
// Make newform 6024.2.a.k in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6024_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_6024_2_a_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_6024_2_a_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 := [-1, 3, 11, -36, 5, 25, -10, -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, 1, 0, 0, 0, 0, 0, 0], [-13, -24, 183, -87, -124, 73, 9, -7], [-3, -11, 36, -5, -25, 10, 2, -1], [-35, 8, 305, -113, -196, 95, 15, -9], [-47, 40, 381, -189, -252, 139, 19, -13], [-23, 0, 277, -109, -192, 95, 15, -9], [17, 6, -171, 59, 114, -53, -9, 5]];
    Rf_basisdens := [1, 1, 8, 1, 8, 8, 4, 2];
    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_6024_a();"
function MakeCharacter_6024_a()
    N := 6024;
    order := 1;
    char_gens := [4519, 3013, 2009, 4273];
    v := [1, 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_6024_a_Hecke(Kf)
    return MakeCharacter_6024_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 := [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, -1], [-1, 1, 1, 1, 0, 0, 0, 0], [0, 0, -1, 0, -1, -1, -1, 0], [-2, 1, 1, 0, 0, -1, 0, 1], [-1, -1, 0, 1, 2, 1, 0, 1], [-2, 1, 0, -1, -2, 1, 0, 0], [0, 1, 1, 0, 2, 0, 3, -1], [-1, 0, 2, 0, -1, -1, 1, 1], [-4, 2, 3, -1, 2, 1, 3, 1], [0, -1, 0, 2, -1, 3, -2, -1], [0, 3, 0, 2, 0, -1, 1, 1], [-1, -2, -1, -2, 2, -1, -1, -1], [-2, 2, 4, -3, -1, 0, -1, 1], [3, -4, -3, 1, 1, 1, -4, -1], [-4, -2, -1, 1, -2, 2, 0, -2], [-4, 1, -1, 1, -5, -1, -1, 1], [2, -1, 0, 0, 3, -3, 3, 3], [-1, 1, -2, 5, 0, 0, -1, 0], [-4, 1, -3, 1, -3, 2, -4, 2], [-1, -3, 1, -2, -2, -2, 2, 2], [0, 1, 1, 0, 4, -3, 4, -1], [-5, -1, 1, -1, 5, -2, 2, -1], [-2, 2, -4, -1, -4, -1, -7, -2], [1, -2, -3, 3, 0, -1, 0, 2], [-2, -1, 0, -4, 2, -1, -1, -4], [-5, -4, 3, -7, 3, -3, 0, -3], [-3, 0, -2, 2, -2, 6, -6, 1], [2, -3, -6, 5, 3, 4, 1, 1], [1, 5, -4, 1, -3, 0, -1, -1], [3, 6, 3, -1, 1, -4, 2, -3], [-6, -1, 3, -3, -3, 0, -2, 0], [-7, 4, 2, -1, -4, 1, 3, -3], [0, 4, 4, -2, 4, -6, 7, 5], [5, -2, -6, 8, 0, 5, -3, 2], [2, 0, 4, -2, 1, -1, 1, -4], [1, -6, -2, 1, 1, 3, 0, 0], [5, -1, 0, 3, -4, 3, 0, 4], [-5, 4, -2, -1, 1, 2, 0, 2], [-3, 2, -5, 0, -5, 5, -3, 1], [3, 3, -3, 3, 