
// Make newform 3024.2.cc.a in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_3024_cc();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_3024_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_3024_2_cc_a();".
// 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_3024_2_cc_a();".
// 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 := [9, 0, -36, 0, 123, 0, -78, 0, 37, 0, -7, 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], [4446, 0, 17052, 0, -3807, 0, 446, 0, 148, 0, -28, 0], [0, -15864, 0, -252, 0, 861, 0, -1369, 0, 259, 0, -49], [-3438, 0, -16197, 0, 17007, 0, -7214, 0, 1481, 0, -164, 0], [-30249, 0, 16296, 0, -1224, 0, -3661, 0, 925, 0, -175, 0], [-777, 0, 17343, 0, -10175, 0, 5217, 0, -987, 0, 148, 0], [0, 8947, 0, 360, 0, -1230, 0, 1751, 0, -370, 0, 70], [0, 66168, 0, -122898, 0, 76698, 0, -30748, 0, 5701, 0, -730], [31473, 0, -123654, 0, 79281, 0, -34855, 0, 6478, 0, -877, 0], [0, -18972, 0, 64821, 0, -39839, 0, 19499, 0, -3689, 0, 543], [0, -42912, 0, 249792, 0, -167049, 0, 81362, 0, -15509, 0, 2237], [0, 32616, 0, -111438, 0, 71935, 0, -33522, 0, 6342, 0, -890]];
    Rf_basisdens := [1, 12897, 4299, 12897, 12897, 4299, 1433, 12897, 12897, 4299, 12897, 4299];
    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_3024_cc();"
function MakeCharacter_3024_cc()
    N := 3024;
    order := 6;
    char_gens := [1135, 757, 785, 2593];
    v := [6, 6, 5, 3];
    // 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_3024_cc_Hecke();"
function MakeCharacter_3024_cc_Hecke(Kf)
    N := 3024;
    order := 6;
    char_gens := [1135, 757, 785, 2593];
    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, -1, 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 := 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, 0, 0, -1, 0], [0, 0, 0, -1, 1, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, -1, 1, -1, 0, 0, -1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 0, -1, 1, 0, -1, 2, 1], [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-4, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0], [-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 2, 0], [0, 2, 0, 3, -1, 2, 0, 0, -1, 0, 0, 0], [0, 0, -2, 0, 0, 0, -2, 1, 0, 1, 1, 1], [-1, -2, 0, -1, -2, 1, 0, 0, -4, 0, 0, 0], [0, 0, 2, 0, 0, 0, -1, 0, 0, -4, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1], [-1, -2, 0, 1, 0, 2, 0, 0, -3, 0, 0, 0], [-2, -2, 0, 3, -2, 7, 0, 0, -4, 0, 0, 0], [0, 0, -3, 0, 0, 0, -3, 1, 0, 3, 2, 3], [0, 1, 0, -2, 3, 0, 0, 0, 3, 0, 0, 0], [0, 0, -4, 0, 0, 0, 2, -2, 0, 