
// Make newform 6018.2.a.r in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6018_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_6018_2_a_r();".
// 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_6018_2_a_r();".
// 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 := [-2, -6, 3, 12, -4, -3, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [-2, -1, 1, 0, 0, 0], [-2, -1, 10, -3, -3, 1], [-5, -7, 15, -1, -4, 1], [10, 5, -27, 5, 7, -2]];
    Rf_basisdens := [1, 1, 1, 1, 1, 1];
    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_6018_a();"
function MakeCharacter_6018_a()
    N := 6018;
    order := 1;
    char_gens := [4013, 1771, 1123];
    v := [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_6018_a_Hecke(Kf)
    return MakeCharacter_6018_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 := [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [-2, 1, 0, 0, 0, 1], [-1, 1, -1, 0, -1, -1], [-1, 0, 0, -1, 1, -1], [-1, 0, 0, 0, 0, 0], [-2, -2, 1, 0, 0, 1], [-1, 0, 1, 3, 1, -1], [-3, 0, 1, 2, -1, -1], [-2, 1, 2, 0, 0, 0], [-4, 2, -1, -3, 2, 1], [-3, 2, -1, 1, -1, -1], [-1, 0, 1, -3, -1, -1], [1, -2, -2, 1, 1, 0], [-5, 1, -2, -1, 1, 2], [-1, 0, 0, 0, 0, 0], [0, 1, 0, -1, -2, -1], [-3, 0, -1, 0, 3, 2], [0, 0, -1, 0, -6, -2], [1, -1, -4, 0, -3, 2], [-2, -2, 1, -2, 0, 1], [3, -3, 1, 1, 3, -2], [-3, 2, 0, 0, -1, 1], [0, 1, 2, 3, 4, 4], [-4, -1, -2, -4, -2, 3], [1, 2, -1, 0, -1, 3], [-4, -2, -2, -1, 2, 1], [1, -4, -1, 1, -3, 0], [-1, -3, -1, 1, 5, 2], [0, -2, 0, -1, 6, 3], [-2, 2, 2, -2, -4, -4], [3, -4, 4, 3, 1, 2], [-5, 1, 1, 0, -1, -3], [0, 0, -3, -3, -4, -2], [3, -4, 2, 3, -1, -3], [3, 1, -1, -2, -1, -2], [-4, 3, -2, -5, 4, 6], [1, 0, -5, -1, -1, -2], [-8, 1, -1, 2, 0, 2], [-4, 4, 1, -3, 2, 4], [3, -4, 2, 6, -3, -3], [6, 5, -4, 0, -2, -1], [-12, 6, 3, 3, 4, 0], [0, -5, 1, 3, -2, 0], [6, -2, 1, 4, -8, -3], [-3, 5, 3, -2, 3, 5], [6, 2, -3, -5, -4, 2], [-5, -4, 0, -5, 3, -2], [3, -2, 4, 1, -3, 7], [-8, 0, -5, -2, 0, 7], [2, -10, 5, 3, 4, 1], [-10, 2, 4, 5, 4, -3], [-1, 2, 1, 3, 7, -3], [-1, -2, 4, 2, -1, 1], [5, -3, -2, 4, 3, -1], [2, 0, 1, 2, -2, 1], [6, 4, -2, -3, 4, 5], [1, 1, -2, -1, 1, -3], [-6, 2, 1, 4, 0, -5], [-3, -3, 6, -1, 5, 3], [9, -2, 4, 5, -5, -9], [-12, 1, 0, -7, 0, -2], [4, -7, 3, 3, -4, -8], [2, 0, -1, 0, 0, -1], [1, 1, 0, -11, 1, 4], [10, -3, 4, 2, 8, 5], [6, -1, -1, 1, -6, 5], [-4, -7, 0, -1, 8, 2], [-1, 7, 0, -5, 