1, -2, 5, -1], [-4, -3, -2, 3, -4, 10, -8, -4], [0, 1, 8, -3, 4, -4, 6, 6], [-5, -10, -4, 2, -2, 7, -8, -4], [-4, 2, 1, -3, -2, 2, -2, -2], [-1, -2, -6, 1, 2, 2, -7, -7], [2, -6, 1, 0, 6, 6, 4, 4], [-1, -1, 0, -8, 2, -3, 4, -1], [-4, -2, 6, -5, 3, -1, 3, -3], [-5, -1, 2, -6, 2, 0, -1, -4], [-6, -5, -1, -6, -2, -1, -6, 0], [1, 0, 0, 0, 0, 0, 0, 0], [9, -4, -3, 7, 5, 3, 8, 0], [-3, 1, 1, 0, -9, 2, -6, 2], [-5, 7, -5, 5, -2, 4, -6, -1], [-4, 2, 0, -2, 1, -3, 5, 4], [-7, -1, 1, -5, 1, 0, -1, 1], [4, -3, -7, 2, 2, 3, -4, 4], [5, -3, 4, -2, 2, -9, 3, -2], [-4, -10, -2, 0, 4, 5, -2, 0], [5, -5, -8, 6, 3, 11, -1, 2], [-3, -3, 0, 1, -3, -1, -3, 6], [-1, -1, -8, 8, -1, -3, 0, 6], [-3, 2, -7, 2, 0, -6, -3, 0], [-10, 1, 4, -1, -4, 3, -2, 1], [0, -3, -1, -3, 5, -8, 9, 3], [8, 4, -2, 1, -3, -5, -1, 5], [-11, -4, 0, 0, 2, 6, -3, -1], [-9, -3, 3, 0, 0, -3, 1, 3], [4, -1, 0, 5, 7, 0, 4, 7], [-5, 2, 2, 0, 0, -3, 8, -1], [-2, 2, 7, -1, 4, -4, 12, -1], [10, 2, 4, -5, 10, -14, 8, -7], [1, 3, -2, 3, -5, -1, 9, -5], [-1, -2, -1, 1, -7, 0, -8, 4], [-2, -1, 8, -6, 3, -10, 10, 0], [4, -8, -13, 3, -3, 8, -13, -5], [-3, 2, -3, 6, -1, 0, 3, 5], [3, 1, 5, -1, 1, 5, 1, -6], [-1, -1, -3, 0, 9, 1, 1, -1], [-3, -1, 2, 8, -9, 5, -3, 1], [-17, 2, -1, -8, -5, -6, -5, -3], [3, -1, 1, -6, 6, -7, 2, 5], [21, -6, -8, 7, -3, -1, -7, 2], [4, -3, 7, -1, 3, -2, 16, 6], [6, 4, 1, 6, -9, 0, -5, 0], [2, -8, -3, -2, 4, -7, 6, 4], [-12, 4, 5, -9, -6, -1, -8, -9], [7, -1, 0, 3, 4, 6, -4, 1], [-5, 5, 5, -1, 0, -1, 4, -3], [-5, -1, 8, -7, 5, 1, 5, 0], [2, -1, 2, 2, -3, -2, 16, -5], [6, 3, -8, -3, -5, -2, -10, -10], [6, 2, 0, 3, 9, -3, -5, -4], [-2, 3, 2, -6, -3, -1, -8, 1], [13, -3, -1, 2, -3, -1, -5, -7], [18, 2, -6, 4, 4, 1, 4, -5], [0, 0, 8, -5, -3, -2, 5, 3], [2, 5, 9, -10, -7, 3, 1, -4], [-1, 4, 5, 0, 5, -4, 1, -3], [17, -4, -5, -3, 2, 4, -4, 5], [6, 9, -7, -1, -2, -11, 2, -6], [-5, 4, 8, 7, 2, 3, 9, 5], [-6, -3, 7, 0, 3, 1, -1, -7], [12, 6, -5, 15, -2, 10, 2, 3], [12, 1, 1, -4, -6, 1, -3, -5], [-1, 14, 3, 5, 3, 2, 8, -2], [-3, -8, 2, -7, -11, -3, -9, -6], [-2, 1, 10, -9, 3, 1, 3, 2], [-12, 0, 10, -2, 6, 5, 3, 5], [4, -13, -6, 5, 1, 5, -9, 10], [-2, 3, -2, -3, -13, 6, -14, 1], [-5, 6, 13, -6, 4, -7, 