
// Make newform 1170.2.bj.c in Magma, downloaded from the LMFDB on 04 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_1170_bj();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1170_bj_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_1170_2_bj_c();".
// 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_1170_2_bj_c();".
// 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 := [2197, -338, -1196, 190, 104, 154, 98, -134, 8, 34, -8, -2, 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], [-81183629852, -128185173545, 33307875431, 8165110694, 5740233327, -4655211661, -6489146722, 4513282461, -97338749, -591783880, 163110633, 203419], [-399707750949, -110551992590, -345701461353, 51767136278, 38321129974, -68535056482, 1368363861, -11046550568, 2834573637, 1099642740, -1446867854, 99774878], [-618192439839, -98318215515, -28687118858, -8309942667, -35262141211, 18436259198, -29967292429, -2513656023, 7036618932, -2051209685, -454030419, 120243408], [11867687, -4439955, -7481036, 77961, -940887, 1844066, 35557, -817691, 233294, 57555, -37023, 4036], [-1308690012227, -68215142970, 189862006481, 204958669994, 94378041302, -70650734586, -49422223697, 45609137136, 1843354751, -5882189980, 1358027358, 164152294], [-997979945989, -141527922965, 197417975542, 124582190083, 13460230639, -37282009602, -5697780079, 2577608327, 8639610832, -1722573835, -958108569, 480376508], [21026586399, -2866001996, -7949637689, -1535131351, -486856544, -1392260235, 1195412299, -6720278, -603932751, 118225633, 44665642, -23159569], [460186493, -57773591330, -120820074499, -73287704061, 45266458632, -30747713501, 6108999933, 2310806556, -6207967149, 1242595595, 346656978, -236542471], [880210105411, 441927290935, -49363987858, -129070461767, -52841609661, 41904457048, 45918505121, -18449268373, -11841029268, 5382274615, 553303131, -632187142], [-144016360059, -286784071080, 100602839757, 27228013423, 35457807644, 21841076813, -25465804119, -4093093078, 9975044447, -1143072025, -1004615314, 320232543], [27977691092, 390356046795, 37700985074, -402415418899, -23732163042, -9821523994, 30148216612, 10960029469, -25210679196, 3624161555, 2460612632, -1027654074]];
    Rf_basisdens := [1, 63907274600, 415397284900, 415397284900, 11796200, 415397284900, 415397284900, 16615891396, 166158913960, 415397284900, 166158913960, 415397284900];
    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_1170_bj();"