9, 8], [10, -1, 1, 2, -4, -2], [-15, 0, -1, -2, -1, -1], [9, -8, 0, 5, -5, -1], [4, 3, -11, -6, -6, 0], [8, -4, 5, 3, -6, -2], [-3, 10, 2, 0, 7, 0], [-2, 1, 9, 2, 0, 1], [-13, 6, -3, -7, 11, 0], [5, -6, 2, 10, -5, -9], [-5, 1, 6, 4, -5, -6], [1, 11, -9, -2, -5, -7], [12, 3, 7, 1, -4, -6], [3, -4, 6, -2, 7, -3], [-1, 8, -3, -2, 1, -6], [7, 9, -1, 1, 5, -2], [4, -4, -1, -10, 0, -5], [-5, -8, -2, 3, -3, 4], [-8, 3, 4, 4, 10, -1], [2, -6, 5, 4, -4, -4], [7, -8, 3, 0, 1, -9], [9, -4, -1, 7, -5, -1], [-7, 3, 1, 6, 5, -4], [18, -14, -2, -2, 0, -2], [7, -7, 3, 8, -3, -9], [0, -8, -1, 10, -8, -9], [3, 15, -5, -3, -11, 0], [-12, 14, 0, 3, -4, -3], [0, -2, -8, 2, 2, 4], [3, 4, -5, 7, -1, -9], [8, -4, 5, 4, -12, -8], [-2, 1, 0, -4, -6, -7], [2, 6, -2, 2, 4, -1], [1, -4, -9, 0, -15, -4], [-13, -5, 1, 0, -1, 5], [13, 0, -1, 4, -9, 2], [15, 11, 2, 3, -1, -9], [11, -5, 0, 0, -9, -10], [8, 5, 5, 1, -4, 1], [7, 5, -11, -3, -5, -1], [-22, 10, -7, -11, 6, 6], [-9, 4, -1, -2, 7, -4], [-6, 7, 10, 2, 12, -4], [-4, 15, 5, -3, -4, -7], [-4, -8, 4, -1, 10, 11], [-3, -2, 0, 6, 7, 5], [6, -14, 0, -6, 4, 0], [-8, -3, 1, -4, 0, 2], [2, 2, 2, 9, 4, 10], [-10, 10, -4, -6, -2, 9], [-8, 0, 2, -4, -4, 6], [0, 4, -8, -7, 0, -1], [6, -7, -5, 5, -2, -5], [7, -2, 0, 8, -15, -8], [-22, 2, 10, 10, 4, 4], [1, -7, -2, -5, 13, 3], [4, 2, -4, -7, 8, -5], [-5, 5, 7, 1, 3, -2], [-15, 5, 0, 4, 1, 10], [17, -5, 4, -6, 7, 2], [8, 6, -2, -5, -12, 7], [2, 7, -11, -4, -2, 4], [-6, 16, 1, -1, -10, -3], [-11, -7, 4, -5, 7, 2], [12, -1, 6, 6, -6, -5], [-10, 9, 0, 4, 8, 13], [10, -2, -5, -4, 4, -3], [13, -4, 11, 3, 11, -3], [2, 2, -9, -12, 0, 5], [-6, 4, -3, 9, -2, -12], [-5, 4, 6, -2, -7, -1], [-6, 3, -4, 3, 0, 10], [-8, 1, -10, -12, -8, 3], [-16, -3, 2, 5, 4, 1], [6, 10, -4, -4, -10, -6], [10, -7, 5, 1, 14, 11], [15, -8, 6, 14, -9, -7], [-4, -3, 1, 1, 2, -5], [-3, -6, -8, 3, 1, 6], [7, 0, -3, 7, 3, 3], [-5, -4, 9, -1, -5, -1], [5, -4, 8, -4, 15, 9], [-21, 11, -2, -9, 7, 5], [-1, 12, 2, -1, -1, -8], [-20, 14, 3, -14, 6, 17], [-27, 15, 3, -7, 3, -4], [25, 0, -4, -9, -1, -3], [8, 11, -5, 0, 4, 7], [0, -1, 9, 3, -10, 3], [-7, -1, 5, -5, 3, -8], [16, -13, -5, -9, 10, 5], [-6, 9, 5, -9, 0, 1], [-4, -2, -5, -3, 4, 10], [-19, 2, -9, -10, 11, 13], [-6, 21, -3, -2, 2, -8], [13, -4, -4, 1, -9, -20], [-1, 17, -1, -2, 3, -1], [27, -4, 2, 0, -9, 2], [-4, -15, 7, 1, 6, -7], [2, 10, -3, -7, -6, 2], [-16, -2, 9, 11, 14, 