
// Make newform 320.6.c.k in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_320_c();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_320_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_320_6_c_k();".
// 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_320_6_c_k();".
// 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 := [588289, 0, 15975501, 0, 3245664, 0, 254984, 0, 9528, 0, 165, 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], [2177766131, 0, -128060923628, 0, -20045402992, 0, -1102611568, 0, -24454244, 0, -170020, 0], [-34380714880, 0, -362353494656, 0, -52857554368, 0, -2780210368, 0, -60010112, 0, -411520, 0], [-96708608876, 0, -4837404881512, 0, -711962887784, 0, -37088343272, 0, -786315016, 0, -5323964, 0], [0, 2576633734216, 0, -1019260920568, 0, -175028468600, 0, -9277834112, 0, -195210058, 0, -1310906], [0, 8621360914288, 0, 2688495819008, 0, 284453317984, 0, 13567743616, 0, 286234304, 0, 1957360], [0, 38667851889478, 0, -57637006550236, 0, -8947051389500, 0, -471366569900, 0, -10019691676, 0, -67875062], [17382114505340, 19752862444721, 421179959346250, 74871373684486, 62703306419780, 11012560403798, 3308494583420, 581043147182, 70984599790, 12477922798, 484184090, 85161215], [-17382114505340, 19752862444721, -421179959346250, 74871373684486, -62703306419780, 11012560403798, -3308494583420, 581043147182, -70984599790, 12477922798, -484184090, 85161215], [0, -173990789836964, 0, 109318479348956, 0, 19636262498968, 0, 1119493454860, 0, 25169463050, 0, 175955038], [-240122345851648, -317433643570484, -2626945209511376, -2234157186356428, -401095958765632, -329909822608880, -21714641655616, -17374777187732, -475746157328, -372595783468, -3284674432, -2541138896], [-240122345851648, 317433643570484, -2626945209511376, 2234157186356428, -401095958765632, 329909822608880, -21714641655616, 17374777187732, -475746157328, 372595783468, -3284674432, 2541138896]];
    Rf_basisdens := [1, 200642913, 66880971, 200642913, 51297704757, 51297704757, 153893114271, 153893114271, 153893114271, 153893114271, 153893114271, 153893114271];
    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_320_c();"
function MakeCharacter_320_c()
    N := 320;
    order := 2;
    char_gens := [191, 261, 257];
    v := [2, 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_320_c_Hecke();"
function MakeCharacter_320_c_Hecke(Kf)
    N := 320;
    order := 2;
    char_gens := [191, 261, 257];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 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, 1, 0, 0, 0, 0, 0, 0, 0], [5, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -3, 11, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 1, 7, 7, 0, 0, 0], [0, 0, 1, -3, 0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, -36, 0, 0, 0, 0, 1, -1, 1], [1740, 106, 0, 0, 0, 0, 0, -42, 42, 0, 0, 0], [0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -7, -7], [0, 0, 0, 0, 0, 98, 118, -53, -53, 0, 0, 0], [-9105, -103, 0, 