
// Make newform 1148.2.n.a in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1148_n();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1148_n_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_1148_2_n_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_1148_2_n_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 := [16, 0, 8, 0, 4, 0, 2, 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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1]];
    Rf_basisdens := [1, 1, 2, 2, 4, 4, 8, 8];
    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_1148_n();"
function MakeCharacter_1148_n()
    N := 1148;
    order := 5;
    char_gens := [575, 493, 785];
    v := [5, 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_1148_n_Hecke();"
function MakeCharacter_1148_n_Hecke(Kf)
    N := 1148;
    order := 5;
    char_gens := [575, 493, 785];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 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, -1, 1, 0, 1, -1], [0, -1, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, -1, -1, 2, -1, -1, 0], [-2, 1, -3, 1, -3, 1, -2, 0], [0, -2, 3, -1, 1, -1, 3, -2], [3, -1, 3, -1, 3, 0, 0, -3], [0, 0, 2, -2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 2, -1, 2], [0, 3, -3, 0, -3, 0, -3, 3], [2, 2, 2, 0, 0, -2, -1, -2], [-3, 4, 1, 1, -1, 0, -1, 0], [0, 0, -5, 1, -5, 0, 0, 0], [3, 2, 2, 5, 2, 2, 3, 0], [-2, 6, -2, 0, 0, 0, -2, 0], [-2, 3, 1, 0, 1, 3, -2, 0], [2, 4, -1, 4, 2, 0, 0, -1], [-4, 1, -4, 0, 0, -1, 1, -1], [0, 1, -4, -2, 1, -2, -4, 1], [-8, 0, 0, -2, -6, -2, -6, -2], [-11, 0, 0, -3, -4, -6, -4, -3], [-3, 0, 0, 5, -4, 3, -4, 5], [-2, 0, -7, 0, -2, 0, 0, 1], [1, 0, 1, 0, 0, 3, -6, 3], [-6, 2, 3, 2, -6, 0, 0, -5], [-1, 8, -4, 8, -1, 0, 0, 3], [-2, 2, 4, 2, -2, 0, 0, 2], [-4, 0, 0, 2, 0, 4, 0, 2], [0, -2, -2, -2, -4, -2, -2, -2], [-6, -1, -6, 0, 0, -1, -5, -1], [0, 1, -9, 3, -8, 3, -9, 1], [-4, 0, 0, 8, -4, 6, -4, 8], [6, 0, -4, 0, 6, 0, 0, -4], [10, -2, 10, 0, 0, -2, 13, -2], [4, -4, -1, -9, -1, -4, 4, 0], [9, 3, 3, 3, 9, 0, 0, 4], [-3, 0, 0, -1, -1, -3, -1, -1], [-9, 0, 0, -3, 2, 3, 2, -3], [4, 0, 0, 6, 2, 4, 2, 6], [-3, 9, -3, 0, 0, 2, 0, 2], [0, -5, 1, 4, -8, 4, 1, -5], [-14, 0, 0, 0, 7, 1, 7, 0], [6, 0, 6, 0, 0, 0, -5, 0], [0, -12, -5, -8, -5, -8, -5, -12], [-1, -2, -2, -13, -2, -2, -1, 0], [11, -1, 11, -10, 11, -1, 11, 0], [19, 1, 21, -3, 21, 1, 19, 0], [-6, 3, -3, 3, -6, 0, 0, 4], [0, -5, 5, -2, 2, -2, 5, -5], [-2, -4, -5, -2, -5, -4, -2, 0], [-7, -4, -3, -4, -7, 0, 0, -1], [-14, -2, -14, 0, 0, 4, -16, 4], [15, 1, 15, 0, 0, -4, 15, -4], [0, -1, 12, 1, -1, 1, 12, -1], [0, 5, 0, 2, -9, 2, 0, 5], [2, -9, 5, -1, 5, -9, 2, 0], [-14, 1, -9, 1, -14, 0, 0, -2], [0, 10, -2, 14, 4, 14, -2, 10], [-15, -8, -5, -8, -5, -8, -15, 0], [-2, 10, -2, 0, 0, 3, 11, 