2, -2, -1], [0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1], [0, 0, -2, 0, 0, 0, -2, -1, 0, 1, -1, 1], [0, 0, 1, 0, 0, 0, 1, -4, 0, 0, -2, 0], [7, -2, 0, 6, -2, -8, 0, 0, -4, 0, 0, 0], [8, -3, 0, -1, 5, -1, 0, 0, 0, 0, 0, 0], [6, -2, 0, 2, -4, 8, 0, 0, -2, 0, 0, 0], [4, -7, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -5, 2], [6, -2, 0, -1, 3, -4, 0, 0, -3, 0, 0, 0], [0, 0, -7, 0, 0, 0, -3, 2, 0, 0, 1, 0], [-6, 11, 0, -3, 6, -9, 0, 0, 3, 0, 0, 0], [0, -1, 0, 3, -4, 5, 0, 0, -4, 0, 0, 0], [0, 0, -3, 0, 0, 0, 1, -2, 0, 0, -1, 0], [1, 5, 0, -1, -3, -1, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 2, 0, 0, -6, 1, -4], [0, 0, -4, 0, 0, 0, 0, 5, 0, 2, 5, 0], [8, -5, 0, 3, -5, -13, 0, 0, -10, 0, 0, 0], [0, 0, 2, 0, 0, 0, 4, 1, 0, -2, 2, -4], [-6, 8, 0, -11, 3, -8, 0, 0, -3, 0, 0, 0], [-2, -7, 0, 10, 0, 12, 0, 0, -4, 0, 0, 0], [8, -2, 0, 5, -2, -11, 0, 0, -4, 0, 0, 0], [0, 0, -1, 0, 0, 0, -5, 0, 0, 1, 0, 5], [5, -6, 0, -2, 0, -7, 0, 0, -14, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 3, -4], [0, 0, -4, 0, 0, 0, -6, 1, 0, 2, 1, 3], [0, 0, -5, 0, 0, 0, -6, -2, 0, 0, -1, 0], [1, -7, 0, 12, -7, 10, 0, 0, -14, 0, 0, 0], [-3, -4, 0, -2, 4, -5, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 3, -2, 1], [0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, -1], [0, 0, 2, 0, 0, 0, 4, 0, 0, -4, -4, -8], [-12, -3, 0, 2, 1, 8, 0, 0, -1, 0, 0, 0], [0, 0, 4, 0, 0, 0, 3, 3, 0, 4, 0, 3], [0, 0, 3, 0, 0, 0, 6, 2, 0, -3, 4, -6], [0, -13, 0, -4, -9, 9, 0, 0, -9, 0, 0, 0], [-18, 7, 0, -4, -3, 5, 0, 0, 3, 0, 0, 0], [0, 0, 6, 0, 0, 0, -4, 2, 0, 0, 1, 0], [0, 0, 6, 0, 0, 0, -1, 0, 0, -12, -1, 2], [0, 0, -6, 0, 0, 0, 3, -2, 0, 6, -4, -3], [0, 0, -3, 0, 0, 0, 0, 0, 0, 6, 4, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 4, -1, -3], [-4, 16, 0, -13, -3, -11, 0, 0, 3, 0, 0, 0], [0, -9, 0, -2, -7, 9, 0, 0, -7, 0, 0, 0], [4, 3, 0, -10, 0, -14, 0, 0, -4, 0, 0, 0], [6, -2, 0, 3, -6, 9, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4, 0, -6, 4, -2], [0, 0, -10, 0, 0, 0, -2, -4, 0, 5, -4, 1], [1, -1, 0, 13, -1, 11, 0, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3, 0, 4, 3, 4], [-11, 11, 0, -13, 0, -2, 0, 0, 9, 0, 0, 0], [-2, 14, 0, -9, 4, -9, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, -2, 0, 0, -4, 7, 4], [-4, 1, 0, 2, -3, 4, 0, 0, 3, 0, 0, 0], [0, 0, -8, 0, 0, 0, 2, -1, 0, 8, -2, -2], [0, -11, 0, -1, 2, -1, 0, 0, 1, 0, 0, 0], [0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 3, 0, 0, -14, -2, -6], [0, -1, 0, 8, -9, -6, 0, 0, -9, 0, 0, 0], [2, 4, 0, 3, 4, -1, 0, 0, 8, 0, 0, 0], [0, 0, -1, 0, 0, 0, 4, -5, 0, 1, -10, -4], [0, 