
// Make newform 1148.2.n.b in Magma, downloaded from the LMFDB on 24 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_b();".
// 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_b();".
// 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, 1, 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], [1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 3, 0, 3, 0, 0, 0], [2, 1, 2, 0, 0, 2, 1, 2], [0, 1, -3, -1, -3, 1, 0, 0], [0, -1, 2, -3, -3, -3, 2, -1], [-1, 0, -1, 0, 0, -2, 3, -2], [-1, -2, -2, -2, -1, 0, 0, -2], [1, 1, -2, -4, -2, 1, 1, 0], [2, -2, -1, -2, 2, 0, 0, -4], [-2, -3, 2, 1, -1, 1, 0, 1], [-4, -2, -4, 0, 0, 2, -5, 2], [3, 1, 3, 0, 0, 1, -5, 1], [-2, 2, -8, 2, -2, 0, 0, 0], [1, 1, 1, 0, 0, 3, 1, 3], [0, 1, 3, 6, -4, 6, 3, 1], [-4, -4, 2, -4, -4, 0, 0, 0], [-4, 2, -6, 0, -6, 2, -4, 0], [-4, 0, 0, -1, 3, -3, 3, -1], [1, 0, 0, 2, -2, -2, -2, 2], [3, 0, 0, 0, -4, 1, -4, 0], [0, -6, -1, 1, -5, 1, -1, -6], [-4, -2, 7, -2, -4, 0, 0, -3], [0, 1, -10, 3, -3, 3, -10, 1], [0, 3, -4, -1, 1, -1, -4, 3], [0, 2, -3, 0, -9, 0, -3, 2], [-3, 0, 0, -10, 1, -4, 1, -10], [-12, -2, -4, -2, -4, -2, -12, 0], [0, 2, 7, 2, 0, 0, 0, 6], [0, 0, 2, 12, 2, 0, 0, 0], [8, 0, 0, 4, 6, 10, 6, 4], [0, 2, 5, -1, 3, -1, 5, 2], [0, -2, -3, -2, 0, 0, 0, -10], [-13, 2, -13, 0, 0, 4, -4, 4], [0, 4, 3, 5, -5, 5, 3, 4], [7, 0, 0, -6, -1, -4, -1, -6], [2, 0, 0, 2, 0, -8, 0, 2], [5, 0, 0, -4, 10, -3, 10, -4], [10, 6, -4, 6, 10, 0, 0, 0], [-1, -3, -4, -4, -4, -3, -1, 0], [0, 0, 0, -2, 1, -2, 1, -2], [2, 0, -8, 0, 2, 0, 0, -2], [6, -4, 12, -4, 12, -4, 6, 0], [0, -5, 0, 0, 0, 2, -3, 2], [0, 4, 0, 0, 0, 4, -1, 4], [2, -4, 2, 0, 0, -6, 12, -6], [0, 4, 2, -2, 0, -2, 2, 4], [16, 3, 9, 1, 9, 3, 16, 0], [-8, -4, -8, 0, 0, -4, 3, -4], [0, 2, -6, -2, 7, -2, -6, 2], [-1, -9, -7, -9, -1, 0, 0, -8], [9, -5, 8, -5, 9, 0, 0, -9], [-12, -6, -10, 2, -10, -6, -12, 0], [-8, 12, -1, 8, -1, 12, -8, 0], [-8, -3, -8, 0, 0, -4, -1, -4], [0, -7, 7, -8, 2, -8, 7, -7], [0, -6, -9, 4, -9, -6, 0, 0], [-5, 8, -5, 0, 0, 6, 0, 6], [7, -1, 1, -1, 7, 0, 0, 0], [0, 10, 0, 0, 0, -2, 6, -2], [0, -8, -12, -4, -10, -4, -12, -8], [-18, -9, -13, -9, -13, -9, -18, 0], [2, -6, -2, -6, 2, 0, 0, -6], [11, -2, 11, 8, 11, -2, 11, 0], [-15, 0, 0, 