4], [4, -1, -5, -6, 12, -2], [2, 4, 3, 18, -4, -10], [-5, 14, -6, 2, -1, -12], [2, -10, 4, 0, -16, 0], [18, -21, 4, 2, 6, 9], [-22, 6, 12, 7, 10, 1], [-3, 1, -12, -3, -17, 1], [-2, 11, 4, -11, 0, -2], [-15, 5, 3, 2, 3, -7], [7, -5, 2, 0, -9, -8], [-21, 4, -3, -2, -3, 10], [12, -4, 1, 7, -14, -12], [7, 12, -4, 1, 11, -9], [-13, 1, -8, -7, -3, 1], [-2, 11, -18, -10, 2, 4], [5, -8, 6, 4, 13, 1], [17, -10, 9, 13, 5, 10], [-6, -7, 8, -3, 8, 12], [-5, -3, 1, -2, 11, 3], [3, -8, -3, 4, -9, -18], [14, -10, -6, -4, -16, 6], [9, -25, 11, 12, 5, -5], [-3, -3, 4, 3, -15, -3], [17, 5, 6, 5, -5, -14], [2, -13, 1, -2, -14, -8], [-36, 3, 3, 6, 0, 12], [-13, -16, -1, -16, -1, 10], [-1, -18, -3, 5, 3, 4], [5, 8, 6, 2, 7, 9], [4, -1, 3, 14, -8, 6], [-4, -7, -3, 2, -4, 1], [10, -1, -10, -6, -8, -7], [19, -2, -7, -14, -13, 4], [-4, 1, -1, -3, -4, 11], [15, -11, 10, 8, -11, 2], [9, -13, -3, 3, -13, 8], [5, -1, -10, 6, 3, 3], [-6, -6, -2, -11, 2, 9], [-19, 0, 3, 15, 13, -7], [6, 1, -8, 1, -4, 10], [6, -4, 2, 12, 0, -6], [-2, 0, -1, 0, 4, -2], [-26, -3, -5, 8, 4, 4], [32, -3, -1, 4, -12, -4], [17, -4, -2, 1, -13, -3], [-2, -14, 3, 0, -20, -1], [-27, 5, 4, 0, 15, 10], [-19, 7, -4, 8, -11, -10], [-2, 11, -5, -3, -18, -15], [-19, -2, -3, -5, 19, 12], [26, -3, -10, 16, 0, -2], [2, 15, -1, -13, 10, 6], [-16, -8, -5, 3, -4, 2], [14, -3, 10, -1, 22, 8], [-2, 8, -1, -23, -8, 0], [1, 6, -8, -11, 19, 7], [25, -15, -10, 10, -7, -12], [0, -2, 21, 13, 0, -10], [16, 10, -2, 6, 0, -1], [-7, -9, -7, 8, 11, 13], [-19, -17, 5, 6, 1, 0], [13, 1, -12, 4, -5, 8], [15, -4, 3, 9, 3, 14], [18, -10, 7, 11, 2, -10], [-2, 1, 3, -21, 0, -1], [-10, 3, -3, -19, 12, 4], [34, -4, -6, -7, 2, -5], [-2, 10, 1, -12, -6, -9], [-5, 5, 3, 0, 17, 7], [-2, 23, -2, -6, 14, 10], [16, 2, 8, -9, 18, 9], [-5, 4, 4, 6, -3, -5], [6, -2, -11, 8, 2, -3], [-18, 14, 2, -8, 4, -10], [-1, -2, -1, 9, -3, -13], [-20, 8, 0, 4, -18, 1], [20, -2, -15, -17, 0, 3], [-29, -7, 9, 11, 7, -8], [5, -20, 14, 14, 3, -15], [-30, 13, 4, -7, 12, 13], [15, -14, 6, 6, -1, 11], [-39, 11, -8, 2, -7, -6], [9, -14, 6, -4, -5, 11], [-16, -4, 0, 8, 4, -12], [25, -26, 13, 14, 13, 11], [11, 5, -21, 5, -5, 4], [-7, 16, 3, -5, -7, 11], [-24, 14, 0, -1, 10, -7], [-24, -3, 17, 6, 8, 4], [-19, 6, -4, -10, 3, 15], [-28, 25, -2, -2, -2, 10], [-17, -10, 11, 15, 15, 5], [-18, -7, -4, -10, -6, -5], [7, -2, 15, 3, 7, 1], [-25, -2, -11, -5, -11, 7], [10, 20, -9, 4, -10, -1], [-10, 5, 