0, 0, 0, 0, 80, -80, 0, 0, 0], [0, 0, 0, 0, -261, 0, 0, 0, 0, 26, -4, 4], [0, 0, 0, 0, -42, 0, 0, 0, 0, -101, -5, 5], [0, 0, 0, 0, 0, 317, 65, -68, -68, 0, 0, 0], [0, 0, 63, -41, 0, 0, 0, 0, 0, 0, -3, -3], [-5820, 1322, 0, 0, 0, 0, 0, -221, 221, 0, 0, 0], [0, 0, 0, 0, 867, 0, 0, 0, 0, -210, 16, -16], [0, 0, 26, 74, 0, 0, 0, 0, 0, 0, 43, 43], [0, 0, 0, 0, 0, 672, 453, 565, 565, 0, 0, 0], [0, 0, -130, 64, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, -1509, 0, 0, 0, 0, 78, 32, -32], [-1040, 2190, 0, 0, 0, 0, 0, -622, 622, 0, 0, 0], [0, 0, 0, 0, 0, 100, 965, 487, 487, 0, 0, 0], [-24248, -3650, 0, 0, 0, 0, 0, -510, 510, 0, 0, 0], [0, 0, 0, 0, -4272, 0, 0, 0, 0, -147, 25, -25], [0, 0, 0, 0, 465, 0, 0, 0, 0, -252, -48, 48], [-63454, -224, 0, 0, 0, 0, 0, -83, 83, 0, 0, 0], [0, 0, 0, 0, 0, 4272, 568, -68, -68, 0, 0, 0], [0, 0, 0, 0, 1374, 0, 0, 0, 0, 151, -116, 116], [0, 0, 13, -351, 0, 0, 0, 0, 0, 0, 53, 53], [0, 0, 0, 0, 0, -5242, 728, -1354, -1354, 0, 0, 0], [0, 0, -46, -433, 0, 0, 0, 0, 0, 0, -236, -236], [84344, -6714, 0, 0, 0, 0, 0, 315, -315, 0, 0, 0], [0, 0, -122, 602, 0, 0, 0, 0, 0, 0, -124, -124], [0, 0, 0, 0, 0, 10284, 4414, 569, 569, 0, 0, 0], [0, 0, 0, 0, -18087, 0, 0, 0, 0, -2032, 10, -10], [0, 0, 0, 0, 4908, 0, 0, 0, 0, 2113, 45, -45], [0, 0, 0, 0, 0, -1534, -5762, -571, -571, 0, 0, 0], [0, 0, -766, -23, 0, 0, 0, 0, 0, 0, 154, 154], [-21692, 17018, 0, 0, 0, 0, 0, 3718, -3718, 0, 0, 0], [0, 0, -428, -472, 0, 0, 0, 0, 0, 0, 134, 134], [0, 0, 0, 0, 0, 4004, -3541, 3393, 3393, 0, 0, 0], [0, 0, 0, 0, 0, 9125, 4319, -6022, -6022, 0, 0, 0], [0, 0, 910, -646, 0, 0, 0, 0, 0, 0, 239, 239], [0, 0, 541, 37, 0, 0, 0, 0, 0, 0, -127, -127], [0, 0, 0, 0, -18150, 0, 0, 0, 0, 3163, 104, -104], [0, 0, 0, 0, 16257, 0, 0, 0, 0, -280, -6, 6], [912920, 1774, 0, 0, 0, 0, 0, 4498, -4498, 0, 0, 0], [0, 0, 0, 0, 0, -5568, -1459, -12123, -12123, 0, 0, 0], [0, 0, 652, 1160, 0, 0, 0, 0, 0, 0, -223, -223], [-544645, 1981, 0, 0, 0, 0, 0, 7192, -7192, 0, 0, 0], [0, 0, 598, -941, 0, 0, 0, 0, 0, 0, -646, -646], [0, 0, 0, 0, 0, -32814, 9312, -6424, -6424, 0, 0, 0], [0, 0, 0, 0, -5376, 0, 0, 0, 0, -1959, -554, 554], [115044, -20102, 0, 0, 0, 0, 0, 6331, -6331, 0, 0, 0], [0, 0, -114, -56, 0, 0, 0, 0, 0, 0, -441, -441], [0, 0, 0, 0, 0, 9394, -2298, -14281, -14281, 0, 0, 0], [328825, 40315, 0, 0, 0, 0, 0, 486, -486, 0, 0, 0], [0, 0, 0, 0, 15357, 0, 0, 0, 0, 5752, -522, 522], [0, 0, 0, 0, 0, -31194, -35956, 5277, 5277, 0, 0, 0], [0, 0, 0, 0, -9681, 0, 0, 0, 0, -918, -1084, 1084], [0, 0, 480, -3614, 0, 0, 0, 0, 0, 0, -1692, -1692], [0, 0, 0, 0, 0, -16710, 18100, -15874, -15874, 0, 0, 0], [0, 0, 0, 0, 0, 56067, -8943, 40678, 40678, 0, 0, 0], [0, 0, -863, 2787, 0, 0, 0, 0, 0, 0, 1859, 1859], [0, 0, 0, 0, 0, 10754, -23706, 13974, 13974, 0, 0, 0], [0, 0, 0, 0, -116577, 0, 0, 0, 0, -10202, -522, 522], [964720, 62526, 0, 0, 0, 0, 0, -6910, 6910, 0, 0, 0], [0, 0, 0, 0, 0, 58856, 25814, 5962, 5962, 0, 0, 0], [0, 0, -2544, -330, 0, 0, 0, 0, 0, 0, -924, -924], [0, 0, 0, 