6, 2, 6, 2, 6], [3, 0, 0, 2, 0, 10, 0, 2], [0, -2, -5, 6, -3, 6, -5, -2], [0, 9, 4, 11, -7, 11, 4, 9], [0, 13, 7, 0, 14, 0, 7, 13], [4, 0, -4, 8, -4, 0, 4, 0], [-11, 7, -11, 0, 0, -11, -17, -11], [11, -8, 19, -8, 11, 0, 0, -20], [3, 0, -3, -14, -3, 0, 3, 0], [0, 0, 0, 0, 20, -2, 20, 0], [0, 4, 13, 12, -2, 12, 13, 4], [13, -4, 13, 0, 0, -5, 4, -5], [8, 0, 0, -2, 7, -12, 7, -2], [0, 0, 0, -3, 5, 9, 5, -3], [10, 0, 0, 0, 4, 4, 4, 0], [0, 0, 4, -20, 4, 0, 0, 0], [0, 4, -6, 0, -12, 0, -6, 4], [4, -9, 4, 0, 0, -2, 7, -2], [-6, 4, 1, 4, -6, 0, 0, -15], [-9, 6, 9, 8, 9, 6, -9, 0], [-13, 2, -13, 0, 0, 6, -15, 6], [-5, 0, -5, 0, 0, 8, 0, 8], [-16, -4, -30, 4, -30, -4, -16, 0], [-2, -6, -8, -6, -2, 0, 0, 0], [0, 2, 11, 5, -1, 5, 11, 2], [2, -6, 2, 0, 0, -6, -4, -6], [10, 4, 29, 4, 10, 0, 0, 4], [-1, 0, 0, 8, 6, 0, 6, 8], [0, 0, 4, -12, -18, -12, 4, 0], [-6, 11, 5, -1, 5, 11, -6, 0], [10, 9, 19, 5, 19, 9, 10, 0], [-10, 6, -9, 6, -10, 0, 0, 19], [-3, 4, -5, -5, -5, 4, -3, 0], [4, -4, -14, 2, -14, -4, 4, 0], [-17, 0, 0, -4, -10, -4, -10, -4], [-9, 2, -4, 16, -4, 2, -9, 0], [21, -2, 5, -3, 5, -2, 21, 0], [-4, 4, 21, 4, -4, 0, 0, 2], [-20, 0, 0, -2, -8, 6, -8, -2], [-13, 0, 0, -11, 13, 0, 13, -11], [17, -5, 17, 0, 0, -7, 23, -7], [0, -2, 6, -6, 2, -6, 6, -2], [0, -2, -1, 4, -4, 4, -1, -2], [-14, 0, 0, 2, -28, 2, -28, 2], [5, -6, -3, 7, -3, -6, 5, 0], [27, -2, 27, 0, 0, -8, 14, -8], [3, 2, 3, 0, 0, 4, -10, 4], [1, -11, 2, -11, 1, 0, 0, -3], [0, 4, -11, 8, -10, 8, -11, 4], [14, -6, -2, -6, 14, 0, 0, 14], [6, -4, 6, 0, 0, -4, -4, -4], [3, 0, 0, -14, -8, 3, -8, -14], [7, 0, 0, -12, -9, -2, -9, -12], [25, 0, 0, 4, 18, 4, 18, 4], [-8, -8, 6, -8, -8, 0, 0, -16], [-11, -10, -5, -16, -5, -10, -11, 0], [0, -15, -8, -13, -9, -13, -8, -15], [-13, 0, 0, 16, -2, 6, -2, 16], [-4, 1, -4, 0, 0, -6, -13, -6], [0, 8, 15, 8, 0, 0, 0, 6], [1, 2, -5, 2, 1, 0, 0, 4], [0, -1, 12, -7, -17, -7, 12, -1], [-1, -8, 5, 5, 5, -8, -1, 0], [-22, 2, -9, 2, -22, 0, 0, 3], [-18, 0, 0, -8, 10, -4, 10, -8], [-10, -8, 4, -8, -10, 0, 0, -14], [-21, 2, -21, 0, 0, 12, -9, 12], [0, -8, 11, -2, 14, -2, 11, -8], [-6, 6, -6, 0, 0, -8, -26, -8], [-29, -6, -29, 7, -29, -6, -29, 0], [-21, -15, -21, 0, 0, -3, -11, -3], [-1, -4, -15, 21, -15, -4, -1, 