15, -10], [0, 8, 4, -9, -5, 4, 8, 0], [11, 4, 1, -4, 4, -4, -5, -1], [9, -2, 8, 0, 12, -10, 4, 3], [-18, 13, 14, -8, -1, 4, 1, 1], [5, -6, -2, -4, 19, -8, 6, -8], [-10, -10, -8, 9, -3, 5, -6, 1], [-11, 3, 3, 1, 8, 1, 9, 3], [-1, 1, -9, 3, -13, -5, -4, -2], [-2, 9, 12, -2, -7, -5, 3, 1], [22, 5, -11, 12, -2, 2, 2, 4], [3, -7, 14, -8, 8, -1, 7, 2], [3, 9, -9, 9, 5, -5, 6, -7], [2, 4, 2, 1, 1, -1, 8, -8], [18, -1, 2, 4, 1, -3, 2, 9], [-2, -4, 9, -7, 1, -12, -4, 5], [13, -3, 3, -1, 6, -10, 9, -6], [13, 0, -7, -7, 2, 1, 5, -5], [-3, -5, -3, 9, 1, 0, -4, 7], [-15, 10, 2, -2, -10, -2, -2, -13], [9, 0, -10, 4, -7, -6, -5, -1], [-13, 10, -5, -5, -6, 4, -3, 1], [-10, 6, 10, -1, -2, -8, 8, 11], [14, 1, -3, -4, 2, 7, -5, -11], [2, 5, 10, -5, -4, -6, 16, 6], [-13, 10, 9, -16, -4, -5, 2, -12], [11, -11, -19, 15, -5, 17, -19, -8], [19, -12, -17, -1, -5, 2, -13, -12], [11, -3, -12, 18, -4, 8, -3, -3], [7, -8, -9, 3, -15, 1, -11, -6], [-11, 2, 4, -3, 17, 1, 6, 2], [14, -10, -1, -1, 10, 2, 4, -2], [9, 2, -7, 6, 1, -10, -1, 1], [-1, -13, -6, -10, 4, 1, -5, 1], [-18, 13, 2, -11, -15, -12, -3, -5], [-7, -11, 7, -5, 1, 10, -9, 0], [-24, 9, -3, 1, -17, 9, -4, -2], [16, 5, -8, -1, -6, -11, 9, 2], [20, -19, -9, -3, 3, -1, -9, -2], [-11, -5, 14, -10, 0, 0, 4, 6], [5, 1, -1, -7, 11, 3, 1, -14], [-17, 0, 6, -9, -16, 4, -14, -6], [-1, 8, 3, -4, -11, 10, 2, -1], [-6, -15, -13, 1, -13, 12, -17, -11], [1, 14, 3, 4, -4, 3, -9, -1], [-10, 3, -2, -7, 7, 0, 1, 6], [8, 14, 1, -3, 3, -21, 13, 3], [1, -11, -11, 0, -18, 16, -24, 0], [13, 4, -12, 0, -4, -10, 6, 1], [4, -1, -2, 2, -2, 1, -15, 15], [11, -11, -17, 10, -10, -2, -6, 0], [-9, -5, -8, 10, 8, 0, 10, 2], [-7, 24, 12, -2, -4, -10, 17, -2], [-22, 4, 2, 2, -4, 5, -11, -5], [-1, -14, -2, -4, -4, 4, -3, -5], [12, 1, 1, 1, 11, 1, 7, -3], [-1, 10, 1, 1, 5, -10, 3, 6], [-16, -2, 13, -14, 1, 1, -3, -4], [2, -8, -14, 0, -17, 3, -22, -10], [-14, 16, 7, 2, -19, -4, -5, 6], [-12, 2, 1, 11, -3, 4, -3, 3], [1, -10, -12, 6, -10, 18, -19, -3], [6, 3, 12, 0, -1, -4, 10, 3], [3, 0, 11, -13, 2, 1, -2, -6], [8, -9, -9, -7, 6, -5, 1, 6], [-1, 4, 5, -3, 7, -17, 13, 12], [-11, -4, -5, -6, -11, 2, -7, 3], [0, 20, 17, -6, -7, -12, 5, 2], [4, -17, -5, 5, 15, 17, -4, 