0, 49026, 0, 0, 0, 0, 2963, 770, -770], [0, 0, 0, 0, 0, -28922, -766, -26605, -26605, 0, 0, 0], [0, 0, 2344, -2989, 0, 0, 0, 0, 0, 0, -1042, -1042], [0, 0, 0, 0, 94890, 0, 0, 0, 0, 14115, 778, -778], [972576, 21470, 0, 0, 0, 0, 0, 18491, -18491, 0, 0, 0], [0, 0, 0, 0, 0, 64595, -3831, -1822, -1822, 0, 0, 0], [-505908, 20930, 0, 0, 0, 0, 0, -61794, 61794, 0, 0, 0], [1970171, -92603, 0, 0, 0, 0, 0, 30860, -30860, 0, 0, 0], [0, 0, -2432, -291, 0, 0, 0, 0, 0, 0, 2900, 2900], [1152740, 55762, 0, 0, 0, 0, 0, -10281, 10281, 0, 0, 0], [0, 0, -2524, -1360, 0, 0, 0, 0, 0, 0, 1255, 1255], [0, 0, 0, 0, 0, 60182, -47205, 63725, 63725, 0, 0, 0], [0, 0, 2956, -5902, 0, 0, 0, 0, 0, 0, 680, 680], [0, 0, 0, 0, 108213, 0, 0, 0, 0, 10984, -2192, 2192], [1698219, 138845, 0, 0, 0, 0, 0, -18208, 18208, 0, 0, 0], [0, 0, 0, 0, 0, 2718, -51010, -6568, -6568, 0, 0, 0], [-5480728, 112262, 0, 0, 0, 0, 0, -1606, 1606, 0, 0, 0], [0, 0, 0, 0, 5466, 0, 0, 0, 0, -22945, -1607, 1607], [0, 0, 0, 0, 84057, 0, 0, 0, 0, 19856, -1004, 1004], [0, 0, 7330, -7544, 0, 0, 0, 0, 0, 0, -2764, -2764], [0, 0, 0, 0, -242304, 0, 0, 0, 0, 11977, -322, 322], [0, 0, 4837, -6157, 0, 0, 0, 0, 0, 0, 1769, 1769], [0, 0, -8880, 449, 0, 0, 0, 0, 0, 0, -3168, -3168], [0, 0, 0, 0, 179064, 0, 0, 0, 0, 38285, 861, -861], [3191580, -104966, 0, 0, 0, 0, 0, -7482, 7482, 0, 0, 0], [-1561022, 163672, 0, 0, 0, 0, 0, 2408, -2408, 0, 0, 0], [0, 0, 0, 0, 116073, 0, 0, 0, 0, -23340, 666, -666], [-544268, -231982, 0, 0, 0, 0, 0, 10286, -10286, 0, 0, 0], [0, 0, 0, 0, 276501, 0, 0, 0, 0, -44508, 1394, -1394], [0, 0, 0, 0, 0, -195056, -85578, 65685, 65685, 0, 0, 0], [0, 0, 0, 0, -175911, 0, 0, 0, 0, 41944, 1062, -1062], [9625859, 187277, 0, 0, 0, 0, 0, -49356, 49356, 0, 0, 0], [0, 0, 9344, -9349, 0, 0, 0, 0, 0, 0, -4160, -4160], [0, 0, 0, 0, 0, -42048, 130642, -101626, -101626, 0, 0, 0], [0, 0, 0, 0, -167481, 0, 0, 0, 0, -4730, 5030, -5030], [0, 0, 0, 0, 0, -5498, -36508, -50880, -50880, 0, 0, 0], [0, 0, 4840, 4454, 0, 0, 0, 0, 0, 0, 6671, 6671], [-186635, 1927, 0, 0, 0, 0, 0, 53418, -53418, 0, 0, 0], [0, 0, 0, 0, 421566, 0, 0, 0, 0, -15157, 1519, -1519], [0, 0, 0, 0, 0, -229269, 53495, -83438, -83438, 0, 0, 0], [0, 0, 0, 0, 0, 150566, 131143, -80949, -80949, 0, 0, 0], [0, 0, -7905, 12451, 0, 0, 0, 0, 0, 0, 13629, 13629], [0, 0, -2962, 8658, 0, 0, 0, 0, 0, 0, 5584, 5584], [5601335, -146695, 0, 0, 0, 0, 0, 1204, -1204, 0, 0, 0], [0, 0, 0, 0, -318957, 0, 0, 0, 0, 45606, 5478, -5478], [0, 0, 0, 0, -287076, 0, 0, 0, 0, -80067, 2526, -2526], [0, 0, 0, 0, 0, -13383, 142697, 34602, 34602, 0, 0, 0], [0, 0, 11466, -11591, 0, 0, 0, 0, 0, 0, -768, -768], [2127390, 160468, 0, 0, 0, 0, 0, 99925, -99925, 0, 0, 0], [0, 0, 0, 0, 0, -334428, -2839, -159005, -159005, 0, 0, 0], [0, 0, 0, 0, 0, -50153, -239639, -40856, -40856, 0, 0, 0], [0, 0, 0, 0, -6117, 0, 0, 0, 0, -4350, 6258, -6258], [0, 0, 3469, -9611, 0, 0, 0, 0, 0, 0, -5641, -5641], [3786210, -324208, 0, 0, 0, 0, 0, -117019, 117019, 0, 0, 0], [1251620, 196234, 0, 0, 0, 0, 