0], [16, 13, 16, 0, 0, 0, 11, 0], [0, 0, -14, -16, -14, 0, 0, 0], [-20, 0, 0, -1, 11, -3, 11, -1], [-11, 0, 0, 10, 11, -4, 11, 10], [-16, 0, 0, -2, 19, 4, 19, -2], [0, -8, 8, -14, -24, -14, 8, -8], [9, 0, 0, -10, 0, -17, 0, -10], [0, -21, -9, -8, 0, -8, -9, -21], [24, -2, 30, -8, 30, -2, 24, 0], [23, 11, 15, 11, 23, 0, 0, 8], [6, 15, 6, 0, 0, 0, 3, 0], [7, 0, 7, 0, 0, -12, 4, -12], [0, 0, 7, -14, -8, -14, 7, 0], [0, 2, 4, 0, 6, 0, 4, 2], [0, -14, 12, -6, 20, -6, 12, -14], [16, 8, 35, 8, 16, 0, 0, 5], [10, 12, -10, 12, 10, 0, 0, 4], [20, 0, 0, 10, -10, -4, -10, 10], [-3, -8, -7, -4, -7, -8, -3, 0], [-23, 0, 0, -5, 15, 0, 15, -5], [10, 23, 10, 0, 0, 16, -15, 16], [12, 17, 12, 0, 0, 12, -25, 12], [3, -8, -9, -8, 3, 0, 0, -22], [6, -6, -2, -10, -2, -6, 6, 0], [12, 10, 21, 8, 21, 10, 12, 0], [-1, 12, -1, 0, 0, 9, -12, 9], [0, -10, -2, -18, -5, -18, -2, -10], [23, 0, 0, -11, 13, -28, 13, -11], [0, -4, -19, 6, -11, 6, -19, -4], [25, -13, 25, 0, 0, -3, -9, -3], [0, 0, 5, 24, 4, 24, 5, 0], [39, 1, 20, 1, 39, 0, 0, -1], [-3, 10, -3, 0, 0, 6, -15, 6], [9, 7, -29, 7, 9, 0, 0, -8], [3, 12, 3, 0, 0, 10, -1, 10], [-5, -20, -5, -16, -5, -20, -5, 0], [20, 0, 0, -15, 9, -15, 9, -15], [-13, 1, 10, 16, 10, 1, -13, 0], [-4, 10, -3, 10, -4, 0, 0, -2], [-2, -18, 1, -18, -2, 0, 0, -4], [-9, 0, 0, 21, -1, 6, -1, 21], [10, 0, 0, 4, -4, 12, -4, 4], [0, -2, -8, 10, 23, 10, -8, -2], [0, 8, 12, 10, -6, 10, 12, 8], [-3, 0, 0, -6, -6, 0, -6, -6], [-15, -15, -20, -2, -20, -15, -15, 0], [-34, 2, -6, 2, -34, 0, 0, -6], [-1, -18, -1, 0, 0, -3, -2, -3], [25, 2, 23, 10, 23, 2, 25, 0], [0, 3, -8, -15, -17, -15, -8, 3], [0, 10, -16, 4, 1, 4, -16, 10], [-13, 0, 0, -4, 4, 17, 4, -4], [5, -1, 24, -1, 5, 0, 0, -3], [16, 4, -10, 4, 16, 0, 0, -14], [10, 4, 10, 0, 0, 8, -23, 8], [-21, -1, -36, -12, -36, -1, -21, 0], [10, -8, 10, 0, 0, -8, -14, -8], [-8, -20, 7, -20, -8, 0, 0, 3], [3, 12, 24, 12, 3, 0, 0, 20], [7, 18, 0, 2, 0, 18, 7, 0], [-8, 17, -8, 0, 0, 8, -9, 8], [0, 25, -13, 22, -16, 22, -13, 25], [29, 0, 0, 6, 15, -10, 15, 6], [-6, 0, 0, 9, 23, -17, 23, 9], [0, -22, -13, -19, -29, -19, -13, -22], [0, -1, 12, -17, -3, -17, 12, -1], [-12, 16, 4, 16, -12, 0, 0, 14], [-17, 7, -17, 0, 0, -13, -17, -13], [3, -9, 36, 8, 