8], [5, -4, -2, 7, 5, 11, -2, 10], [14, 11, 3, 3, 12, -15, 11, -8], [4, 6, 1, -1, -10, -2, 2, -8], [1, 2, 1, 10, 1, -5, 14, 3], [14, -6, -6, 6, -14, 7, -19, -7], [10, -18, -5, 12, 10, 13, -9, 3], [1, 16, -3, 6, 4, -1, 13, -3], [-18, 17, 12, 3, 0, 9, 18, 1], [3, 0, -14, 14, -4, 19, -12, 0], [16, -23, -12, -4, 1, -2, -16, -5], [9, -23, -10, -12, 2, 3, -9, -4], [11, -7, 7, 2, 0, 0, -2, 1], [23, -5, -1, 0, 20, -11, 8, -6], [-9, 2, -12, 12, -7, 7, -14, 0], [3, 1, -3, 8, -1, -1, -8, -2], [-4, -15, -2, -3, 15, -4, 2, -7], [-4, 4, 8, 5, -8, -5, -4, 12], [4, -15, -5, 17, 3, 5, 1, 1], [8, 1, 8, 6, 26, -6, 11, 7], [-9, 2, -11, 2, -17, 16, -19, 7], [-1, 0, 13, 5, 4, 5, 0, 3], [0, -11, -5, 18, 6, 12, 4, 13], [3, 15, 2, 2, -12, -9, -4, 1], [10, -26, -5, -2, 17, 0, 0, -13], [0, -6, 10, 2, 19, -2, 6, 2], [23, -13, -3, 1, -2, 3, -6, -2], [4, -8, 1, 14, 13, -1, 21, 7], [10, -2, -17, 0, -2, 3, -16, -16], [-10, 12, 26, -11, 11, -7, 10, -3], [15, 6, 0, 11, -19, 1, -9, 4], [17, -4, -6, 13, 16, -3, 0, 4], [-11, 8, 0, -6, -9, 0, 2, -15], [15, -5, -3, -10, 2, -1, -15, -5], [-21, 11, 6, 3, -7, 0, -11, 7], [9, 23, 4, 3, -8, -10, 2, 7], [-23, 0, -4, -11, -13, 0, -10, 7], [12, -5, -11, 20, 11, 15, 2, 6], [22, 13, 3, 1, -1, -3, 14, 9], [-6, 6, -7, 4, -2, 11, -8, 14], [2, -11, -14, 7, 15, 3, -2, 4], [-14, 16, 13, -13, 4, -3, 18, -2], [-15, -8, 16, -18, 10, -8, 22, 5], [6, -2, 3, -18, 6, -13, 12, 0], [2, 9, 10, 3, -3, -9, 13, 25], [-14, 14, 11, 2, -3, 10, -5, -4], [28, -4, -5, -8, -1, 6, -5, -12], [-7, -2, 1, 1, -9, 2, 15, -2], [-9, 13, 10, -2, -12, -3, -16, -2], [10, -8, -9, -7, 9, 9, 10, 6], [3, -13, -7, 5, 7, 4, -22, 6], [8, 13, 17, -14, 9, -29, 20, 8], [13, -20, -17, 6, -1, -1, -15, 13], [2, -12, -24, 4, -9, 9, -24, -17], [-15, -1, -5, -2, -16, 9, 2, 6], [20, -5, 10, 4, 10, -1, 13, 11], [-3, -19, 5, -10, 1, 7, 3, -11], [-22, 8, 3, -13, -6, 4, -7, -10], [16, 2, 11, -4, 7, 5, 5, -10], [2, 3, 1, 2, 0, 1, -9, 7], [-23, -19, 1, -7, -13, 6, -13, -8], [-13, -6, 8, -10, -8, -11, -14, 6], [-20, 10, -15, 3, -15, 5, -19, 5], [14, 16, -8, 15, -5, 1, -3, 13], [-4, -3, 1, -5, -9, -13, 13, 11], [2, 0, -5, 0, -17, 9, -22, 4], [-4, -2, 14, -13, 2, 3, 3, 2], [0, 13, -3, -6, 7, 2, 5, 3], [14, -1, -16, 