function MakeCharacter_1170_bj()
    N := 1170;
    order := 6;
    char_gens := [911, 937, 1081];
    v := [6, 3, 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_1170_bj_Hecke();"
function MakeCharacter_1170_bj_Hecke( : Kf := false)
    N := 1170;
    order := 6;
    char_gens := [911, 937, 1081];
    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], [0, 0, 0, 0, -1, 0, 0, 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 := 2;
    raw_aps := [[-1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 1, -1, -1, 1, 1], [1, -1, 0, 0, 0, 1, -1, 1, -1, -1, 1, 0], [3, 1, 0, 0, 2, -1, 0, 1, -2, 0, 0, 1], [-1, 2, 0, 0, 0, -1, -1, -1, -1, -1, 1, -1], [-1, 0, -2, 0, -1, 0, 0, -1, 2, 1, -1, -1], [-2, -1, 0, 1, -2, 0, 2, 2, 1, 2, 0, 0], [1, 1, 1, -2, 2, -1, 3, -1, 1, 1, -2, 1], [3, 1, 1, 1, 4, -2, 2, 1, 0, 3, -1, -1], [1, -2, -1, -1, -2, 0, 0, 2, -1, -2, 2, 2], [5, 0, 0, 0, 2, 1, -1, 2, -2, -1, 1, 2], [1, -1, 0, 1, 0, 0, 2, -1, 1, 1, -2, -1], [2, -1, 0, 2, 4, 0, 3, 5, 1, 2, 0, 1], [4, 2, 0, 1, 2, 0, 1, 0, -1, 0, 2, -1], [0, -1, 0, 1, -2, 0, 0, 1, 1, -1, 1, 2], [1, 2, 1, -1, 2, -2, 4, 0, -1, 2, -3, 1], [1, -2, 0, 1, 0, 1, 4, 0, 3, 3, -1, -1], [-2, 1, -1, 1, 0, -1, 0, 3, -3, -4, 4, 3], [1, 1, -1, 2, 0, -1, 1, 1, -1, 1, 2, 1], [4, 0, -1, 0, 0, -1, 0, -2, 2, -1, -2, -2], [-3, -4, -5, 0, -2, 0, 0, 3, 1, -3, 3, 3], [-2, -6, -4, 2, -12, 2, -2, 4, 0, -4, 4, 2], [0, 4, 0, 0, 0, 0, 0, 0, -4, 0, -1, 1], [-2, 2, 0, 0, -4, 0, -4, -4, -2, -1, 0, -2], [1, -2, 1, -3, 0, 0, 0, 4, -3, -4, 1, 1], [2, -4, -4, 2, 4, 4, -2, 2, 2, -2, 2, 2], [-2, -2, 0, 1, -1, 0, 1, -1, 4, 4, -2, -2], [-3, 0, 1, -4, 4, 0, 0, -1, -1, 1, -1, -1], [0, -1, 1, -2, 0, 1, -1, 0, 0, 2, -1, 0], [0, -2, 0, -3, -1, 0, -1, -3, 0, -2, 2, 2], [-2, -2, -4, 3, 2, 2, -1, -1, 4, 0, 0, 2], [4, 1, 0, 2, 2, 0, -5, -3, 4, 3, 1, -5], [-4, -6, -1, 0, -8, 1, -4, 0, 2, -5, 4, 2], [0, 0, 1, -5, 0, -1, 3, -1, -1, -1, 1, -1], [2, 2, 4, -3, 8, -2, 1, -2, -1, 0, 0, 1], [-8, 6, 1, -1, -7, -2, 0, -2, -5, 0, 0, -2], [-2, 2, 0, 1, -2, 2, -3, 3, -4, -2, 4, 2], [-1, 3, 1, 0, 0, -2, -6, -4, -2, -2, 2, -4], [4, -1, -2, -3, 0, -2, -2, 1, -1, -7, 0, 1], [2, 6, 4, 2, 2, -2, 0, -4, 0, 4, -4, -2], [-1, 2, 1, 1, 0, -2, 4, 2, -1, 4, 4, -6], [-2, 2, 0, 2, -2, 0, 2, 3, -2, 3, -2, 2], [-1, 4, -2, -1, -2, 1, 2, -2, 1, 5, -5, -5], [0, 6, 2, -6, 2, -4, 2, -7, -4, -3, -2, -2], [1, -4, -1, 2, 0, 2, 0, 3, 3, 1, -1, 3], [3, 8, 6, -7, 6, -3, 4, -6, -1, 5, -5, -3], [0, -2, -4, 0, 0, 4, -2, 0, 0, -2, 2, 