3], [0, 0, 16, 4, 16, 0, 0, 0], [-11, -3, -9, -3, -11, 0, 0, -7], [0, -11, 1, -16, -7, -16, 1, -11], [-1, 11, -1, 0, 0, -1, 1, -1], [0, -4, 5, 4, -2, 4, 5, -4], [3, 0, 0, -1, 6, 12, 6, -1], [6, 0, 0, -10, -2, -4, -2, -10], [-3, -7, 2, -7, -3, 0, 0, -16], [1, 5, 8, 5, 1, 0, 0, -3], [-16, 0, -9, 0, -16, 0, 0, 7], [0, 17, -8, 12, -19, 12, -8, 17], [2, 12, -2, 12, -2, 12, 2, 0], [-2, -8, -2, 0, 0, -8, -8, -8], [0, 9, -6, 10, 3, 10, -6, 9], [-10, 0, 0, 3, 5, -12, 5, 3], [20, 4, 16, 4, 20, 0, 0, 4], [-10, 0, -8, 10, -8, 0, -10, 0], [3, 0, 0, 4, 19, -6, 19, 4], [1, 0, 0, 2, -12, -7, -12, 2], [5, 0, 0, -3, -8, -7, -8, -3], [0, -4, 0, -6, 0, -6, 0, -4], [13, -5, 12, -5, 13, 0, 0, -18], [-15, 1, -20, -8, -20, 1, -15, 0], [8, 16, 8, 0, 0, 8, -12, 8], [0, 1, -26, 0, -21, 0, -26, 1], [14, -4, 0, -10, 0, -4, 14, 0], [16, -2, 13, 10, 13, -2, 16, 0], [0, -5, 16, -5, -3, -5, 16, -5], [-2, -5, -2, 0, 0, -5, -25, -5], [18, -1, 15, -1, 18, 0, 0, 2], [-2, -2, 14, 4, 14, -2, -2, 0], [-6, 9, -6, 0, 0, -1, -15, -1], [-5, 0, 0, -9, 1, -17, 1, -9], [8, -2, 0, -2, 8, 0, 0, 8], [0, -4, 16, 5, 3, 5, 16, -4], [0, 10, 2, -6, 0, -6, 2, 10], [3, 5, 3, 0, 0, -1, -5, -1], [0, 8, 10, 5, 23, 5, 10, 8], [0, -4, -4, -2, 14, -2, -4, -4], [-6, 0, 0, -2, 1, -1, 1, -2], [0, -4, -7, 18, 4, 18, -7, -4], [0, 3, -5, -3, 8, -3, -5, 3], [-6, 6, -6, 0, 0, 14, -14, 14], [17, 0, 0, -9, -6, 0, -6, -9], [8, 0, 0, 1, -1, 15, -1, 1], [32, -2, 18, 0, 18, -2, 32, 0], [17, 1, 2, 1, 17, 0, 0, -3], [-10, 0, -22, 0, -10, 0, 0, -6], [-12, 0, 0, -5, 5, -1, 5, -5], [0, -2, 8, 7, -13, 7, 8, -2], [7, 2, 2, 0, 2, 2, 7, 0], [-5, 8, -9, 8, -9, 8, -5, 0], [6, 4, 6, 0, 0, 3, 25, 3], [0, -14, -20, -14, 0, 0, 0, -8], [2, 0, 2, 0, 0, 6, 13, 6], [-2, 7, 5, 0, 5, 7, -2, 0], [14, 0, 0, -6, 2, 4, 2, -6], [-1, 0, 0, 0, -11, 6, -11, 0], [-15, 0, 0, 3, -11, 13, -11, 3], [-8, -10, -8, 0, 0, -10, -4, -10], [0, -4, 3, -2, 17, -2, 3, -4], [2, -8, -3, -8, 2, 0, 0, 1], [-19, 0, 0, -15, -8, -12, -8, -15], [-7, 1, 5, -19, 5, 1, -7, 0], [-14, -2, -14, 0, 0, -2, 16, -2], [-17, 0, -17, 0, 0, -4, 14, -4], [-4, 13, -5, 13, -4, 0, 0, 12], [0, 7, -11, 6, -19, 6, -11, 7], [6, 17, 6, 0, 0, -2, 1, -2], [24, 0, 0, 12, -12, -2, -12, 12], [6, -13, 6, 0, 0, -5, -29, -5], [6, 12, -6, -6, -6, 12, 6, 0], [6, 8, -17, 8, 6, 0, 0, 8], [-23, -3, -16, 0, -16, -3, -23, 0], [0, -2, -15, -17, 7, -17, -15, -2], [3, 12, 11, -7, 11, 12, 3, 0], [0, 6, -10, 1, -7, 1, -10, 6], [-1, -8, 3, 7, 3, -8, -1, 0], [0, 8, -4, 0, 14, 0, -4, 8], [17, 0, 0, -12, 9, -17, 9, -12], [-7, 0, 0, 6, 4, -20, 4, 6], [16, 0, 0, -2, 10, -22, 10, -2], [-2, 14, -12, 14, -2, 0, 0, 18], [7, 0, 0, 13, -11, -2, -11, 13], [-4, -7, -15, -7, -4, 0, 0, -16], [0, -6, -6, -4, -16, -4, -6, -6], [7, 15, 7, 0, 0, 1, -11, 1], [-18, 4, 0, 6, 0, 4, -18, 0], [9, -9, 22, 7, 22, -9, 9, 