11, -14, 1, -6, -12], [-5, -3, 14, -22, 5, -16, 5, -12], [12, -12, -9, -3, -3, -4, -1, 0], [4, 1, 1, 15, 5, 14, 3, 7], [7, -9, -21, 0, -6, 18, -10, -2], [5, 13, -15, 8, -12, -6, 2, -2], [18, 11, -8, 1, -8, -9, -1, -6], [2, -11, -16, -1, 14, 14, 2, -8], [16, -14, -3, 4, 11, 8, 1, -12], [-8, 18, 7, 5, -8, -7, 26, -3], [-17, 9, 12, -11, 3, -16, 8, -3], [-6, 7, 11, -9, -23, 3, -15, 2], [-2, 4, 10, -6, 11, 2, 5, 7], [26, -6, -14, 2, -5, -6, 5, 3], [3, 0, 4, -4, 15, -21, 24, 4], [13, 14, 12, -6, 5, -4, 5, -19], [18, 5, -4, 16, 6, -1, -20, 9], [13, 4, 14, -5, -3, -14, 16, 2], [-2, -1, 5, 0, 4, 10, 2, 4], [27, -14, -12, 5, 2, 6, -8, -4], [-1, -2, -8, 4, 9, -9, -6, -3], [30, -27, -6, -6, 11, 10, -8, -10], [-4, 6, 6, -10, 2, 8, 6, 2], [-5, 2, -5, 2, -11, 2, 6, 3], [-30, 2, 6, 4, 9, -14, 11, 5], [7, 15, -1, -6, -8, -5, -18, -9], [-10, 11, 11, -12, -4, -27, 12, -5], [21, 1, -1, 5, 0, 0, -10, 4], [3, 8, -4, -18, 0, -6, -6, -25], [14, 24, 20, -6, 13, -15, 22, 8], [8, 4, 14, -15, 11, -15, 15, 0], [-1, 4, -6, -1, 7, 5, -2, -14], [6, -8, 1, -5, 8, -21, 14, 5], [-7, 13, -3, 10, -13, 4, 4, 6], [13, -4, -10, 2, -7, 1, 10, -7], [-17, 0, 0, -6, -9, -14, 2, 10], [7, 19, 20, 2, 9, -11, 12, 0], [-10, -14, -22, 19, 9, 12, -16, 3], [-21, 12, 10, -9, 5, 9, 4, -12], [6, -8, -17, -8, 5, 3, -12, -11], [9, -4, -7, 12, 1, -5, -1, 0], [-12, -4, -4, -17, -20, -3, -14, -14], [20, 4, 5, 5, 1, -8, 0, -11], [17, -4, -1, 5, 20, 2, 20, 4], [7, -2, 12, 7, -8, -7, 3, 5], [14, 4, 7, 13, 5, 7, 13, 12], [-7, -8, 3, -8, 20, 9, 1, -1], [-11, -9, 8, 14, 3, 16, 3, 10], [-16, -6, 6, -22, 2, -4, -7, -12], [-15, 5, -15, 4, 1, -9, -11, 2], [3, -25, -23, 4, 2, 13, -37, -14], [-8, -1, -4, 0, -20, 14, -28, 1], [-8, 13, 0, -8, -1, -20, 7, -13], [18, 6, 8, 8, 8, 6, -1, -6], [-37, 25, 30, 2, 14, 2, 20, 8], [-22, 7, 19, -11, 6, -7, 11, -23], [-11, 13, 21, 12, 9, -3, 1, 7], [11, -12, -8, -4, 15, 10, -2, 3], [-25, 12, 14, -3, 16, 5, 3, 2], [19, -2, -6, 2, 10, -17, -4, -1], [-6, 2, 18, 11, -8, 18, 0, -3], [-25, 3, 10, -10, -6, -9, 9, 6], [19, 3, -3, -1, 29, -28, 25, 3], [-16, 1, 6, 13, -6, 6, -2, 24], [2, -8, 17, 6, 14, -10, 9, 7], [6, 7, 9, -6, 1, -5, 18, -29], [17, -12, -13, 20, 4, 6, -4, 1], [-8, 7, 8, 6, -25, 