0], [1, 3, 3, -6, 2, -3, 1, -5, -3, -1, 0, -3], [0, 0, -3, 4, 0, 3, -6, -4, 2, -1, -2, 2], [2, -4, 0, 0, 1, 0, 6, -4, 8, 4, -4, -4], [-1, -2, -2, 5, 10, 1, -1, 5, 0, -1, 1, 0], [-1, -6, 0, 0, 1, 0, 0, 5, -6, -5, 4, 4], [-7, -4, 0, -2, 7, 0, 0, 6, -4, -6, 1, 1], [0, 6, 0, -2, 8, 0, 6, -2, 6, 6, -6, 0], [-2, 6, 7, -1, 9, 0, 0, -3, -1, 3, -2, -2], [7, 3, 0, 4, 4, -1, 1, 4, -3, 6, 2, 0], [-2, -3, -1, -7, -4, 1, 2, -1, -1, -4, 4, -1], [-5, -3, -3, 2, 2, 0, 0, 4, 0, -4, 0, 0], [0, -3, 0, 0, -6, 0, -3, -4, 1, -3, 3, 4], [0, 2, 1, -4, 0, 1, -6, -2, 2, -1, 0, -2], [6, -2, -1, 2, 0, -1, 4, 0, 0, 1, -2, 0], [-8, 2, -2, 4, -16, 2, 2, 4, 0, 4, -2, 0], [-8, 3, 0, 2, 0, 0, -1, -9, 9, 2, -6, -9], [-12, 2, 0, 2, -6, 0, -4, 2, -2, 2, 2, 0], [-4, -7, -3, 1, -8, 3, -2, 1, 5, -4, 2, 5], [11, -10, 0, -5, 4, 3, 2, -2, 7, -3, -7, 3], [0, -2, -2, 2, -2, 0, 0, -4, 0, 4, 2, 2], [-5, 4, 1, -3, -4, -2, 0, -4, -3, -2, 0, -2], [2, -2, -3, 6, 4, 3, -10, 2, -4, -3, 6, -4], [-1, -2, -1, 1, 0, 0, 0, -2, -1, 2, -1, -1], [0, 5, 0, 0, 4, -8, -5, -5, 0, 3, -3, -5], [-4, 2, 0, -10, 4, 0, 0, -1, 2, 1, -2, -2], [1, -3, 2, 3, 1, -1, -7, -2, -6, -4, 4, -1], [6, 2, -2, 3, 0, -2, 1, -9, 9, 11, -7, -9], [1, 2, 2, 3, 8, -1, -3, -9, 4, 1, -1, 4], [-8, -8, -2, -1, 6, 0, 0, 9, -6, -9, 5, 5], [9, 7, 0, 1, 4, 1, -3, 0, -6, -6, 8, -1], [-8, -6, -4, -4, -12, 8, 8, 4, 2, -4, 2, 6], [-8, -7, -2, -9, -16, 2, -2, -11, 7, -9, 0, 7], [5, 2, 1, -7, -4, 0, 0, 0, 1, 0, 1, 1], [-1, -3, 0, 0, 0, -1, 10, -1, 4, 4, -4, -1], [-11, -4, -3, 5, -14, 6, -12, 2, 1, -4, 7, -1], [4, -2, -4, 0, 8, 4, -6, 0, -4, -4, 6, -4], [-1, 2, 0, 2, 0, -1, 6, -5, 5, 3, 1, -7], [-7, -6, -3, 3, -10, 6, 4, 8, 3, 2, 2, 4], [14, -1, 0, 4, 6, 2, 1, 5, 0, 7, 1, 1], [-18, 2, -1, 6, 0, -1, 4, -8, 8, 9, -6, -8], [-2, 2, 3, -8, -4, -3, 8, -6, 4, 1, -6, 4], [10, -4, 4, -8, -6, 0, 0, 4, -8, -4, 6, 6], [2, 2, 4, 3, -14, -2, 0, -1, 2, 0, 0, 4], [-8, 0, 2, 3, -6, -4, 4, 3, 2, 7, -4, 0], [-2, 0, 4, -6, -4, -4, 10, 2, 2, 2, -2, 2], [-5, -4, 0, -4, -2, -1, 1, -5, 5, -3, -5, -1], [-4, -3, -6, 11, -2, 0, 0, -4, 3, 4, -2, -2], [14, -1, 2, -1, 0, 2, 0, 7, -7, -6, 6, 7], [-5, 7, 1, 2, 6, 0, 0, -6, 6, 6, -10, -10], [-2, 3, -4, 1, -4, 4, 2, 1, -1, 3, -2, -1], [10, 0, -5, -2, 20, 5, -4, -2, -4, -3, 4, -4], [4, -4, -4, -2, 0, 8, 2, 3, 0, -5, 7, 1], [-6, 0, 0, 2, 0, -6, 4, -2, 4, 10, -6, -4], [-1, -4, -3, 0, -4, 6, 12, 9, 1, 3, -5, 11], [6, 0, 5, 1, 0, 5, 1, 4, -4, -8, 4, 4], [-18, 7, -1, 9, 0, -1, 2, -9, 9, 8, -2, -9], [8, 