0], [2, 4, 14, 4, 2, 0, 0, -4], [-8, -18, -22, -18, -8, 0, 0, -12], [0, -5, -19, -5, 0, 0, 0, 9], [-17, -1, -17, 0, 0, -3, -18, -3], [-15, -10, -15, 0, 0, -7, 29, -7], [-1, 0, 0, -7, -10, 10, -10, -7], [0, -28, 3, -23, -2, -23, 3, -28], [-2, 0, 0, -12, 28, 6, 28, -12], [-26, 2, 8, 4, 8, 2, -26, 0], [-29, -4, -29, 13, -29, -4, -29, 0], [5, 2, 5, 0, 0, 9, 27, 9], [0, -18, 3, -18, 22, -18, 3, -18], [0, -15, 4, 4, 7, 4, 4, -15], [-51, 1, -47, -1, -47, 1, -51, 0], [10, -8, 10, -8, 10, 0, 0, -10], [-29, 0, 0, 4, -13, -9, -13, 4], [-3, -1, -6, -1, -3, 0, 0, 10], [-8, 0, -14, 20, -14, 0, -8, 0], [5, -6, -3, -6, 5, 0, 0, -2], [13, 1, 13, 0, 0, -7, 31, -7], [-12, -18, -13, -13, -13, -18, -12, 0], [13, -10, 13, 0, 0, -1, 2, -1], [9, 1, 6, -9, 6, 1, 9, 0], [0, 10, 3, 18, -22, 18, 3, 10], [-3, 0, 0, 9, -2, 7, -2, 9], [0, 5, -20, 11, 9, 11, -20, 5], [0, -11, 0, 0, 0, -11, 1, -11], [6, 8, 6, 0, 0, 4, 0, 4], [-20, 0, 0, 12, -2, 16, -2, 12], [9, 0, 0, 20, 14, 13, 14, 20], [22, -18, -4, -18, 22, 0, 0, 6], [-8, -6, 2, -6, -8, 0, 0, 10], [19, 0, 0, 10, 22, 18, 22, 10], [0, -11, 8, -19, 1, -19, 8, -11], [11, -22, 11, 0, 0, -9, 13, -9], [26, -1, 27, -23, 27, -1, 26, 0], [0, 34, 9, 28, 9, 28, 9, 34], [-19, -2, 22, -2, -19, 0, 0, -1], [12, -4, -7, -4, 12, 0, 0, 8], [-4, 0, 0, -1, 1, 22, 1, -1], [-17, -13, -17, 0, 0, -5, 15, -5], [12, 9, 12, 0, 0, 3, 21, 3], [-19, 15, -21, -4, -21, 15, -19, 0], [0, -6, -4, -8, 18, -8, -4, -6], [4, 0, 28, -2, 28, 0, 4, 0], [12, -4, 12, 0, 0, 16, 36, 16], [-30, -14, -30, 0, 0, 2, -32, 2], [0, 6, -17, 2, 6, 2, -17, 6], [3, 0, -1, 23, -1, 0, 3, 0], [-9, -7, -7, -7, -9, 0, 0, -1], [1, 0, 0, 6, 10, -4, 10, 6], [12, 0, 0, -1, 3, 26, 3, -1], [12, -10, 28, -10, 12, 0, 0, -28], [-18, -12, 23, -12, -18, 0, 0, 15], [-4, 8, -4, 0, 0, -1, -5, -1], [-15, -14, -21, -7, -21, -14, -15, 0], [0, 6, -32, 1, -15, 1, -32, 6], [-3, 6, -3, 0, 0, -11, 21, -11], [4, -28, 12, -2, 12, -28, 4, 0], [-32, 8, -24, 8, -32, 0, 0, 20], [-14, 2, -14, 0, 0, 2, 21, 2], [0, -10, -2, -12, -32, -12, -2, -10], [17, 0, 0, 3, -3, -19, -3, 3], [-14, -18, -14, 0, 0, -11, 31, -11], [13, 25, -17, 25, 13, 0, 0, 7], [11, 0, 0, 6, -14, 13, -14, 6], [29, 12, 29, 0, 0, 3, 7, 3], [0, 5, -8, -17, -3, -17, -8, 5], [-30, 0, 0, -12, 5, -5, 5, -12], [14, -2, 21, -2, 14, 0, 0, -16], [-19, -24, -20, -14, -20, -24, -19, 0], [-15, -11, -15, 0, 0, 10, -27, 10], [14, 2, 14, 0, 0, 12, -21, 12], [5, 8, 5, 0, 0, 1, -27, 1], [0, 10, -20, 8, -40, 8, -20, 10], [-8, 18, 11, 16, 11, 18, -8, 0], [39, -16, 41, -9, 41, -16, 39, 0], [21, 12, 21, 0, 0, -9, 31, -9], [-16, -26, -16, 0, 0, -6, -4, -6], [7, 21, 22, 21, 7, 0, 0, 28], [-20, 6, -29, -2, -29, 6, -20, 0], [0, 24, 10, -3, 15, -3, 10, 24], [4, -5, 4, 0, 0, -9, 11, -9], [-18, -4, -18, 0, 0, 14, -10, 14], [-22, -13, 1, -13, -22, 0, 0, 4], [0, 