3, -11, 18], [5, 1, 2, 1, -11, 17, -2, 10], [28, -14, -17, -4, 8, 3, 5, 12], [-2, -2, 17, -4, -4, 5, 6, 6], [-23, 2, 11, -21, 10, -5, 0, 10], [2, -6, -5, 6, -4, -4, -3, 16], [-22, -4, 1, -1, -16, 17, -25, 1], [-1, 0, -12, 16, -10, 32, -16, 2], [-10, -15, -1, 17, 10, -1, -2, 7], [-17, 34, 10, 4, -20, -8, -4, 17], [-4, -13, 0, -7, -13, 8, -11, 13], [-19, 29, 10, 2, 0, -4, 21, 2], [21, -11, 6, -1, 26, -5, 10, 4], [-21, 21, 19, -20, -12, 5, 11, -8], [-10, 29, 18, -21, -18, -14, 21, -4], [-5, 17, 28, -21, -7, -3, 2, -8], [-8, 4, -2, -4, -26, 11, -27, 1], [-7, 2, 6, 20, 13, -3, -8, 5], [-19, -4, -7, 11, -14, 28, -9, -11], [24, -10, -25, 17, -12, 8, -10, -8], [-14, -6, 0, -3, -8, 12, -2, -2], [-16, 8, 7, 2, -5, 20, 18, -7], [-56, 9, 8, 4, -5, -3, -5, -1], [23, 14, -16, -11, -4, -26, 7, -6], [1, 3, 11, -2, 7, -8, 8, 4], [-10, 2, 0, 2, 4, -3, 4, 6], [2, 6, 21, -10, -9, -6, -9, 12], [26, -4, 6, -4, -8, -9, 17, -5], [-24, 3, 42, -13, 26, -5, 22, -4], [-3, -12, -5, 7, 4, 26, 9, 5], [-22, 1, 8, -10, -10, 18, -12, 9], [-11, -17, -4, 11, 11, 3, -22, -2], [17, -4, -15, 21, 23, 3, 20, 2], [17, -7, -4, -11, 3, -3, -2, -1], [5, 21, 5, -13, 11, -3, 8, -19], [-44, 17, 6, 0, -8, 0, 16, -13], [18, 5, -15, 19, -4, 7, 10, 0], [16, -15, 0, -3, -19, -9, -19, 0], [5, -5, -11, -3, 4, 17, 4, -14], [-4, 1, -11, 1, -12, -4, -18, -10], [-7, -1, -17, 12, 2, 10, 2, -6], [-11, -23, -18, 8, -10, 1, -6, 2], [1, 17, 25, -10, 5, -6, 17, -11], [-18, 4, 10, -12, -8, -9, 4, -9], [36, -4, -10, 17, 23, -9, 14, -6], [-37, 6, -11, 21, 14, 3, 3, 10], [23, -17, -40, 17, -14, -7, -10, 12], [24, -18, -17, 4, -1, 0, -26, 12], [-4, 7, -19, -12, -24, 3, -11, -8], [-22, 1, 19, -16, 31, -6, 19, -7], [-19, 23, 25, 6, 14, -5, 43, 9], [12, -7, -8, 3, -6, -14, -11, 10], [-28, -11, -10, 10, 12, 5, 2, 9], [25, -3, -21, -8, -14, -6, 6, -4], [-18, 0, 27, -19, 17, -14, 8, -1], [4, 3, 8, -4, 24, -14, 23, -13], [-12, 6, 14, -8, 12, -12, 17, -10], [-5, 10, 6, -1, -14, -15, 24, 11], [-17, -8, -10, -3, -19, 16, -9, -22], [-16, 8, 10, -16, 8, -7, 17, 9], [17, 2, -8, 16, 24, -6, 25, 2], [31, 4, -12, 10, -8, 8, 17, 10], [-11, -18, -7, -18, 14, -9, 12, -5], [17, 0, -7, 14, -11, 20, 7, -11], [9, -19, 8, -13, -4, 12, -13, 