
// Make newform 912.2.cc.d in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_912_cc();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_912_cc_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_912_2_cc_d();".
// 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_912_2_cc_d();".
// 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 := [19683, 0, 0, -729, -4374, 2916, 270, 162, 270, -567, 90, 18, 10, 36, -18, -1, 0, 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, 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, 729, 4374, -2916, -270, -162, -270, 567, -90, -18, -10, -36, 18, 1, 0, 0, -1], [-65610, 150903, -82377, 11421, 11421, -31374, 29268, -9261, -117, 2313, -3075, 1568, -198, -57, 97, -81, 21, 2], [334611, 63423, -237654, 91125, -60507, 24003, 51273, -38475, 10098, -4167, -2637, 4675, -1485, 207, -22, -153, 99, -5], [-72171, 75087, -24786, -81, 12420, -19359, 11025, -1809, -822, 1629, -1366, 409, 9, -47, 50, -27, 2, 1], [603612, -373977, -41553, 67554, -103761, 127062, -25272, -20493, 12609, -12420, 6165, 1406, -1422, 477, -335, 36, 81, -16], [-225261, 74358, 8262, 10854, 26001, -36045, 3645, -504, 1350, 3108, -1425, -137, -255, 48, 92, -6, -3, -11], [-787320, 183708, 210681, -81648, 125469, -114507, -25110, 36126, -11367, 12492, -2247, -4181, 1296, -318, 275, 90, -105, -5], [452709, 50301, -292329, 125388, -88857, 40041, 64233, -52947, 15525, -6660, -3183, 6451, -2259, 375, -43, -216, 147, -11], [63423, -237654, 103518, 13851, -25569, 46683, -41229, 5508, 5472, -4167, 4369, -1655, -405, 284, -136, 99, -5, -17], [56862, -20412, -24057, 18198, -12825, 9666, 2430, -5760, 2619, -1234, 197, 536, -332, 82, -23, -10, 17, -4], [-247131, 26973, 7290, 35640, 23436, -32373, -1377, -4941, 4716, 2814, -908, -41, -717, 161, 86, 6, 10, -23], [-34992, -67068, 41553, 5913, 270, 6345, -14598, 2520, 1797, -393, 1220, -717, -174, 94, -21, 39, -4, -9], [-551124, -649539, 546750, -13851, 39366, 45090, -167832, 50193, 9774, -1521, 13104, -9724, -522, 747, -194, 459, -108, -76], [10935, 37179, 7047, -26811, 7695, -5103, 2817, 5787, -4125, 807, -413, -283, 525, -145, 13, -3, -17, 11], [669222, 74358, 22599, -216513, -24057, 60615, 12150, 39960, -30429, -3555, 621, -1265, 4140, -1026, -157, -27, -99, 103], [-78732, -55404, 20412, 26973, -702, 1161, -10746, -3078, 4680, -351, 874, -269, -576, 188, -10, 27, 10, -17]];
    Rf_basisdens := [1, 1, 6561, 4374, 13122, 1458, 13122, 4374, 13122, 13122, 4374, 1458, 4374, 1458, 13122, 1458, 13122, 1458];
