
// Make newform 1152.2.k.c in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1152_k();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1152_k_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_1152_2_k_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_1152_2_k_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 := [2, -12, 30, -44, 43, -28, 14, -4, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, 0, 0, 0, 0, 0], [-1, 4, -5, 2, -1, 0, 0, 0], [-10, 42, -84, 105, -75, 45, -13, 4], [14, -64, 120, -135, 95, -51, 15, -4], [-31, 126, -223, 256, -175, 98, -28, 8], [38, -154, 266, -310, 210, -120, 34, -10], [-46, 178, -304, 340, -230, 126, -36, 10]];
    Rf_basisdens := [1, 1, 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_1152_k();"
function MakeCharacter_1152_k()
    N := 1152;
    order := 4;
    char_gens := [127, 901, 641];
    v := [4, 3, 4];
    // 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_1152_k_Hecke();"
function MakeCharacter_1152_k_Hecke(Kf)
    N := 1152;
    order := 4;
    char_gens := [127, 901, 641];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [1, 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, -1, 0, -1, 0], [0, -1, 0, -1, 1, 1, 1, -1], [-1, 1, -1, 0, 0, -1, -1, 0], [0, 1, 1, 0, 0, 0, 0, 2], [0, 0, -2, -1, -1, 0, -2, -2], [1, -1, -1, -2, 0, -1, 0, -2], [0, 0, 0, 0, 0, 0, -1, 1], [-2, 0, 0, -1, 0, 2, 0, 1], [3, 0, -1, -1, -1, 0, -1, -1], [2, 1, -1, 0, -2, 2, 0, 0], [0, 2, 0, 1, -1, 0, 0, 0], [1, 1, -1, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1], [2, 0, 0, 0, 1, 2, 3, 0], [4, 0, 0, 0, 0, 4, 0, 0], [-2, -1, -1, -2, 0, 2, 0, -4], [2, -2, -2, 0, 0, -2, 0, 0], [0, -2, 0, -2, 2, 2, 2, -2], [0, 2, 0, 2, -2, 2, -4, 4], [-3, 0, -3, 1, 1, 0, 1, 1], [-5, -1, -1, -4, 0, 5, 0, -3], [0, 0, 0, -2, 2, 2, -2, 2], [0, 0, 0, -2, -2, 0, -4, -4], [0, 2, -2, 0, -1, 0, -5, 0], [0, 3, 0, -1, 1, 1, -1, 1], [-4, -4, 4, 0, 4, -4, 6, 0], [0, -1, -1, 0, 0, 0, 0, 2], [-2, 0, 4, 0, 0, 0, 0, 0], [3, 0, -1, -1, -1, 0, -3, -3], [2, 2, 2, 0, 0, -2, 0, 4], [0, -2, 0, 1, -1, 0, 2, -2], [-6, -2, 2, 0, 0, -6, 4, 0], [-4, 0, 0, 0, -1, -4, 3, 0], [0, -3, 0, 1, -1, -1, 5, -5], [4, 3, 3, 2, 0, -4, 0, 0], [1, 3, 3, 2, 