0, 0, 0, 0, 0, 0, 3, 0, 4, -3, 1], [16, -4, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0], [-1, 5, 0, -15, 5, -13, 0, 0, 10, 0, 0, 0], [0, 1, 0, 6, -5, 4, 0, 0, -5, 0, 0, 0], [0, 0, -12, 0, 0, 0, 10, -10, 0, 6, -10, -5], [5, 1, 0, 10, 0, 5, 0, 0, 12, 0, 0, 0], [0, 0, 2, 0, 0, 0, -2, -3, 0, 2, 0, -2], [0, 0, -10, 0, 0, 0, -2, -5, 0, 5, -5, 1], [-20, -10, 0, 3, 4, 3, 0, 0, 0, 0, 0, 0], [1, -11, 0, 3, -6, 4, 0, 0, -3, 0, 0, 0], [14, -2, 0, 2, 0, -12, 0, 0, -2, 0, 0, 0], [0, 0, -5, 0, 0, 0, 2, -12, 0, -5, 0, 2], [0, 0, 5, 0, 0, 0, 1, 0, 0, -10, 8, -2], [0, 0, 1, 0, 0, 0, -6, 3, 0, 1, 0, -6], [0, 0, -6, 0, 0, 0, -3, -1, 0, 6, -2, 3], [-7, -8, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0], [0, -5, 0, 7, -12, -12, 0, 0, -12, 0, 0, 0], [8, -2, 0, 11, -2, -5, 0, 0, -4, 0, 0, 0], [0, 0, -3, 0, 0, 0, -2, 0, 0, 6, -8, 4], [6, -24, 0, 16, 8, 13, 0, 0, -8, 0, 0, 0], [14, 11, 0, -10, 0, -24, 0, 0, 12, 0, 0, 0], [0, 0, 3, 0, 0, 0, -9, 0, 0, -3, 0, 9], [0, 0, 6, 0, 0, 0, 12, 4, 0, -3, 4, -6], [0, 0, 1, 0, 0, 0, 5, -3, 0, 1, 0, 5], [6, 4, 0, -6, 12, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4, 0, -11, 4, -12], [0, 0, 3, 0, 0, 0, -4, -10, 0, 0, -5, 0], [-25, 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0], [-4, 17, 0, -3, 6, -7, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 1, -4, 7], [-14, 3, 0, 6, -15, 6, 0, 0, 0, 0, 0, 0], [-18, 7, 0, -1, -6, 8, 0, 0, 6, 0, 0, 0], [0, 0, -2, 0, 0, 0, 1, 18, 0, 0, 9, 0], [0, 0, 5, 0, 0, 0, 3, -3, 0, 5, 0, 3], [9, -4, 0, -9, 18, 0, 0, 0, 9, 0, 0, 0], [0, -1, 0, 10, -9, 10, 0, 0, 9, 0, 0, 0], [0, 0, 14, 0, 0, 0, -1, 6, 0, 0, 3, 0], [0, -2, 0, -9, 7, -5, 0, 0, 7, 0, 0, 0], [0, 0, -8, 0, 0, 0, 10, -7, 0, 4, -7, -5], [16, -2, 0, 0, -2, -32, 0, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, -1, -4, -12], [2, -10, 0, 18, -10, 14, 0, 0, -20, 0, 0, 0], [0, -2, 0, -12, 10, -20, 0, 0, 10, 0, 0, 0], [0, 0, 2, 0, 0, 0, -3, 3, 0, 2, 0, -3], [0, 0, 0, 0, 0, 0, 0, 3, 0, -2, -3, -14], [0, 0, 1, 0, 0, 0, 6, -10, 0, 0, -5, 0], [-2, 20, 0, -1, -18, -1, 0, 0, 0, 0, 0, 0], [-9, 22, 0, 3, -6, -6, 0, 0, -3, 0, 0, 0], [8, 0, 0, 7, 0, -1, 0, 0, 7, 0, 0, 0], [-1, 3, 0, 5, -13, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 2, 16], [0, 0, -9, 0, 0, 0, -5, -4, 0, 0, -2, 0], [0, 0, 7, 0, 0, 0, 0, -9, 0, 7, 0, 0], [0, 0, -2, 0, 0, 0, -2, -10, 0, 0, -5, 0], [0, 0, 8, 0, 0, 0, 5, 0, 0, -16, 8, -10], [-1, 5, 0, -9, 5, -7, 0, 0, 10, 0, 0, 0], [0, 0, 5, 0, 0, 0, 1, -8, 0, -5, -16, -1], [-24, 15, 0, -8, -7, 4, 0, 0, 7, 0, 0, 0], [-28, 2, 0, -16, 0, 12, 0, 0, -12, 0, 0, 0], [4, 8, 0, 13, 8, 5, 0, 