, 5, -1], [-6, 6, -2, 5, -2, -4, -1, 2, 4, -9, -2, -9, 6, -5, 3, 7], [11, -9, -4, 4, 1, -3, -1, 0, 1, -6, -5, 1, -6, -1, 1, 2], [0, 3, -9, 0, 8, -4, 1, 13, 2, -1, -6, 0, -2, 2, -2, -2], [-8, 0, 4, -10, 5, -2, 4, 4, 1, -1, -2, 5, -5, 4, 1, 0], [-6, 2, 6, 0, -6, -2, 0, -8, -2, 0, 4, 4, -4, -4, 0, 0], [-17, -4, -5, 5, -5, -5, -5, -1, 0, -6, 2, 7, -2, -8, 1, 3], [-2, 0, 2, -9, 3, -1, 1, -1, 0, 0, -7, -3, 7, 3, -4, -3], [-16, 9, 3, -1, -6, -1, 1, -4, -6, 3, 7, -3, 0, 5, -4, 2], [18, 1, 2, 4, -8, 8, -2, -3, 6, 6, 3, 0, 1, -1, 4, 6], [12, 0, -1, -4, -2, 2, -1, 8, -2, -5, -3, -8, 3, 1, 6, 2], [-2, -13, -2, 15, -6, 8, 3, -4, 6, -7, 9, 7, 0, -3, 2, 3], [-10, 7, -1, 4, 6, -7, -1, 4, 2, -1, 1, 3, -4, 0, -8, -5], [1, -4, 0, -5, 5, -6, -1, -7, 2, -8, -6, -2, -1, 4, -1, 2], [14, 4, -8, -4, 3, -5, -2, 4, -8, -2, -8, -8, 3, 3, 0, -1], [0, 1, -6, 0, -2, -5, 1, 4, -5, -5, -7, -11, 6, 1, 4, 2], [-2, -10, 0, -2, -3, 1, 5, -1, -6, 2, 0, 3, 1, 3, 3, -9], [1, 7, -10, 2, -11, -3, 5, -1, -3, -2, 7, 0, 0, -2, 2, 4], [-15, -5, 0, -2, -6, 0, 5, -4, -3, 3, -1, -7, 6, 5, 0, 5]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_8034_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_8034_2_a_bd();".
// 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_8034_2_a_bd(:prec:=16)
    chi := MakeCharacter_8034_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 1;
    while true do
        trunc_vec := Vector(Kf, [0] cat [f_vec[i]: i in [1..prec]]);
        B := Basis(S, prec + 1);
        S_basismat := Matrix([AbsEltseq(g): g in B]);
        if Rank(S_basismat) eq Min(NumberOfRows(S_basismat), NumberOfColumns(S_basismat)) then
            S_basismat := ChangeRing(S_basismat,Kf);
            f_lincom := Solution(S_basismat,trunc_vec);
            f := &+[f_lincom[i]*Basis(S)[i] : i in [1..#Basis(S)]];
            return f;
        end if;
        error if prec eq maxprec, "Unable to distinguish newform within newspace";
        prec := Min(Ceiling(1.25 * prec), maxprec);
    end while;
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8034_2_a_bd();".
// 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_8034_2_a_bd( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-66432, 94528, 185524, -296326, -122680, 270913, 19731, -113788, 6763, 25368, -3150, -3101, 498, 196, -36, -5, 1]>,<7,R![31456, 84352, -301910, -921151, 136818, 1185952, -137971, -487663, 80924, 85712, -17210, -7137, 1592, 277, -66, -4, 1]>],Snew);
    return Vf;
end function;