0, -1, 0, 4], [0, 6, 0, 2, -2, 10, -3, 3], [-6, -2, -2, -1, 0, 6, 0, -7], [-2, 2, 2, 8, 0, 2, 0, 6], [-2, -3, 3, 0, 4, -2, 2, 0], [10, 0, 2, 2, 2, 0, 5, 5], [-4, 0, 2, 6, 6, 0, 4, 4], [-2, 0, 0, 0, 3, -2, -3, 0], [0, -3, 0, 1, -1, 7, 3, -3], [-10, -2, -2, 0, 0, 10, 0, -4], [-3, 0, 5, 1, 1, 0, 7, 7], [5, 1, 1, 4, 0, -5, 0, 3], [6, -3, 3, 0, 8, 6, 6, 0], [0, -4, 0, -6, 6, -2, 6, -6], [-14, 0, 2, -2, -2, 0, 5, 5], [4, 0, 6, 4, 4, 0, 4, 4], [3, -3, 3, 0, 8, 3, 7, 0], [-10, 0, 0, 2, 2, 0, 2, 2], [0, 0, 0, 4, -4, 16, -4, 4], [8, -6, -6, -7, 0, -8, 0, -7], [-13, 0, 3, -1, -1, 0, 5, 5], [-2, -5, 5, 0, 4, -2, 6, 0], [0, 4, 0, 2, -2, -10, -2, 2], [4, 0, 0, 0, 0, 4, 6, 0], [6, -8, 8, 0, 3, 6, 9, 0], [-2, 2, 2, 8, 0, 2, 0, 4], [0, 4, 0, 0, 0, -4, 4, -4], [0, 6, 0, 6, -6, -4, -8, 8], [8, 6, 6, 5, 0, -8, 0, 9], [-6, 6, -6, 0, -8, -6, -16, 0], [-10, 0, -6, -2, -2, 0, -4, -4], [9, 3, -3, 0, -4, 9, 3, 0], [-2, -7, -7, -2, 0, 2, 0, -4], [2, 0, 4, -2, -2, 0, -2, -2], [0, -14, 0, -6, 6, 6, 12, -12], [-7, 0, -3, -3, -3, 0, -9, -9], [-4, 5, -5, 0, -10, -4, -12, 0], [-3, 1, -1, 0, 6, -3, 2, 0], [10, 0, -6, -6, -6, 0, -1, -1], [-10, -2, 2, 0, 3, -10, 9, 0], [4, 1, 1, -2, 0, -4, 0, -4], [0, 0, 10, 5, 5, 0, 10, 10], [0, -4, 0, -6, 6, 4, 4, -4], [7, 3, 3, -4, 0, -7, 0, 1], [6, 1, -1, 0, -8, 6, -6, 0], [-4, 0, 4, 8, 8, 0, 11, 11], [-4, 0, 0, 0, 0, 0, -4, -4], [0, -9, 0, -5, 5, -11, 1, -1], [13, -1, 1, 0, -4, 13, -1, 0], [16, 0, -6, -1, -1, 0, -4, -4], [0, 0, 0, 2, -2, 16, 0, 0], [10, 2, 2, 5, 0, -10, 0, 7], [9, 0, -3, -3, -3, 0, 3, 3], [-9, -5, -5, 4, 0, 9, 0, 5], [6, 0, -10, 2, 2, 0, -6, -6], [0, -3, 0, -3, 3, 19, 1, -1], [0, 4, -4, 0, -4, 0, -4, 0], [0, -4, -4, 0, 0, 0, 0, 2], [0, -6, 0, 2, -2, -18, 8, -8], [2, -4, -4, 1, 0, -2, 0, -13], [0, -2, 0, 1, -1, 0, -8, 8], [15, -1, 1, 0, 2, 15, 6, 0], [-10, 1, 1, -8, 0, 10, 0, -2], [7, -7, -7, -10, 0, -7, 0, -12], [-8, -4, -4, -7, 0, 8, 0, -3], [-13, 3, 3, 0, 0, 13, 0, 11], [0, 6, 0, -1, 1, 16, -4, 4], [12, 0, 0, 0, 0, 12, -2, 0], [-2, 0, 6, 2, 2, 0, 12, 12], [-10, -2, 2, 0, 4, -10, 14, 0], [-2, 0, -4, -8, -8, 0, 0, 0], [0, 4, 0, 4, -4, -12, -11, 11], [0, 2, 0, 2, -2, -2, -4, 4], [-1, 0, -5, -5, -5, 0, -1, -1], [4, 3, -3, 0, -2, 4, -4, 