0, -6, -8, -6], [-10, 8, 0, -10, 0, 22], [-22, 17, 1, -3, -4, 9], [-26, 6, -8, 5, -18, 4], [13, -6, -2, -8, 11, 2], [15, -2, -11, 14, -5, 4], [20, 1, 3, -1, 4, 5], [-26, 19, 2, 9, -8, -8], [4, -5, -11, -7, 12, 7], [-1, 6, 1, 6, 5, -1], [2, 0, -7, 13, -8, -2], [-6, 6, -7, 2, -12, -1], [31, -18, 16, 28, -13, -19], [-41, 1, -14, -9, 3, 13], [0, 3, -6, -13, -6, 13], [15, -11, 15, 2, 23, 16], [-4, -11, 2, 6, 10, 19], [-20, 17, 15, -1, -8, -8], [-14, 1, 4, 1, 12, -4], [-22, -9, 1, -1, 0, -3], [10, -10, 8, 3, 10, 15], [0, -8, 11, 10, 12, -6], [-15, -5, 15, 16, 27, 6], [-3, 4, -9, -18, -11, -16], [1, -7, 0, -21, 5, -3], [4, 4, -1, 0, -4, -15], [-54, 0, 11, 5, 2, 6], [17, -10, 1, 7, 5, 1], [-35, 3, 8, -3, -7, -1], [-28, -2, -12, -19, 2, 11], [11, -1, -14, -10, 17, 12], [20, 5, -9, 10, -2, -9], [-23, 4, 3, -4, -15, -6], [8, -4, -15, -9, -22, -8], [-8, 14, -10, -17, 12, 13], [4, -5, -13, 5, 8, -15], [6, -23, 15, 6, 12, -7], [26, -13, 5, 5, -12, -9], [-3, 4, 8, 11, -9, 12], [-20, 5, -11, 8, -14, -8], [7, -19, 15, 7, 15, 8], [-31, 4, -3, -23, 1, 6], [-12, 8, 0, -2, 0, -2], [-2, 11, 4, -12, 4, 8], [26, 2, 5, 13, -22, -1], [-16, 5, -9, -2, -4, -3], [0, -1, -7, -17, -12, -9], [-3, 0, -14, -23, 5, -4], [-18, -4, 10, 24, 10, 1], [18, -14, 8, 1, 14, 17], [5, 3, 5, 2, -9, 7], [-5, 15, -2, 3, 9, 20], [0, 14, -11, 13, -10, -6], [2, -15, -5, 3, -14, 1], [18, -3, -12, -18, 6, -5], [-19, -3, 8, 20, 1, -4], [-8, -6, 11, -4, 10, -8], [22, -4, -3, 7, -12, -6], [-22, 5, -5, 7, 10, 1], [-14, 21, -9, -15, -2, 15], [26, 3, -5, -13, -24, -31], [25, 9, 4, 8, -1, -24], [3, -19, 15, 20, 7, -7], [-5, -2, 3, 2, -15, -2], [-15, -6, -3, -21, -7, -6], [-5, 4, 19, 15, -13, -11], [-20, 21, -10, -23, -12, -11], [10, 14, -10, 8, 10, 6], [6, 5, 8, 24, -2, -7], [-28, 2, -3, -8, 20, 15], [11, 0, -7, 5, -11, 7], [-10, 0, -1, -15, 16, 24], [-1, 0, 3, -7, 5, 21], [-32, 10, -7, -10, -8, -3], [20, -8, -7, -6, -6, -13], [9, 9, -2, 10, -21, -6], [-53, -2, 0, -9, 7, 12], [18, 0, -12, -12, -10, -7], [0, 14, -12, -11, 8, -9], [-25, 0, -2, 0, 5, 17], [-15, 21, 0, -7, 5, 16], [-49, 6, -2, 7, -9, 6], [12, -24, -4, 5, 4, 3], [-4, -1, 18, 21, 14, -4], [-26, 22, 3, 3, 0, 8], [-1, -11, 7, 4, 11, -19], [-17, 9, 3, -3, 9, 3], [-4, -30, 17, 11, 16, 11], [9, -26, -2, 0, -11, 9], [-30, 8, 9, -12, 16, 3], [-3, -20, 10, -3, 13, 6], [24, -2, -1, -1, -2, -10], [-45, 5, -7, -7, 13, 4], [22, -13, -4, 4, -26, -22], [33, -15, -7, 16, 