    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_912_cc();"
function MakeCharacter_912_cc()
    N := 912;
    order := 18;
    char_gens := [799, 229, 305, 97];
    v := [18, 18, 9, 17];
    // 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_912_cc_Hecke();"
function MakeCharacter_912_cc_Hecke(Kf)
    N := 912;
    order := 18;
    char_gens := [799, 229, 305, 97];
    char_values := [[1, 0, 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], [-1, 0, 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, 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 := 2;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, -1, 0, 0, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, -1, 0, 1, -1, -1, -2, 2, 0, 1, 0, 1, 0, -1, 0, 0, -1], [-1, 1, 1, 0, -1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, -1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1, -1, 1, 1, -1, 0], [0, 1, 0, -1, 0, 1, 1, -1, 0, 0, 2, -1, 1, 1, 0, -1, 1, 0], [0, 0, 2, -1, 0, 0, 2, 1, 0, -1, 0, 0, -1, -1, 1, -2, 0, 1], [0, 0, 1, -1, 0, 1, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 2, 1], [0, 1, 1, -1, 1, 0, 1, 0, 1, -1, 0, 0, -1, -1, -1, 0, -1, -2], [0, -1, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, -2, 1, 0, -1, 0, 0], [-1, 2, 1, 0, 0, -1, 1, -1, 0, -2, 0, 2, -1, -1, 0, -1, -2, -2], [0, 0, 2, 2, -3, 0, 0, 1, -3, -1, -1, 1, 1, 2, 0, 1, 0, -1], [2, 1, 2, 2, -2, 0, 2, -2, -1, 0, 1, -1, 1, 0, 2, 2, 0, -1], [2, 1, -1, 0, 2, -1, 0, 0, -2, -1, 1, 2, 0, 1, -1, -1, 1, -1], [-1, -3, 1, 0, 3, 1, -2, -1, 0, -1, 0, 2, 0, 0, 0, 0, 2, 1], [3, 1, 1, 0, -2, 2, 0, 0, -3, -2, 1, -2, 0, 2, 1, 1, -2, -1], [1, 1, -1, -1, -1, -3, -1, 1, 0, 3, 3, -1, 1, 0, -1, -1, 3, -3], [3, -2, -1, 3, 0, -1, -3, 0, 0, -1, 0, 0, 3, -2, 1, 0, -2, 1], [-1, -1, -2, -1, 0, -1, -3, -1, 3, 1, -1, -2, 1, 2, -3, 1, 0, 0], [-1, -2, 1, 0, 0, 2, 0, 1, 0, -2, 0, 1, -2, 1, -1, 2, -2, 2], [2, 1, 1, -1, -3, -2, 0, 3, 0, -1, -2, 2, -1, -1, 3, 2, -3, 2], [5, 2, -2, 0, -4, -2, -3, 0, 1, 1, -2, -1, 0, -1, 0, 2, -1, 0], [-1, 1, 1, 3, 2, -1, 2, 1, 4, -2, 3, 2, 3, 1, -1, 0, -1, -2], [-4, -2, 0, -1, -2, 3, 0, 0, 2, 3, -1, 2, 1, 0, 1, -1, 0, 1], [-2, -1, 4, -2, -5, 3, 5, 0, 0, 0, -2, 1, -3, 1, 1, -2, -2, 4], [-3, 2, -2, -3, 4, -2, -2, 2, 2, 3, 2, 3, 0, 0, -1, 1, 4, -1], [5, 0, 0, -4, 0, -1, 5, 4, 0, 1, 0, -4, 4, -1, -1, 0, 0, -1], [0, -2, -2, -1, -1, -1, 2, 1, 1, -2, 3, 0, 4, 3, 0, -2, -1, 0], [-4, -2, 