0], [0, 4, 0, 8, -8, -6, -8, 8], [0, -8, 8, 0, 8, 0, 6, 0], [0, -1, 0, -1, 1, -15, -7, 7], [-8, 0, -2, 1, 1, 0, -6, -6], [7, 5, 5, -2, 0, -7, 0, 0], [0, 4, 0, -4, 4, -12, -1, 1], [10, 6, 6, 5, 0, -10, 0, 7], [4, 0, 0, -4, 0, -4, 0, -12], [0, -1, 1, 0, -2, 0, 8, 0], [-12, 0, 0, -4, -4, 0, 4, 4], [20, 4, -4, 0, -7, 20, -3, 0], [-7, 3, -3, 0, -4, -7, -13, 0], [-5, -7, -7, -10, 0, 5, 0, -16], [4, -2, -2, -9, 0, -4, 0, -5], [-6, 7, -7, 0, -12, -6, -22, 0], [-10, 0, 6, 10, 10, 0, 4, 4], [0, 11, 0, 7, -7, 1, -5, 5], [-10, 3, 3, 12, 0, 10, 0, 14], [-4, 0, 0, 8, 0, 4, 0, 6], [0, -6, 0, -6, 6, 22, 7, -7], [3, 0, -13, -1, -1, 0, -9, -9], [10, -3, 3, 0, -8, 10, -2, 0], [0, 6, 0, 5, -5, -8, 0, 0], [12, 0, -10, 2, 2, 0, -8, -8], [-24, -2, 2, 0, 3, -24, 7, 0], [-9, 5, 5, 2, 0, 9, 0, 10], [-8, 12, 12, 5, 0, 8, 0, 13], [0, 6, 0, -5, 5, -8, 0, 0], [-3, 9, -9, 0, -10, -3, -10, 0], [4, -6, 6, 0, 11, 4, 15, 0], [0, -1, 0, 7, -7, 25, -9, 9], [-6, -2, 2, 0, 4, -6, 12, 0], [16, -7, -7, -8, 0, -16, 0, -2], [0, -14, 0, -2, 2, 14, 6, -6], [-12, -7, 7, 0, 2, -12, 0, 0], [0, -10, 0, -3, 3, 8, 10, -10], [9, -3, 3, 0, 2, 9, -12, 0], [6, 0, -2, -10, -10, 0, -11, -11], [-22, -7, -7, -2, 0, 22, 0, -4], [2, 0, 0, 10, 10, 0, 6, 6], [11, 5, 5, -2, 0, -11, 0, 8], [0, 8, 0, 8, -8, 8, -6, 6], [-13, -1, 1, 0, -2, -13, 16, 0], [2, 0, 10, -2, -2, 0, 1, 1], [0, -5, 0, 3, -3, -19, 1, -1], [-8, 0, -2, 1, 1, 0, 0, 0], [0, -16, 0, 0, 0, -10, 8, -8], [-14, -2, -2, 5, 0, 14, 0, -5], [-2, -6, -6, -16, 0, 2, 0, -10], [0, 2, 0, -1, 1, 8, 4, -4], [0, -1, 0, -1, 1, -23, 5, -5], [11, 1, -1, 0, 4, 11, 5, 0], [-16, 0, -6, 3, 3, 0, 0, 0], [0, 12, 0, 8, -8, -12, -10, 10], [5, 0, 5, -7, -7, 0, -3, -3], [6, 1, -1, 0, 14, 6, 4, 0], [12, 0, -4, 2, 2, 0, 4, 4], [-2, 2, -2, 0, -11, -2, -5, 0], [-16, 4, -4, 0, -12, -16, -20, 0], [12, -7, -7, 10, 0, -12, 0, -8], [0, 2, 0, -2, 2, -10, 3, -3], [0, -8, 0, -4, 4, -22, 12, -12], [3, 0, 11, 7, 7, 0, 13, 13], [0, -4, 0, -2, 2, -26, -6, 6], [8, -4, 4, 0, 0, 8, 18, 0], [20, -4, 4, 0, -3, 20, -3, 0], [0, 13, 0, 9, -9, 15, -7, 7], [6, -1, -1, -14, 0, -6, 0, -16], [-5, 0, 3, -1, -1, 0, -5, -5], [-15, 5, 5, 12, 0, 15, 0, -1], [-4, -11, 11, 0, 4, -4, 22, 0], [0, -12, 0, 2, -2, 10, 