6, 0, 6, 8, 0, -8, 2, -6, 2, -6, 6], [-5, -4, 0, -5, 0, 0, -1, 6, -6, -1, 2, 6], [4, -2, -2, -4, 0, -2, -2, 8, -8, -4, 6, 8], [7, 0, 0, 2, 7, 0, 8, 6, 0, 6, 2, -2], [19, -8, 0, -6, 10, -1, 8, -5, 7, -3, -9, 1], [-5, 1, 1, 5, -4, -2, -10, -1, 0, 1, 1, -3], [-4, -6, -8, -1, -17, 4, 3, 3, 8, -2, 2, 6], [2, -6, 2, -9, 4, -2, 9, 4, 2, -3, 4, 2], [-4, 6, 0, 4, -2, 0, 2, 0, -2, 2, 6, -4], [2, -5, 4, -10, 8, -2, 4, 6, -3, -7, 7, 6], [-4, -12, -8, -2, 4, 4, 0, 8, 2, -8, 8, 6], [-6, 12, 2, 8, 8, 0, 0, -17, 10, 17, -14, -14], [2, -8, -8, 2, -10, 0, 0, 7, 0, -7, 2, 2], [2, 0, 4, -9, -2, -2, 1, -6, -1, -2, 2, 3], [-4, -12, -8, -2, -4, 0, 0, 10, -4, -10, 7, 7], [7, 8, 5, 1, -2, 0, 0, -10, 3, 10, -8, -8], [-4, -14, -10, 12, -8, 10, -10, 12, 4, -6, 10, 4], [-2, -12, -4, 6, -4, 2, -4, 8, 2, -10, 10, 10], [-9, 4, 1, 3, 10, 0, 0, -9, 3, 9, -3, -3], [2, 11, 2, 10, 0, 2, -1, -10, 10, 12, 1, -10], [2, 5, 0, -1, 4, -6, -6, -1, -5, -1, -1, 0], [2, 4, 4, 0, -16, -2, -6, -8, -8, 2, -2, -8], [-10, -10, -2, 2, -20, 2, -2, 4, 6, -5, 4, 6], [10, -1, -3, 1, 0, -3, 2, 1, -1, 1, 0, 1], [4, -2, 0, 4, -4, 0, 0, 11, -2, -11, 10, 10], [-4, 6, 1, 1, -3, -2, 10, 5, -5, 7, 4, -6], [-7, -8, -4, -4, -11, 8, -2, -1, 4, -9, 1, 7], [-3, -4, 1, -12, 4, 0, 0, 5, -5, -5, -1, -1], [-3, -2, 0, -4, 0, -3, 0, -9, 7, -3, -5, -5], [0, -2, 3, -13, 3, 0, 0, 5, -5, -5, 0, 0], [0, 8, 0, 9, 18, 0, -1, -5, 4, 8, -8, -4], [2, 14, 4, 7, 16, -2, 1, -8, 3, 12, -12, -7], [12, 6, 0, 8, 6, 0, 2, 8, -6, 10, 6, 0], [-3, 6, 3, -13, 0, -6, 16, -8, -3, -2, -2, -4], [4, 0, 4, -3, 8, -4, -11, -10, -4, -7, 4, -4], [-4, 3, -2, -1, 2, 0, 0, -8, 5, 8, -11, -11], [-5, 12, 0, 2, 2, -9, 2, -1, -9, 1, 3, -3], [2, 0, 4, 0, 0, 4, 0, 6, -6, -10, 6, 6], [4, -2, 0, -6, 4, 0, 12, 0, 2, 0, -9, 9], [-12, 0, 0, 2, -8, 4, 6, -2, 4, 0, 4, -4], [4, -8, 4, -1, 0, 4, 7, 17, -17, -9, 9, 17], [-1, 2, -2, -3, -2, 2, -9, -14, 0, -5, -2, 0], [-22, 4, 1, 11, 0, 1, 7, -8, 8, 16, -4, -8], [-5, 1, -2, 2, 0, -2, 1, -7, 7, 4, -6, -7], [-2, 3, -4, -8, -12, 2, 5, -11, 10, 5, -5, 3], [-28, -10, -4, -1, -32, 8, -20, -7, 6, -15, 7, 1], [8, 13, 4, 6, 16, -4, 5, 2, -4, 12, -9, -4], [8, 4, 7, -7, -1, 0, 0, -6, -3, 6, -2, -2], [-4, 3, -8, -1, -4, 0, 0, -4, 11, 4, -3, -3], [-16, 2, -2, 4, 0, -2, 2, -4, 4, 2, -2, -4], [4, 12, 8, 4, 4, -4, 0, -4, -4, 8, -8, -8], [-9, -3, 0, -10, -6, 3, -6, -3, -4, -20, 0, 7], [10, -1, 5, 1, 20, -5, 16, 17, 1, 8, 0, 1], [0, -2, 2, -8, 0, -2, 6, 0, 0, -2, 2, 0], [6, 10, 8, -4, 14, -16, 