2, 0, -2, 2, 0, 0, 2, 0, -2, 2, 0, 2, 0, 2, -2, 0], [2, 0, 0, -1, -2, 0, -7, -5, -4, 0, 2, -7, -1, 0, 0, -3, 0, 0], [-5, 2, 2, -1, -1, 5, -2, -1, -5, 3, -2, 1, -4, 3, 1, -2, 5, 2], [0, 0, -1, -2, -2, -3, 3, 0, -2, 5, 2, 2, 2, 2, -2, -1, 2, -2], [6, -2, 0, -1, 4, -1, 0, -6, 2, -2, 1, -6, -1, 0, 1, 1, -4, 4], [-1, 3, -3, 0, 2, -1, 1, 2, 1, -1, -2, 2, -3, 2, 0, 1, 0, 0], [5, -4, -2, 1, 0, 2, -5, -3, 0, 0, 0, -3, 1, 0, -2, 0, -4, 4], [0, 0, 1, 3, 4, 0, 4, 1, 1, 1, 1, -3, 0, -1, 0, 2, -2, -1], [0, -2, -3, 0, -3, -3, 0, -6, 0, 2, -2, -3, 0, -2, -3, -3, 3, 2], [0, -4, 1, 3, 6, 1, 6, 6, 0, -2, -5, -6, -3, 0, 0, -2, 2, 2], [0, 0, 2, -1, 0, 3, 0, 3, 3, 3, 1, -6, 3, 2, 0, -4, 4, -2], [-1, 3, 1, 1, 1, -3, 5, -5, 2, 3, 5, -1, 3, -3, 1, 1, 0, -5], [2, 1, -1, 2, -5, 1, -1, -5, -4, -2, -3, -4, -2, 3, 0, 2, -2, 0], [0, 0, -2, 0, 2, 1, 1, 0, 1, 0, 0, -1, -2, -2, -3, 2, 0, 0], [-2, 5, 5, 2, -6, 0, 0, 6, 0, 2, 0, -2, 0, 0, 3, 3, -1, -2], [2, -3, -1, 1, 2, -4, -3, -3, 8, -4, 2, 6, 3, -3, 1, -1, -1, 2], [5, -2, -2, 1, -2, 2, -6, -1, -4, -1, 1, -6, 1, 3, -3, 0, -3, -1], [1, 1, 4, -1, -1, 2, 1, 0, 1, 2, -1, 0, 0, -2, 2, -1, -1, -3], [-6, 5, 4, 0, -4, -1, -1, 4, -5, -1, 3, 0, 4, 3, -1, -1, 0, -1], [0, -6, -2, -2, -4, -4, 0, 4, -4, 4, 0, 0, 4, 0, 4, 4, -2, 4], [5, -2, 3, -1, -4, 4, 5, 10, 4, 4, 1, -10, 2, 1, 4, 1, 2, -2], [-8, 0, 0, 4, 2, 0, -2, -4, 4, 0, 0, 4, 0, 0, 0, 4, 4, 0], [-2, 0, 1, 0, -8, 2, 5, 10, -6, -1, -2, -6, -2, 3, 0, 1, -3, -2], [5, 2, -2, 2, 1, 1, 0, 0, 5, 0, -2, -1, -3, 0, 0, 2, 1, 1], [-5, 3, -2, 2, -5, 2, -9, -9, -4, 2, -1, 1, -3, 2, -3, 3, 0, -1], [-5, -3, -1, -1, -8, -3, 4, 5, -4, -3, 1, 1, 1, -1, 2, -1, -3, 3], [-10, 1, -3, 3, 0, 1, -8, -10, 0, -1, 3, 2, 4, 3, -2, 4, -5, -5], [-3, -2, -4, -2, -2, -1, 3, 6, -2, 2, -2, 6, -4, -5, 1, 2, -2, 4], [0, 0, 0, 0, 4, -2, 4, 5, 5, -1, -1, 5, -2, -1, 0, 1, -1, 0], [-1, 1, 1, 4, 5, -4, 0, 6, 1, 0, 1, 5, 2, 0, -3, 1, 4, 1], [1, -4, -6, -2, 5, -6, -1, -2, 0, -5, 0, 1, 2, -4, -4, -2, -1, 5], [0, -3, 0, -3, 8, -2, 8, 4, 4, 0, -4, 6, -2, 2, -3, -3, 3, 0], [-2, 1, -3, -1, 0, -3, 1, 2, 0, 1, 1, 1, 1, -3, 0, -1, 3, -3], [6, 4, 4, 2, -6, 4, -3, 3, -3, 2, 4, 6, 1, 1, 1, 3, -1, -3], [1, -2, -2, 2, 1, -5, -5, -5, 8, -5, -2, 7, 2, -4, 1, -1, -1, -2], [12, -3, 0, -4, -6, -1, 0, 0, 6, -2, 5, -6, 2, -3, -4, -4, -3, -2], [-8, 4, -3, 5, -3, -1, 3, -2, 2, -4, 1, 4, 1, 0, -4, 1, 1, -3], [1, -2, 9, 5, 2, 6, 1, 4, -2, 1, 1, -4, -4, -3, 6, 1, 2, 1], [1, 0, 7, -2, 2, 5, 1, -1, -2, 1, 2, 1, 