9], [-11, -11, -14, -7, -7, -12, -12, 4], [-29, 22, -4, 18, 1, 19, -1, 5], [7, -7, -6, 2, -3, 0, -24, 17], [-17, 5, -5, -5, -2, -12, 3, 15], [-31, 3, 6, 2, 0, -4, -4, 8], [-14, -4, -21, -4, -4, 3, -28, -6], [-28, 0, 4, -1, 17, -9, 21, 3], [-12, 11, -15, 10, 0, 7, -1, 5], [19, 1, -9, 11, 9, -8, 1, -7], [-1, -7, -15, 0, 28, -8, 11, 2], [24, -7, 1, -12, 8, -26, 16, -7], [17, -9, -20, 21, -6, 19, -13, -6], [-31, -5, 8, -18, 0, -22, 0, 5], [16, -19, 8, -1, -2, -14, -10, 10], [-2, -8, 7, 1, 11, 4, 11, 27], [-34, 10, 6, 14, 3, 13, -10, 8], [-1, 3, -8, 18, -22, -6, 7, -4], [-10, 0, -16, 8, -3, 8, -20, -20], [10, -5, 10, 22, 8, 8, 11, 7], [8, 6, -2, 9, 8, -8, 1, 31], [-37, 20, 28, -8, 4, 8, 6, -12], [-3, -22, -1, -13, 8, 7, -2, -16], [3, 18, 5, 8, -13, -21, -20, -2], [-16, 18, -9, 16, 3, 27, -3, 2], [-23, 15, 26, 15, -11, 10, -14, 5], [-28, -15, 15, 6, -9, 19, -16, 3], [-6, -8, 8, -18, -8, -9, 10, 12], [-22, -10, 14, -5, -17, 6, -23, 7], [6, 4, 16, 11, 10, 6, 28, 21], [-42, 6, 10, -8, -17, 2, -4, 24], [-9, -21, -20, 0, 22, 11, -3, -11], [24, -6, -14, 28, 26, 13, 17, 16], [-22, 14, 7, 6, 5, -14, 14, 28], [-15, -20, 6, 2, -18, 15, -15, 0], [-21, -7, -14, -4, -30, 5, -13, -11], [32, 1, 0, -12, 20, -33, 10, -19], [-9, 3, 9, -10, 18, 1, 7, -16], [-8, -6, -13, 12, -18, 17, -34, -9], [-18, 6, 14, -24, -1, -20, 5, -16], [7, 11, 18, 8, 3, 4, 18, 0], [-30, 7, -16, 12, 9, -3, -2, -11], [-37, 8, 7, -17, -22, -12, 5, 7], [-33, -6, 26, -13, 29, 5, 19, -9], [-38, -13, -4, 5, 9, 10, -6, -7], [5, 19, 4, 3, -3, -24, 2, -14], [4, 5, -15, 7, -13, -8, -1, -16], [11, 2, -8, -3, 1, -24, 18, -4], [-8, -15, -12, 32, 4, 6, 3, 25]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6024_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6024_2_a_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_6024_2_a_k(:prec:=8)
    chi := MakeCharacter_6024_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_6024_2_a_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_6024_2_a_k( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6024_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-8, -31, 41, 75, -19, -42, -4, 5, 1]>,<7,R![-4, 28, -35, -69, 72, 16, -17, -1, 1]>],Snew);
    return Vf;
end function;