0, 16, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, -3, 0, -1, -6, 1], [0, 0, 14, 0, 0, 0, 12, 7, 0, -7, 7, -6], [0, 0, 0, 0, 0, 0, 0, 3, 0, 5, -3, -13], [0, 0, 2, 0, 0, 0, -10, 8, 0, -1, 8, 5], [0, 0, -9, 0, 0, 0, -10, -2, 0, 0, -1, 0], [-23, -1, 0, -5, -1, 41, 0, 0, -2, 0, 0, 0], [-17, -4, 0, -7, 0, 10, 0, 0, -15, 0, 0, 0], [0, 0, -8, 0, 0, 0, 4, -3, 0, -8, 0, 4], [13, -19, 0, 6, 7, 6, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, 3, 0, 0, -10, 16, -6], [0, -4, 0, -12, 8, 5, 0, 0, 8, 0, 0, 0], [-32, 11, 0, -17, 6, -1, 0, 0, -6, 0, 0, 0], [22, -31, 0, 12, 7, 12, 0, 0, 0, 0, 0, 0], [0, 0, 16, 0, 0, 0, 6, -7, 0, -8, -7, -3], [0, 0, -2, 0, 0, 0, -1, 4, 0, 2, 8, 1], [0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -7, 8], [-2, 23, 0, -17, -6, -16, 0, 0, 6, 0, 0, 0], [10, 8, 0, 0, 8, -20, 0, 0, 16, 0, 0, 0], [-25, 20, 0, -13, 0, 12, 0, 0, 27, 0, 0, 0], [0, 0, -8, 0, 0, 0, 3, 0, 0, -8, 0, 3], [-7, -10, 0, 18, -36, 11, 0, 0, -18, 0, 0, 0], [0, 0, 2, 0, 0, 0, -6, 16, 0, -1, 16, 3], [4, 17, 0, -3, -11, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, -10, -6, 2], [-13, 13, 0, -5, -3, -5, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 1, 0, 0, 2, -1, -2], [-8, 5, 0, -5, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, -13, 0, 0, 0, 2, 12, 0, 0, 6, 0], [-17, -2, 0, 6, -12, -11, 0, 0, -6, 0, 0, 0], [0, 2, 0, -10, 12, 27, 0, 0, 12, 0, 0, 0], [0, 0, 17, 0, 0, 0, -6, 18, 0, 0, 9, 0], [0, 0, -3, 0, 0, 0, 6, 0, 0, 6, 2, -12], [0, -4, 0, 17, -21, -2, 0, 0, -21, 0, 0, 0], [11, 5, 0, 0, 5, -22, 0, 0, 10, 0, 0, 0], [0, 0, -19, 0, 0, 0, 1, 4, 0, 19, 8, -1], [0, 0, 0, 0, 0, 0, 0, -1, 0, 18, 1, -2], [0, 1, 0, 1, 0, 24, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, -6, -17, 0, 1, -17, 3], [22, -4, 0, 14, 0, -8, 0, 0, 6, 0, 0, 0], [0, 0, -3, 0, 0, 0, 3, 15, 0, -3, 0, 3], [21, 7, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0], [0, 0, 18, 0, 0, 0, 10, -7, 0, -9, -7, -5], [-1, -5, 0, -6, 17, -6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11], [4, -19, 0, 35, 0, 31, 0, 0, -3, 0, 0, 0], [0, 0, -3, 0, 0, 0, -5, -9, 0, -3, 0, -5], [0, 0, 16, 0, 0, 0, 5, -1, 0, -16, -2, -5], [42, 0, 0, -1, 1, -22, 0, 0, -1, 0, 0, 0], [4, 12, 0, -11, 10, -11, 0, 0, 0, 0, 0, 0], [0, 0, -10, 0, 0, 0, -24, 2, 0, 5, 2, 12], [17, -11, 0, 24, -11, -10, 0, 0, -22, 0, 0, 0], [0, 0, -13, 0, 0, 0, -5, 0, 0, 26, 2, 10], [28, 0, 0, -7, 0, -35, 0, 0, -7, 0, 0, 0], [0, 5, 0, -16, 21, -6, 0, 0, 21, 0, 0, 0], [0, 0, 24, 0, 0, 0, -2, 2, 0, -12, 2, 1], [0, 0, -1, 0, 0, 0, 0, 15, 0, -1, 0, 0], [5, 26, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0, -1, -5, 