4, -2, 5, 2, 0, -1], [-3, 4, -4, 3, -6, 1, -2, -8, 2, -3, -1, 3, -5, 5, -7, 1, -2, 3], [-10, 2, 0, 4, -7, 2, 7, -1, 1, -7, -3, 5, -2, -1, -2, -3, -3, 0], [0, 2, 2, 4, 0, -2, -6, -6, 0, 0, 6, -6, 4, -6, 6, -2, 2, 0], [-1, 2, 1, 3, -5, 2, -3, 0, -6, -3, -3, 6, -1, -1, 3, 2, -1, 1], [1, 2, 2, -1, 0, -5, -6, -6, -6, -1, -5, 1, -5, -5, 5, -1, 0, 3], [4, 2, -1, 1, -10, 0, -7, -10, -3, 0, -4, -8, -4, 4, 1, 0, -1, -1], [3, 2, 0, -2, 0, -2, 6, 3, 3, -2, -2, 3, -1, 0, -2, -1, -3, -3], [2, 3, -2, -2, -2, -7, -8, 8, 2, 7, 5, -4, 3, -6, 4, 4, 1, -5], [-3, 6, -4, -4, -9, -4, 1, 4, 0, 1, 4, -1, 4, -1, -1, 0, -5, -1], [1, -3, 0, -1, -9, 0, 2, 1, 0, 1, 3, -2, 1, 0, 0, 2, 4, -1], [-6, -2, -1, -1, 6, -4, -2, 2, -6, 4, -3, 12, -2, 3, -2, -2, 7, 3], [1, 0, -3, -2, 7, 0, 8, 7, -1, -2, -4, -2, -4, 4, -3, 2, 2, 3], [-1, -3, 3, -4, -6, 1, -7, 1, -3, -3, 4, 8, -2, 3, 2, 2, 0, 0], [0, -1, -6, -7, -3, -6, 12, 0, -3, 5, -5, 3, -6, -1, -7, -1, -1, 6], [-6, -2, 2, 0, 4, 4, 16, 8, -6, 4, 2, -4, 0, 4, 2, -2, 4, 2], [8, 2, 0, 9, 1, 0, -3, 5, 2, -3, 7, -3, 9, 0, 0, 2, -1, -3], [10, 0, -5, -2, 5, -5, 1, 2, -5, 0, 4, -5, 4, -5, 2, -7, 5, 4], [0, -2, 2, 1, -2, -4, -2, -4, 2, -1, 4, 0, 2, -2, 2, 3, 2, 0], [-12, 0, -3, 7, 3, 1, 5, -3, 8, 2, -1, 0, -2, -1, -3, 2, 7, -3], [-4, 2, -5, 2, 2, 3, -4, -8, -2, -2, 3, 8, 1, 8, 3, 3, -2, 0], [-3, 3, -3, 0, 6, 1, -1, 5, 1, 0, -1, 3, -2, 2, -2, 4, 4, -1], [-2, 4, -1, 1, -3, 0, 3, -3, 3, -6, 1, 1, 0, 1, -4, -5, -5, -1], [-2, 0, 4, -7, 2, 10, 6, 3, -2, 9, 0, -2, 1, 9, -3, -4, 10, -1], [-3, 1, 1, -2, -12, 3, -9, 3, -9, -2, 3, -3, -2, -2, 4, -8, 6, 3], [-2, -3, 1, 1, -12, -2, -5, 2, -6, -3, -1, 7, 0, 1, 3, 0, -6, 6], [-5, 2, -1, 1, -6, 5, 5, 3, -6, 7, 2, 3, 3, 4, -5, -2, 2, 5], [2, 6, -3, -3, -2, 3, 1, -1, 5, -3, 8, -7, 6, 2, -3, -3, -1, -8], [4, -9, 2, 4, 4, 1, 0, 0, -4, 1, -9, 4, 0, -1, -2, 2, -1, 9], [0, 3, -4, -2, -1, -4, -1, -2, -2, 5, 0, 6, -4, -4, 3, -7, 7, 4], [-10, 0, 0, 0, 10, -4, -7, 7, 6, 4, 4, 4, 0, -8, 7, 7, -4, -4], [-1, 2, 2, -2, -1, 0, 9, 9, -3, 0, 3, -2, -2, -4, -3, 3, 4, 3], [-12, 1, -1, 4, -2, -1, 2, 1, -12, -2, -1, 2, -3, -2, 3, 1, -1, 2], [2, -7, -2, 3, 4, -5, 2, 4, 2, -6, -3, 2, 4, 1, -3, 1, -1, 4], [0, 3, -3, 2, -5, -2, -2, -7, 2, -2, 2, 0, 1, -1, -1, -3, -5, -2], [3, 7, 6, -4, 10, -4, 1, -10, 11, -2, 2, 0, 6, 2, -1, -2, -4, -1], [3, 2, 7, 2, -12, -1, 7, 12, -5, 4, -2, 0, -1, -2, 5, 4, 2, 5], [-4, -2, 2, 4, 1, 0, 4, 5, -4, -4, 0, 4, 4, -4, -6, 4, 0, 8], [-7, -8, -5, -3, -3, 5, 14, 7, -6, 