0, 87798, -87798, 0, 0, 0], [0, 0, -4610, 17136, 0, 0, 0, 0, 0, 0, -3451, -3451], [0, 0, 0, 0, -623832, 0, 0, 0, 0, 32873, -1666, 1666], [0, 0, 0, 0, 0, -248088, -50240, -227553, -227553, 0, 0, 0], [0, 0, 14566, -22875, 0, 0, 0, 0, 0, 0, -1078, -1078], [0, 0, 0, 0, -528444, 0, 0, 0, 0, 71397, -6866, 6866], [0, 0, -13442, -8148, 0, 0, 0, 0, 0, 0, 9566, 9566], [0, 0, 0, 0, 0, -34008, 25332, -63007, -63007, 0, 0, 0], [-12576588, -262286, 0, 0, 0, 0, 0, -92754, 92754, 0, 0, 0], [2701810, -398528, 0, 0, 0, 0, 0, 176320, -176320, 0, 0, 0], [0, 0, 0, 0, 0, 495029, -52827, 28956, 28956, 0, 0, 0], [0, 0, 0, 0, 262683, 0, 0, 0, 0, 147486, -4140, 4140], [0, 0, 0, 0, 0, 167383, -8693, -35524, -35524, 0, 0, 0], [-8340910, -38392, 0, 0, 0, 0, 0, -39496, 39496, 0, 0, 0], [0, 0, 18802, 16735, 0, 0, 0, 0, 0, 0, 19274, 19274], [-2124750, 478360, 0, 0, 0, 0, 0, -154815, 154815, 0, 0, 0], [0, 0, 0, 0, 603012, 0, 0, 0, 0, 18049, -603, 603], [0, 0, 0, 0, -621933, 0, 0, 0, 0, 66066, 5102, -5102], [315004, -111166, 0, 0, 0, 0, 0, 109643, -109643, 0, 0, 0], [0, 0, 2558, -4642, 0, 0, 0, 0, 0, 0, 9832, 9832], [0, 0, 0, 0, 0, -345345, 80877, 170784, 170784, 0, 0, 0], [0, 0, 0, 0, 0, 471158, -212314, 401276, 401276, 0, 0, 0], [0, 0, -2887, 34623, 0, 0, 0, 0, 0, 0, 14521, 14521], [0, 0, 0, 0, 183774, 0, 0, 0, 0, -56685, 5609, -5609], [0, 0, 0, 0, 0, 273390, -265300, 32527, 32527, 0, 0, 0], [-4216775, 716787, 0, 0, 0, 0, 0, -61294, 61294, 0, 0, 0], [0, 0, 0, 0, 80769, 0, 0, 0, 0, -139480, -4792, 4792], [0, 0, 0, 0, -1005276, 0, 0, 0, 0, -17091, -1874, 1874], [0, 0, 0, 0, -592035, 0, 0, 0, 0, 51760, 10266, -10266], [0, 0, -34352, 32192, 0, 0, 0, 0, 0, 0, 1913, 1913], [0, 0, 54084, -3178, 0, 0, 0, 0, 0, 0, -25425, -25425], [1898731, -1185987, 0, 0, 0, 0, 0, -4368, 4368, 0, 0, 0], [0, 0, 0, 0, 0, -728182, 259933, -311603, -311603, 0, 0, 0], [-9484292, 404394, 0, 0, 0, 0, 0, -21674, 21674, 0, 0, 0], [0, 0, 0, 0, -637617, 0, 0, 0, 0, 50386, -3878, 3878], [0, 0, 0, 0, 0, 796482, -105270, 373792, 373792, 0, 0, 0], [0, 0, 0, 0, -790200, 0, 0, 0, 0, 73917, -497, 497], [0, 0, 35125, 8827, 0, 0, 0, 0, 0, 0, -19459, -19459], [0, 0, 0, 0, 0, -169442, -473381, 233381, 233381, 0, 0, 0], [0, 0, 0, 0, 1585764, 0, 0, 0, 0, -95979, -5856, 5856], [0, 0, -4776, -2952, 0, 0, 0, 0, 0, 0, 6012, 6012], [0, 0, 0, 0, 0, 589797, 238517, 34468, 34468, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_320_c_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_320_6_c_k();".
// 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_320_6_c_k(:prec:=12)
    chi := MakeCharacter_320_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_320_6_c_k();".
// 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_320_6_c_k( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_320_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,6,sign)));
    Vf := Kernel([<3,R![24038400, 0, 350800, 0, 1148, 0, 1]>,<11,R![-6940560693657600, 0, 138141388800, 0, -746112, 0, 1]>],Snew);
    return Vf;
end function;