6], [0, 0, 0, 0, 0, 0, -11, 10, 0, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 5, -8, 8], [0, 0, 1, 0, 0, 0, 4, 0, 0, 1, 0, 4], [0, 0, -1, 0, 0, 0, 10, -6, 0, -1, 0, 10], [0, 0, -20, 0, 0, 0, 2, 0, 0, 20, 0, -2], [15, -13, 0, -8, 16, 7, 0, 0, 8, 0, 0, 0], [12, -12, 0, -8, 20, -14, 0, 0, -20, 0, 0, 0], [0, 0, -7, 0, 0, 0, -6, 4, 0, 0, 2, 0], [-4, 25, 0, -20, 15, -20, 0, 0, 0, 0, 0, 0], [0, 0, 11, 0, 0, 0, 5, 0, 0, -22, -7, -10], [0, 18, 0, -2, 20, 0, 0, 0, 20, 0, 0, 0], [0, 0, -2, 0, 0, 0, -4, 4, 0, 1, 4, 2], [0, 0, -2, 0, 0, 0, -1, 0, 0, 4, 4, 2], [0, 0, 0, 0, 0, 0, 0, -7, 0, -16, 7, 17], [35, -9, 0, 16, 0, -19, 0, 0, -2, 0, 0, 0], [0, 0, -4, 0, 0, 0, -16, -13, 0, 2, -13, 8], [-17, -1, 0, -11, -1, 23, 0, 0, -2, 0, 0, 0], [18, 13, 0, -4, 8, 14, 0, 0, 4, 0, 0, 0], [46, -9, 0, 2, 0, -44, 0, 0, -16, 0, 0, 0], [0, 0, -14, 0, 0, 0, 4, 0, 0, 0, 0, 0], [-10, -4, 0, 12, -24, 2, 0, 0, -12, 0, 0, 0], [-5, 11, 0, -18, 25, -18, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 2, 0, 0, -16, -2, -4], [0, -3, 0, 2, -5, 21, 0, 0, -5, 0, 0, 0], [0, 0, 18, 0, 0, 0, 4, 20, 0, -9, 20, -2], [-1, 4, 0, -15, 4, -13, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2], [-6, -12, 0, 17, -5, 20, 0, 0, 5, 0, 0, 0], [-11, -7, 0, 19, 0, 30, 0, 0, 5, 0, 0, 0], [0, 0, 8, 0, 0, 0, -8, 6, 0, -8, 12, 8], [2, -2, 0, 8, 0, 6, 0, 0, 4, 0, 0, 0], [24, 4, 0, -1, 2, 23, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -12, 0, -10, 12, 6], [0, 0, 0, 0, 0, 0, -4, -11, 0, 0, -11, 2], [0, 0, 6, 0, 0, 0, 4, 28, 0, 0, 14, 0], [-17, -10, 0, -15, -10, 19, 0, 0, -20, 0, 0, 0], [-3, 19, 0, 9, -18, 6, 0, 0, -9, 0, 0, 0], [0, 0, -9, 0, 0, 0, -5, 3, 0, -9, 0, -5], [-44, 8, 0, -17, 9, 5, 0, 0, -9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 9, -3, 0, 0, -6, -9], [0, 0, 1, 0, 0, 0, 4, 16, 0, 0, 8, 0], [2, 4, 0, -9, 14, -9, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0, 0, -2, 2, 2], [0, 0, 16, 0, 0, 0, -10, -8, 0, -8, -8, 5], [0, 0, 2, 0, 0, 0, 7, -1, 0, -2, -2, -7], [0, 0, -5, 0, 0, 0, 2, 0, 0, 10, -8, -4], [-4, -26, 0, 37, 0, 41, 0, 0, -15, 0, 0, 0], [5, -20, 0, 6, -20, -4, 0, 0, -40, 0, 0, 0], [-50, 9, 0, -13, 0, 37, 0, 0, 5, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, -12, 0, 2, 0, 2], [7, -17, 0, 6, -12, 13, 0, 0, -6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 20, -2, 11], [0, 0, -6, 0, 0, 0, 2, 17, 0, 3, 17, -1], [5, 13, 0, -9, 13, -19, 0, 0, 26, 0, 0, 0], [32, -5, 0, 13, -21, 13, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 0, 11, -7, 9], [0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, -2], [0, 