2, -2], [-14, 0, 2, 2, 2, 0, 3, 3], [-10, 14, -14, 0, -11, -10, -25, 0], [-2, 5, 5, 16, 0, 2, 0, 10], [-20, 0, 0, -8, 0, 20, 0, -6], [0, 6, 0, 0, 0, 4, -20, 20], [-24, 0, -16, -8, -8, 0, -16, -16], [-6, 0, 20, 0, 0, 0, 12, 12], [16, 4, -4, 0, 8, 16, -12, 0], [16, 4, 4, 0, 0, -16, 0, 18], [-10, -6, -6, -3, 0, 10, 0, -9], [-2, -2, -2, 0, 0, 2, 0, 0], [0, -12, 0, 4, -4, 18, -4, 4], [2, 0, 10, 10, 10, 0, 8, 8], [6, 5, 5, 4, 0, -6, 0, -14], [14, 0, 4, -2, -2, 0, 6, 6], [0, 16, 0, 0, 0, -8, -6, 6], [16, -12, -12, -11, 0, -16, 0, -11], [-1, 0, 11, 3, 3, 0, 5, 5], [-4, 7, -7, 0, -4, -4, -10, 0], [10, 0, -2, 6, 6, 0, 0, 0], [3, -3, 3, 0, -16, 3, -1, 0], [18, 4, 4, 15, 0, -18, 0, 9], [21, 0, -3, 1, 1, 0, -3, -3], [-7, 1, 1, -8, 0, 7, 0, 13], [0, -4, 0, -8, 8, -18, 16, -16], [-1, -9, 9, 0, -2, -1, 12, 0], [12, 0, -14, -6, -6, 0, -4, -4], [-4, -4, 4, 0, 7, -4, 19, 0], [0, 11, 0, -1, 1, 25, -9, 9], [0, -4, 4, 0, 0, 0, -12, 0], [0, -2, 0, 6, -6, -30, 2, -2], [0, -4, 0, 4, -4, 16, -4, 4], [25, 0, 5, 5, 5, 0, 9, 9], [-8, 0, 18, 9, 9, 0, 12, 12], [0, 2, 0, 2, -2, 38, 5, -5], [-4, 4, 4, 11, 0, 4, 0, 27], [0, 5, -5, 0, -12, 0, 10, 0], [0, -5, 0, 3, -3, -3, 7, -7], [8, 0, 2, -1, -1, 0, 18, 18], [-11, 0, -27, -7, -7, 0, -21, -21], [-1, 3, 3, 12, 0, 1, 0, -7], [-4, 17, -17, 0, -10, -4, -24, 0], [0, 16, 0, 8, -8, -6, -12, 12], [-2, 0, 6, -2, -2, 0, 4, 4], [0, 7, 0, -1, 1, -15, -5, 5], [8, -4, 4, 0, -4, 8, -8, 0], [-24, -1, -1, -4, 0, 24, 0, 2], [33, -1, -1, 10, 0, -33, 0, 0], [-17, 0, -5, 3, 3, 0, 9, 9], [0, -12, 0, -18, 18, 18, 22, -22], [-1, 7, -7, 0, -26, -1, -28, 0], [50, 0, -6, -2, -2, 0, -4, -4], [8, 0, -16, -10, -10, 0, -4, -4], [-8, 0, 0, 0, -5, -8, 23, 0], [-17, -3, 3, 0, 20, -17, 21, 0], [0, 0, 0, -8, 8, 8, -1, 1], [3, -5, -5, -8, 0, -3, 0, -25], [-22, 2, -2, 0, 8, -22, 12, 0], [0, 1, 0, 5, -5, -13, -5, 5], [4, -9, -9, -22, 0, -4, 0, -16], [26, 0, -12, 4, 4, 0, -4, -4], [0, -18, 0, -10, 10, 10, 20, -20], [21, 0, 21, 9, 9, 0, 19, 19], [-4, -4, -4, -4, 0, 4, 0, -6], [-10, 6, -6, 0, 0, -10, -8, 0], [20, 0, 12, -4, -4, 0, 2, 2], [-8, 3, 3, -8, 0, 8, 0, -6], [2, 0, 4, -12, -12, 0, -8, -8], [0, -16, 0, -8, 8, -24, 7, -7], [0, -4, 0, -8, 8, -6, -4, 4], [18, 0, 0, 3, 