21, -17, 15, -10, 15, -17, 21], [-11, -3, -28, 14, -28, -3, -11, 0], [0, -8, -7, -2, 5, -2, -7, -8], [29, 1, 35, -2, 35, 1, 29, 0], [-21, 5, 1, 27, 1, 5, -21, 0], [-22, 2, 28, -10, 28, 2, -22, 0], [5, 0, 0, -2, -13, 9, -13, -2], [-5, 25, -5, 0, 0, 3, -2, 3], [-11, 0, 0, -6, 8, -4, 8, -6], [4, 25, 4, 0, 0, -8, 21, -8], [5, 0, 0, -19, -12, -3, -12, -19], [19, 0, 0, -5, 24, 17, 24, -5], [30, -2, 0, 0, 0, -2, 30, 0], [-9, 19, -20, 19, -9, 0, 0, -4], [-26, -5, -51, -5, -26, 0, 0, -7], [-14, -2, 10, 8, 10, -2, -14, 0], [-4, 23, 1, -3, 1, 23, -4, 0], [0, 6, -10, 6, -20, 6, -10, 6], [0, -34, 1, -17, 1, -17, 1, -34], [-21, 0, 0, -14, -8, -39, -8, -14], [10, 14, 6, 14, 10, 0, 0, -4], [26, -10, 12, -10, 26, 0, 0, 20], [7, -17, 25, 5, 25, -17, 7, 0], [-1, 0, 0, -32, 4, -17, 4, -32], [0, 23, -12, 17, -23, 17, -12, 23], [31, -1, 10, 9, 10, -1, 31, 0], [18, 0, 0, 28, -3, 13, -3, 28], [6, -1, 6, 0, 0, -18, 29, -18], [-11, -1, -11, 0, 0, 9, -13, 9], [-23, -5, -7, -5, -23, 0, 0, 10], [2, -4, -20, -18, -20, -4, 2, 0], [-12, 28, 1, 30, 1, 28, -12, 0], [6, 0, 0, -14, 6, 16, 6, -14], [-9, 0, 0, 9, -24, 14, -24, 9], [0, 18, 44, 16, 27, 16, 44, 18], [7, 15, -3, 15, 7, 0, 0, -16], [-29, -5, 0, -5, -29, 0, 0, -6], [0, 9, 24, 11, 41, 11, 24, 9], [-15, -13, -15, 0, 0, 12, -4, 12], [-11, 0, 0, -18, 10, -21, 10, -18], [-22, -7, -9, -7, -22, 0, 0, 22], [0, -21, -1, -17, -17, -17, -1, -21], [27, -18, 27, 0, 0, -4, 26, -4], [-26, 0, 0, -12, -41, -6, -41, -12], [21, -29, -15, -29, 21, 0, 0, -3], [2, -19, -17, -19, 2, 0, 0, -18], [2, 0, 0, 24, -6, 26, -6, 24], [6, -28, 18, -4, 18, -28, 6, 0], [4, -4, -20, -4, 4, 0, 0, 6], [-22, 5, -3, 5, -22, 0, 0, 0], [-7, -15, -7, 0, 0, -8, 24, -8], [49, 10, 26, 16, 26, 10, 49, 0], [23, 0, 0, -28, 10, -14, 10, -28], [-9, -8, -44, -8, -9, 0, 0, -21], [12, 0, 0, -8, 24, -18, 24, -8], [14, -10, 14, 0, 0, -12, -39, -12], [23, 2, 20, 2, 23, 0, 0, -23], [4, 0, 0, 26, -14, 8, -14, 26], [-15, 9, -15, 0, 0, 15, -22, 15], [1, -20, 3, -4, 3, -20, 1, 0], [28, -8, 33, -8, 28, 0, 0, -27], [0, 28, -8, 18, -24, 18, -8, 28], [15, 4, 15, 0, 0, 1, 28, 1], [0, -30, 2, -16, -12, -16, 2, -30], [-10, 2, -8, 2, -10, 0, 0, 6], [-22, 0, 10, 0, -22, 0, 0, 28], [43, 14, 43, 0, 0, 8, -8, 8], [0, -20, 16, -10, 40, -10, 16, -20]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1148_n_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1148_2_n_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_1148_2_n_a(:prec:=8)
    chi := MakeCharacter_1148_n();
    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_1148_2_n_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_1148_2_n_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1148_n();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-9, -18, -7, 2, 1]>],Snew);
    return Vf;
end function;