3, -6], [-14, -7, -3, 6, -16, 8], [33, -1, -6, 14, -5, -7], [-24, 9, -23, -8, -16, 10], [-18, -17, 3, 3, 6, 5], [-31, -7, -13, -1, 15, 8], [-25, 5, 16, -14, 5, -2], [0, -3, 6, 15, -10, -6], [-7, 0, 9, 9, 31, 9], [-5, -14, 0, -12, -11, -5], [-17, -6, -16, -21, -13, 14], [33, 21, -5, -7, -17, 6], [45, -11, -2, -2, 9, -1], [-8, -22, 2, -1, -2, 6], [12, -25, 13, 4, 8, -20], [-5, -2, -12, 2, 11, -13], [8, 4, -5, -18, -10, 11], [-29, 11, -17, -13, 13, 14], [-39, 27, 1, -13, 9, 10], [18, -13, 12, 22, -2, -13], [-20, 14, -15, -12, -8, -18], [-13, 5, 6, 1, 7, 15], [-1, 6, -6, -10, -9, 5], [7, 16, -17, 6, -7, 10], [2, -6, -14, -3, 8, 3], [-6, -5, 8, -4, 4, 13], [-11, -6, 15, -11, 5, -5], [-21, -6, -9, -2, 19, 6], [26, -2, 5, 16, -20, -1], [9, 8, -19, -21, -3, -1], [-30, 10, -12, -7, -2, -3], [1, -41, 13, 9, 9, -2], [-11, -2, -4, 2, -7, 3], [-25, -9, -3, -12, 17, 29], [11, 7, -4, 4, 9, 20], [31, -19, 4, 9, -23, -23], [-13, 23, -4, -8, 21, 2], [-10, -2, -18, 0, -12, 12], [-34, 12, -8, 0, -8, -14], [29, 8, -3, 0, 17, -7], [-1, -25, -2, 6, -15, -16], [-2, -1, 2, 12, -22, -17], [37, -31, -5, 10, -1, 3], [15, -34, 1, -7, 17, 9], [-19, 1, 22, -3, -9, -10], [19, 12, -1, -16, -9, -9], [-22, -19, 11, 1, -6, -2], [-13, 18, 10, -11, 9, -4], [-13, -18, 9, 5, -9, -5], [19, -4, 5, 18, -11, -4], [-33, 6, 14, -14, 1, 5], [-44, 5, 8, -9, 4, -3], [17, 15, -1, -17, 1, 6], [22, -5, -11, -2, 4, -8], [-35, 33, -13, -13, -15, -6], [-33, 16, -4, -12, 17, 12], [39, 21, -11, -1, 9, 12], [15, -7, -23, -20, -21, 4], [-4, 12, -5, -4, 6, 7], [-20, -15, -12, 11, 22, 21], [-24, -2, 11, -8, 26, -7], [-15, 16, -3, -26, 19, 24], [19, 16, -16, -21, -19, 5], [6, -20, 12, -3, -4, -5], [-21, -11, 8, 10, -5, 6], [-6, -12, -21, 4, 24, 12], [18, 17, 9, -15, -24, -7], [-62, 31, -2, -14, 0, 1], [-4, -11, -2, -39, 6, 14], [-39, 22, 0, -13, 7, -1]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6018_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6018_2_a_r();".
// 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_6018_2_a_r(:prec:=6)
    chi := MakeCharacter_6018_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_6018_2_a_r();".
// 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_6018_2_a_r( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6018_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-2, 6, 3, -12, -4, 3, 1]>,<7,R![188, 140, -77, -69, 1, 7, 1]>],Snew);
    return Vf;
end function;