12, -6, -2, 10, -12, -4], [7, 3, 0, 1, 5, -3, -5, -2, 0, 2, 0, -3], [-4, -4, 6, -2, 0, 6, 2, 4, -4, 3, 0, 4], [-3, 6, -6, 8, 0, 3, 4, -7, 17, 9, -9, 5], [-7, 2, 0, 6, -7, 0, -10, 1, -2, 1, 10, -10], [-13, -3, -3, -5, 0, -3, -2, 3, -3, -2, 0, 3], [7, -4, -6, 2, 1, 12, 10, 13, -2, 1, -1, 13], [33, 1, 0, -1, 16, 1, 2, -2, 0, -4, 2, -1], [-3, 9, 7, -11, -6, -7, 2, -7, -11, 0, 2, -11], [-10, -13, -2, -11, -20, 2, 6, 7, 1, -9, 12, 1], [14, 16, 11, -4, 28, -11, -2, -18, -4, 5, -12, -4], [-6, 3, 0, -5, -2, -2, -14, -7, -1, -11, 1, -2], [0, -2, 0, -6, 14, 0, 0, 6, -10, -2, 2, -8], [5, 19, 10, -4, 30, -5, 10, -5, 2, 14, -14, -7], [31, -1, -1, 0, 0, -1, 1, -1, 1, 1, -2, -1], [0, 3, 0, 4, 16, 0, 4, 6, 3, 3, -3, 0], [-19, -2, -5, -3, 14, 0, 0, 8, 3, -8, 9, 9], [0, -5, -4, 9, 0, 4, 10, 19, 5, 7, 0, 5], [10, -8, -6, 14, -16, 0, 0, 6, -2, -6, 10, 10], [-10, -8, -2, 6, -12, 4, -16, 0, 6, -4, 0, 4], [14, 0, -3, 2, 0, -3, 2, 0, 0, 7, 0, 0], [-12, 1, 1, -4, 0, 1, -5, -4, 4, -14, -3, -4], [8, 10, 9, 1, 16, -9, -5, -1, -13, 3, 3, -13], [-17, 7, -1, 0, 0, -1, -7, -7, 7, 1, 0, -7], [13, 6, 4, 2, 17, -8, 24, 10, -2, 18, -9, 1], [0, 9, 0, 20, -2, 0, -7, -7, 4, 9, -9, -5], [-4, 7, 5, 4, -8, -5, -3, 4, -10, 4, 3, -10], [12, -3, 6, -2, 0, 6, 1, -2, 2, 6, -5, -2], [1, -4, 6, 4, 5, 0, 0, 6, -10, -6, 0, 0], [-5, 0, 0, 7, -10, 15, -12, 8, -1, -1, 15, 1], [-27, -1, 0, -2, -16, 5, -2, 5, -6, -8, 4, 7], [-1, 8, -2, 21, -6, 1, -4, -2, 7, 9, -9, -3], [16, 2, -1, -1, 0, -1, -3, 2, -2, 6, 4, 2], [-14, 1, 8, -3, 22, 0, 0, -2, -7, 2, -3, -3], [-23, -6, 0, -3, -12, 1, 8, 2, 1, -1, -5, 5], [2, -8, -2, -8, -4, 0, 0, 12, -6, -12, 10, 10], [-3, 0, -4, 5, -6, 4, 1, 2, 4, 3, -4, 4], [1, 1, 0, 2, -4, 9, -3, -2, 3, -6, 10, -4], [7, -10, 2, -3, 0, 2, 7, 8, -8, 3, -2, 8], [-25, -15, -1, -10, -50, 1, -5, -3, 3, -15, 12, 3], [16, -5, 0, -3, 8, 0, 12, -3, 5, -1, -5, 0], [-5, -5, -10, 15, -1, 5, -5, 10, 0, 0, 0, -5], [-24, -8, -4, 4, -28, 8, 0, 8, 4, 0, 5, 3], [24, -9, 3, -6, 0, 3, 3, 19, -19, -15, 10, 19], [6, 2, 0, -7, -6, 0, 0, -11, 2, 11, -8, -8], [-10, -8, -8, 12, 2, 0, 0, 2, 0, -2, 1, 1], [8, 2, 1, -10, 16, -1, 18, 0, 6, 5, -8, 6], [8, 8, 0, -2, 4, 0, -2, 6, -16, -12, 8, 8], [-2, 8, 8, 5, 10, 0, 0, -7, 0, 7, -9, -9], [-8, -12, -16, 17, 8, 8, -9, 9, 2, -4, 4, -2], [-3, 14, 9, 3, 12, 0, 0, -22, 5, 22, -14, -14], [6, -7, -8, 2, 0, -8, 9, 6, -6, -4, -1, 6], [-6, -8, 2, -1, 8, 0, 0, 13, -10, -13, 14, 14], [7, 6, 14, -5, 4, -7, -4, 2, -21, -1, 1, -13], [-8, -10, 