0, -18, 0, -7], [22, -10, -10, -12, 0, -22, 0, -8], [4, -11, 11, 0, 0, 4, 2, 0], [0, 0, 0, 0, 16, 0, -6, 0], [10, -16, 16, 0, 9, 10, 11, 0], [0, 16, 0, 0, 0, -4, -4, 4], [-15, 0, -3, -11, -11, 0, -3, -3], [0, -4, -4, -8, 0, 0, 0, -4], [-4, 11, -11, 0, 4, -4, -10, 0], [0, -3, -3, -10, 0, 0, 0, -32], [-8, 0, 2, 1, 1, 0, 0, 0], [-6, -10, -10, -24, 0, 6, 0, -20], [-24, 8, 8, 3, 0, 24, 0, 15], [0, -20, 0, -4, 4, 10, 16, -16], [15, 3, -3, 0, 10, 15, 2, 0], [-20, 4, -4, 0, -11, -20, -27, 0], [18, 15, 15, 22, 0, -18, 0, 36], [12, -4, -4, -8, 0, -12, 0, -22], [0, -4, 0, 0, 0, 26, -4, 4], [-15, 0, -3, 5, 5, 0, -3, -3], [-6, 0, 16, 8, 8, 0, 16, 16], [0, -5, 0, -5, 5, -11, 11, -11], [-7, -1, 1, 0, 8, -7, -7, 0], [12, -1, -1, 2, 0, -12, 0, 20], [0, 22, 0, 2, -2, -14, -16, 16], [22, -10, -10, -4, 0, -22, 0, -16], [6, 0, -2, 14, 14, 0, 12, 12], [0, 17, 0, -3, 3, -21, -1, 1], [0, 0, 0, 8, -8, 16, -15, 15], [-24, -1, 1, 0, 6, -24, 12, 0], [-7, -3, 3, 0, 6, -7, -14, 0], [24, 0, -24, -16, -16, 0, -10, -10], [-20, 0, 22, 4, 4, 0, 8, 8], [8, 0, 0, 0, -11, 8, 1, 0], [0, -15, 0, -7, 7, -1, 3, -3], [10, 0, 4, 10, 10, 0, 18, 18], [-10, -2, -2, 13, 0, 10, 0, -1], [-10, 18, 18, 16, 0, 10, 0, 30], [0, -8, 0, -8, 8, -30, 4, -4], [2, 2, -2, 0, -8, 2, -30, 0], [-18, 1, 1, -10, 0, 18, 0, 8], [-6, -10, -10, -21, 0, 6, 0, -39], [-9, 0, -1, -5, -5, 0, -11, -11], [8, 10, -10, 0, 1, 8, 1, 0], [-21, 5, -5, 0, -8, -21, -5, 0], [13, 23, 23, 14, 0, -13, 0, 34], [0, -18, 0, -10, 10, 36, 28, -28], [2, 2, 2, 7, 0, -2, 0, -7], [-37, 0, 19, 15, 15, 0, 9, 9]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1152_k_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1152_2_k_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_1152_2_k_c(:prec:=8)
    chi := MakeCharacter_1152_k();
    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_1152_2_k_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_1152_2_k_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1152_k();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![64, 128, 128, -192, 128, -16, 0, 0, 1]>,<11,R![1024, -2048, 2048, 256, 0, 0, 32, 8, 1]>,<19,R![256, 1536, 4608, -1408, 224, 32, 32, -8, 1]>],Snew);
    return Vf;
end function;