0, -17, 0, 0, 0, 20, -9, 0, 17, -18, -20], [0, 1, 0, 25, -24, 18, 0, 0, -24, 0, 0, 0], [18, -13, 0, 4, 9, -5, 0, 0, -9, 0, 0, 0], [0, 0, -13, 0, 0, 0, 14, -16, 0, 0, -8, 0], [0, 0, 5, 0, 0, 0, 10, 11, 0, -5, 22, -10], [0, 0, -12, 0, 0, 0, 8, 0, 0, 24, -4, -16], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 12], [2, -5, 0, -13, -5, -17, 0, 0, -10, 0, 0, 0], [0, 0, -12, 0, 0, 0, 12, -13, 0, 6, -13, -6], [-4, 5, 0, 11, 0, 15, 0, 0, 21, 0, 0, 0], [9, 7, 0, -16, 32, -7, 0, 0, 16, 0, 0, 0], [0, 0, 16, 0, 0, 0, 9, 4, 0, 0, 2, 0], [40, -25, 0, 9, 7, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -5, 0, 21, 5, 10], [-37, 6, 0, -23, 0, 14, 0, 0, -11, 0, 0, 0], [0, 0, 6, 0, 0, 0, -17, 14, 0, 0, 7, 0], [0, 0, 3, 0, 0, 0, -6, 5, 0, -3, 10, 6], [15, -5, 0, 6, -12, 21, 0, 0, -6, 0, 0, 0], [0, 7, 0, 6, 1, 52, 0, 0, 1, 0, 0, 0], [20, 4, 0, -18, 32, -18, 0, 0, 0, 0, 0, 0], [0, 0, 16, 0, 0, 0, 12, 19, 0, -8, 19, -6], [0, 0, 7, 0, 0, 0, -6, 0, 0, -14, 13, 12], [20, -17, 0, 7, 0, -13, 0, 0, -27, 0, 0, 0], [0, 0, 10, 0, 0, 0, 14, -8, 0, -5, -8, -7], [0, 0, 0, 0, 0, 0, 0, 7, 0, -22, -7, -7], [0, 0, -2, 0, 0, 0, -11, 8, 0, 0, 4, 0], [4, -1, 0, -11, -1, -19, 0, 0, -2, 0, 0, 0], [-10, 9, 0, -7, 5, -7, 0, 0, 0, 0, 0, 0], [0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -11, 0, -8, 11, 1], [0, 0, -10, 0, 0, 0, -9, -6, 0, -10, 0, -9], [-54, 7, 0, -7, 0, 20, 0, 0, 0, 0, 0, 0], [0, 0, 10, 0, 0, 0, 10, 6, 0, 10, 0, 10], [-24, 26, 0, 9, -18, -15, 0, 0, -9, 0, 0, 0], [0, 0, -9, 0, 0, 0, -9, 0, 0, 18, 1, 18], [0, 17, 0, 17, 0, 12, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, -8, 0, 0, -4, -7, 16], [0, 0, 0, 0, 0, 0, 0, 3, 0, -6, -3, -1], [0, 0, 8, 0, 0, 0, 4, 2, 0, -4, 2, -2], [0, 0, -8, 0, 0, 0, 0, -15, 0, -8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 21, -1, -10], [0, 0, -29, 0, 0, 0, 6, -2, 0, 0, -1, 0], [-11, 8, 0, 9, 8, 31, 0, 0, 16, 0, 0, 0], [-38, 32, 0, -25, 18, -25, 0, 0, 0, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_3024_cc_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_3024_2_cc_a();".
// 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_3024_2_cc_a(:prec:=12)
    chi := MakeCharacter_3024_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(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_3024_2_cc_a();".
// 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_3024_2_cc_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_3024_cc();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![6561, 0, 5346, 0, 3141, 0, 828, 0, 159, 0, 15, 0, 1]>],Snew);
    return Vf;
end function;