8, -2, 14, -3, 2, -2, -1, 0, 8], [-2, -1, 6, 0, -1, 2, -4, -2, -2, -4, 1, 1, 0, -4, 6, -6, 2, 1], [9, 0, -5, 5, 9, -3, 6, 6, 9, -3, -4, 0, 0, -1, -10, 10, -2, -4], [-3, -4, -4, -4, 0, 3, 5, 5, 5, -4, 3, -3, 6, 6, -5, -2, -2, -1], [5, 0, -7, 0, -6, -8, -2, -6, -4, 1, 1, -10, -7, -1, -7, -1, 0, 7], [6, 1, -3, 4, -17, -1, -6, -9, -17, 4, -8, -9, -4, -4, 1, 8, 1, 3], [-6, -8, 3, 3, 6, -2, 6, -6, 6, 2, -3, 0, -8, 1, -2, -2, 3, 3], [0, -5, -1, 6, 6, -5, 6, -4, -4, -3, -8, 12, -5, 3, -5, 9, -9, 1], [5, 5, -6, -2, -2, 2, 0, -12, -5, -4, 5, -2, 2, 4, -4, -6, -2, -3], [-2, -1, -2, 4, -15, 1, 2, -2, -15, -2, -2, -2, 2, -1, -1, 2, -1, -1], [1, -2, 5, -1, 0, 4, -12, 1, 12, 2, -1, -13, 1, -5, 9, 1, 0, 0], [0, -7, 3, 7, 1, 1, -10, 1, 11, -9, -3, 0, -2, 3, -4, 9, -7, 4], [-8, 7, 7, 0, -4, 6, 4, 8, 4, 0, 6, -8, 7, 7, 1, -3, 3, -6], [-16, -1, 8, 2, 8, 2, -3, 0, -8, -3, 6, 8, 5, -1, 2, -6, -1, -5], [5, 0, 4, -1, 10, -5, -2, -1, 5, -8, 0, -10, -7, -8, 3, -4, -5, 7], [-10, 5, -6, 6, 7, -3, -7, 2, -2, -8, -1, 5, 3, -4, -5, -2, -2, -6], [6, 12, -12, 2, -2, -8, -2, -4, 2, -2, 8, -6, 5, -5, -4, 2, 0, -8], [12, 1, 7, 1, -2, 0, -2, 2, -4, -2, 1, 0, 1, 1, 6, -2, 1, 6], [-10, 6, -6, 5, 6, 3, -3, 3, 3, -5, -3, 10, -4, 4, -2, 0, -5, -4], [-6, -2, -1, 1, 2, 1, 0, -6, 4, 4, 9, 0, 1, 0, 0, -8, 2, 4], [4, 7, 5, 8, 5, -2, -9, 0, 9, -1, 5, -9, 12, -3, 8, 3, -3, -12], [0, -5, 0, -7, 8, 0, -3, 0, 4, -5, 7, 3, -1, 0, 0, 1, -3, 3], [-7, 0, -2, 10, 6, 5, 7, 0, 6, -2, -6, 0, 4, 3, -5, 6, 0, -2], [0, 1, 1, 12, 0, 0, 0, 6, 6, 5, 1, -5, 0, -1, 1, 7, -7, -1], [-6, 11, 4, 3, -12, 4, -14, -8, 0, 4, 1, 14, -3, -2, -2, 4, -7, -4], [-11, 4, -2, -1, 3, -2, 5, 16, 0, 7, 6, -5, 1, 4, 4, 5, 3, -7], [0, -6, 2, 2, 0, -4, 4, -4, 2, 4, -8, -2, -6, -2, 2, 2, 2, 8], [10, -6, -2, -12, 0, 2, 0, 10, -6, 6, -12, -10, -4, 2, 0, -4, 6, 6], [10, 0, 3, -6, 1, 3, -1, 1, 2, 3, 1, -20, 4, -1, 3, -3, 6, -3], [-8, -8, -3, 3, -8, 2, -9, -9, 3, 2, 7, 11, 8, 5, -2, 2, -3, 7], [-10, -2, -4, -5, -4, -5, 0, 0, -14, 11, -9, 14, -11, 6, -5, -1, 6, 11], [0, -7, 3, -7, 0, -5, 0, 1, -1, -1, -1, 0, 5, -6, 7, -8, -8, 3], [-12, 1, 0, -1, -6, 0, -6, 6, -12, -1, 8, 0, 8, 8, -1, -1, -1, -1], [4, 10, -6, 6, 13, -5, -13, -8, 8, -7, 1, -2, 5, -4, -10, -1, -1, -6], [-10, 4, 1, -3, -8, -6, 1, 2, 2, 2, 2, 2, -2, -8, 3, -2, 8, -2], [16, 2, -4, -4, 8, -2, 4, 2, 16, 5, -2, -8, 1, 5, -8, 4, -2, -3], [-13, -2, 8, 9, 14, -1, -8, 0, 1, -6, 5, -1, 3, -7, 9, 1, -7, -3], [4, -1, -2, 2, 4, -5, -9, -9, -1, -5, -1, -5, 