0, -2, -2, -4, 4, -4, 12, 10, -14, -2], [-9, 16, 6, 6, -18, -6, 2, 0, -8, 12, -8, -8], [8, -2, 8, -10, 16, -8, 8, 0, 0, -2, 2, 0], [0, -11, 0, 4, -26, 0, -6, 8, -5, -11, 11, 6], [-12, -16, 2, -2, -10, -4, 6, -1, 18, 3, -4, 0], [8, 4, 8, -3, 0, 8, -7, 2, -2, -5, 6, 2], [8, -4, 2, 4, 10, -4, 0, 2, 6, 6, 9, -13], [6, 14, 2, 4, 12, -2, 10, -2, 2, 14, -16, 2], [0, -9, -10, 7, 0, 10, 2, 7, 11, 0, -2, 11], [-4, -8, -8, -4, -4, 4, 6, 8, 8, -4, 4, 8], [3, -2, 1, -3, -2, 0, 0, -12, -3, 12, -9, -9], [-10, -3, 2, 3, 0, 2, 6, -1, 1, 5, -4, -1], [7, -6, 8, -14, 1, 0, 0, 1, -14, -1, 2, 2], [-4, 4, -8, 4, -28, 4, 0, 2, -2, 8, -8, -14], [-4, 6, 0, 8, -6, 8, -6, 14, -12, 2, 14, 6], [-14, 9, 7, -8, -28, -7, -1, -6, -12, 0, 3, -12], [9, 5, 5, 11, -4, 0, 0, -9, 0, 9, -11, -11], [-6, -12, -2, 8, -8, 4, -26, -3, 10, -7, -2, 6], [12, -12, 2, 0, -10, 0, 0, 12, -14, -12, 12, 12], [-8, 3, -4, 5, 0, -4, 2, 7, -7, 2, 10, 7], [0, -5, 2, -16, 0, -2, 29, 14, 4, 4, 1, 4], [-10, -2, 0, -1, 0, 0, 1, 6, -6, -7, 4, 6], [-23, -13, 0, -9, -19, 15, -7, 0, 4, -20, 2, 9], [2, -6, -4, 18, -2, 8, -16, 14, 2, 6, 7, 1], [1, 2, 2, 20, -4, -1, -8, 5, -3, 1, -1, -3], [17, -16, -7, 11, 10, 14, -4, 16, 9, 2, 7, 7], [27, -16, -7, 3, 20, 14, 0, 10, 9, -4, 1, 13], [-5, -6, 3, -17, -2, -6, 4, -18, 9, -12, -5, -1], [-12, -12, 0, 5, -8, 4, 12, 11, 6, 18, -8, 6], [12, -6, 8, -14, -4, 0, 0, 4, -14, -4, 3, 3], [-3, -9, -6, 16, 8, 3, -4, 11, 6, -6, 6, 9], [-14, 6, 2, -2, 0, 2, -8, -2, 2, -8, 4, -2], [0, -16, 0, -26, -12, 0, 4, 4, -6, -16, 16, 10], [-5, -14, -1, 6, 4, 0, 0, 11, -13, -11, 3, 3], [7, 0, 0, -2, 6, -5, 11, -1, -1, 1, -5, 1], [-11, 0, 0, 6, 11, 0, 0, -8, 0, 8, -3, -3], [-28, 13, 0, -3, -28, 0, -6, -6, -13, -6, 1, -1], [1, 10, 5, 8, 4, 0, 0, -7, 5, 7, 1, 1], [21, -5, -7, 1, 0, -7, 6, 9, -9, -10, 4, 9], [13, -8, 4, -4, 17, -8, 2, -7, 12, 1, -4, -4], [-8, 2, 4, 9, -16, -4, -1, 2, 4, 5, -6, 4], [20, -6, 0, -3, 10, 0, 14, 11, -8, 0, -6, 14], [6, 4, 12, -8, 18, -6, 4, 2, -6, -2, 2, 2], [-3, 14, 9, -3, 6, -18, -4, -14, -5, 4, -3, -15], [-2, 4, -2, 13, -4, 2, -11, 8, -10, 3, 6, -10], [1, 13, 2, 10, -28, -1, -6, -7, -8, 12, -12, -19], [10, 16, 11, 2, 20, -11, -10, -16, -8, 4, -8, -8], [-8, 0, 0, -10, 8, 0, 0, 0, 0, 0, -12, -12], [-6, -3, 4, -21, -12, -4, 6, -15, 3, -9, 0, 3], [6, 8, -2, 8, -8, 0, 0, -8, 10, 8, -15, -15], [-6, -2, -12, 17, -7, 6, 7, 15, 18, 4, -4, 8], [5, 14, 10, 7, 16, -5, 2, 4, -7, 9, -9, -11], [-32, 12, 0, 4, -12, -8, -14, 2, -10, 4, 