1, -2, 9, -9, -3, -1], [16, 0, 0, -1, 1, -6, 0, -1, 0, -1, -6, 16, -11, -11, 5, 0, -1, 5], [-17, -6, -4, -4, 0, 0, -16, -17, 3, 6, -4, 1, 3, 4, -4, 3, 5, 5], [-6, 2, 0, 10, -12, 0, -8, -2, 0, -10, -6, 8, -10, 4, 4, 4, -12, 10], [-10, 3, 2, 5, 9, 2, 4, 14, 0, 1, -3, -4, -5, 7, 7, 2, -2, -1], [4, -12, -8, -7, 3, 1, 0, -9, -4, 0, -12, 3, -3, 0, -1, -8, -1, 9], [0, -9, -8, 9, -6, -6, -6, 3, 3, 1, -7, 3, -6, 1, -9, 8, -8, 8], [5, 3, -3, -7, 6, 3, -6, -5, 3, 3, 7, 1, 3, -3, -6, -3, 2, -2], [3, -10, -10, -5, 0, -1, -6, -6, -6, -5, -1, 3, 0, 0, -6, 0, -5, 4], [-15, 1, 11, -11, -15, 1, 6, 6, -4, 1, 5, 11, -1, -6, 8, -8, 7, 5], [9, 7, -11, -11, -6, 1, -3, 0, 3, 9, -3, -3, 4, 10, -11, 0, 10, -4], [3, -4, 0, 6, -8, -3, 3, -12, 8, -3, 1, 12, -5, -3, -3, 1, 4, 7], [-3, 9, 2, 2, -8, -2, -5, 8, -13, 0, -3, 0, -1, -3, -7, 0, 2, -7], [15, 10, -10, -5, -1, -11, 0, -1, 0, 5, 11, -15, 9, -9, -5, -4, 1, -5], [-1, -10, -3, -3, -12, 3, -7, -8, -24, 12, -9, -7, -3, 6, -6, 6, 2, 12], [-12, -2, 7, 7, 7, 1, -3, 0, -5, 6, -6, 5, -8, 7, 7, 0, 7, 8], [0, -2, -3, 3, 0, -3, -6, -6, -6, -3, -7, -6, 2, -5, -6, 6, 2, -7], [9, 2, -1, 5, 16, 4, 9, -9, 8, 2, -5, -18, -7, -1, -5, 7, 2, -2], [14, -5, 4, -4, 0, 3, 4, 14, -6, 5, -4, -10, 3, -4, 7, 3, 1, 1], [7, -5, 8, -4, 15, 8, 0, -7, 0, -5, 1, 0, 4, -4, -4, -3, 0, 5], [12, -6, -3, -6, 6, -3, 18, 6, 0, 2, -4, -18, 6, -3, -3, -10, 8, -2], [0, 4, 0, 13, -7, 9, -7, 1, 1, 4, 9, 6, 9, 0, 4, 9, -9, 0], [1, -11, -3, -3, 3, 9, -1, -5, 3, -3, 1, -5, -2, 6, -9, -1, -11, 8], [4, 6, 0, -5, 14, 0, -7, -4, 7, 6, 5, 3, -5, 0, 0, 5, 9, -9], [3, -5, -1, 1, 3, 9, 3, 3, 10, 9, -1, 7, 5, 5, -1, 1, 4, -1]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_912_cc_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_912_2_cc_d();".
// 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_912_2_cc_d(:prec:=18)
    chi := MakeCharacter_912_cc();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    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_912_2_cc_d();".
// 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_912_2_cc_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_912_cc();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![1728, -10368, 11232, -72, 70344, -60552, 141193, -5202, -30258, 1458, -1458, -324, 46, 162, 108, 0, 9, 0, 1]>,<7,R![87616, 113664, 216720, 148720, 195300, 100062, 117161, 41064, 43740, 9622, 11985, 1494, 2222, 90, 297, 4, 21, 0, 1]>],Snew);
    return Vf;
end function;