4, -2], [-12, 7, 4, -7, -24, -4, 4, -7, -3, 2, -4, -3], [-3, -2, -6, 4, -10, 3, 5, 16, 0, 1, -1, -4], [-2, -5, 0, -9, -2, 2, -2, 5, -9, -15, -3, 14], [10, 11, 4, 7, 0, 4, -4, 5, -5, 5, 16, 5], [-4, -17, 0, -8, 0, 0, 9, 22, -22, -16, 5, 22], [21, 4, 5, -5, 26, -10, 8, -6, 1, 4, -12, 2], [-7, -23, -14, -13, -27, 7, 3, 16, 0, -16, 16, 9], [56, 0, 0, -4, 28, 0, -8, 0, -4, -8, 0, 4], [-1, -12, -1, 7, -2, 2, 12, 14, 11, 12, 1, 1], [8, 18, 16, -2, 14, -8, 8, -6, 2, 10, -10, 0], [14, 7, 0, 3, 28, 0, 8, 13, -9, 9, 2, -9], [6, -4, 0, 1, -1, 8, -1, -3, 8, -2, 4, -4], [-1, 0, -2, -12, 16, 1, -1, -14, 0, 1, -1, -2], [29, 0, 3, -1, -26, 0, 0, -1, -3, 1, 3, 3], [-2, -2, 5, -15, 7, 0, 0, 3, -7, -3, 2, 2], [9, 7, 3, -22, 18, -3, 25, -5, 1, 5, -8, 1], [-6, 6, 10, 0, 16, 0, 0, 8, -4, -8, -1, -1], [24, -15, 7, -12, 0, 7, 3, 4, -4, -1, -11, 4], [28, -6, 1, -10, 0, 1, -4, 14, -14, -1, 8, 14], [0, -27, -13, 7, 0, 13, 12, 25, 21, -4, 6, 21], [14, 3, 2, -2, 0, 2, -5, -9, 9, 12, -6, -9], [10, 1, 0, 4, 5, 0, -3, 14, -11, 7, 1, 10], [2, -9, 4, -12, -10, -2, 0, -4, 1, -11, 11, 14], [-2, -7, -8, 15, -10, 16, -2, 22, -1, 6, 11, 5], [23, 12, 0, -1, 18, -13, 8, 4, -17, -1, -1, 5], [9, 2, 2, -8, 11, -4, 6, -7, 0, -3, -8, 4], [-47, -4, 0, -3, -18, -11, 15, -3, 4, 9, -15, 0], [-44, -12, 0, -6, -24, 4, -12, -12, 18, -4, -8, -6], [30, 2, 8, -3, 0, 8, -5, 11, -11, -5, 13, 11], [23, 7, -3, 2, 0, -3, -5, -1, 1, -9, 6, -1], [-2, 10, 6, 4, 8, 0, 0, -7, 4, 7, 5, 5], [6, -3, 4, -5, 10, -8, -2, -10, 7, -2, 1, -9], [-23, -13, -3, -6, -26, 6, 22, 8, 10, 2, 12, -6], [-21, -3, 0, 8, -14, 7, 14, 1, 10, 12, 4, -7], [16, -3, -6, -13, 0, -6, -10, -3, 3, -7, -6, -3], [-41, -20, -6, -2, -47, 12, -14, -3, 14, -15, 11, 1]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1170_bj_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1170_2_bj_c();".
// 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_1170_2_bj_c(:prec:=12)
    chi := MakeCharacter_1170_bj();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(1999) - 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_1170_2_bj_c();".
// 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_1170_2_bj_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1170_bj();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![1024, 512, 1664, 64, 1648, 112, 708, -20, 205, 6, 19, -2, 1]>,<17,R![65536, 491520, 1269760, 307200, -300288, -85248, 75744, -4632, -2695, 234, 95, -18, 1]>],Snew);
    return Vf;
end function;