36, -9, 3, 0], [-17, -10, -29, -10, -17, 0, 0, -32], [9, -2, 9, 0, 0, -26, 19, -26], [0, -5, 2, -5, -11, -5, 2, -5], [-24, 10, -36, 10, -24, 0, 0, 4], [18, -4, 2, -12, 2, -4, 18, 0], [-6, 0, 0, 10, -20, -10, -20, 10], [-38, -4, -14, -4, -38, 0, 0, 2], [0, -10, 1, 1, 15, 1, 1, -10], [19, 0, 0, 15, -13, -6, -13, 15], [18, -4, 11, -4, 18, 0, 0, -4], [-22, 10, -8, 14, -8, 10, -22, 0], [-31, 0, 0, -8, 20, 6, 20, -8], [0, -4, 1, 6, 7, 6, 1, -4], [-12, 8, -12, 0, 0, 10, 11, 10], [-28, -8, 20, -8, -28, 0, 0, 4], [7, 12, 3, 12, 7, 0, 0, 8], [28, -6, 0, -6, 28, 0, 0, 24], [-38, 9, -17, 3, -17, 9, -38, 0], [1, 10, 1, 0, 0, 2, 0, 2], [14, -14, 14, 0, 0, 4, 8, 4], [0, -4, 55, -4, 0, 0, 0, 0], [3, 11, -6, 11, 3, 0, 0, -9], [0, 6, -12, -18, -1, -18, -12, 6], [18, 10, 18, 0, 0, -18, 34, -18], [6, -10, 8, 20, 8, -10, 6, 0], [-19, -8, -10, -8, -19, 0, 0, 8], [-21, 2, -8, 2, -21, 0, 0, -12], [0, -10, -10, -28, -12, -28, -10, -10], [20, 16, 2, 20, 2, 16, 20, 0], [3, -12, 3, 0, 0, -15, -34, -15], [-4, 0, 6, -16, 6, 0, -4, 0], [6, -24, 6, 0, 0, -20, -10, -20], [-18, -5, -18, 0, 0, 12, 1, 12], [-18, 2, -18, 0, 0, 18, -26, 18], [-24, 0, 0, 5, 15, -11, 15, 5], [12, 14, -11, 14, 12, 0, 0, -21], [-26, 0, 0, 8, -32, 30, -32, 8], [-6, -12, -37, -12, -6, 0, 0, -3], [-20, 0, 0, 7, -35, -11, -35, 7], [10, 0, 0, -12, -12, -26, -12, -12], [-9, 1, -9, 0, 0, 3, 13, 3], [0, -2, -16, 4, -19, 4, -16, -2], [0, -4, 21, 16, -10, 16, 21, -4], [41, -10, 41, 0, 0, -16, 17, -16], [-12, 13, -12, 0, 0, 26, 3, 26], [9, 0, -31, -10, -31, 0, 9, 0], [-33, -2, -41, -3, -41, -2, -33, 0], [2, 0, 0, 22, 6, 20, 6, 22], [0, -14, 32, -26, -18, -26, 32, -14], [0, -18, 11, -8, -18, -8, 11, -18], [-6, -3, -6, 0, 0, -16, -17, -16], [-22, 0, 0, 1, -13, -23, -13, 1], [-35, 6, -35, -3, -35, 6, -35, 0], [-3, 20, -3, 0, 0, -6, 34, -6], [-17, 0, 0, -28, 15, 2, 15, -28], [56, 2, 32, 2, 56, 0, 0, -6], [-20, -22, -9, -22, -20, 0, 0, -5], [0, -15, 21, -10, 4, -10, 21, -15], [-4, -23, -4, 0, 0, -2, -3, -2], [12, -10, 12, 0, 0, -2, 19, -2], [14, 0, 0, 0, 20, -18, 20, 0], [22, 0, 0, 12, -11, 0, -11, 12], [-3, -2, 1, -18, 1, -2, -3, 0], [0, -5, -19, 12, 2, 12, -19, -5], [0, -22, 14, -8, 28, -8, 14, -22], [32, 7, 7, 11, 7, 7, 32, 0], [-13, 18, -10, 18, -13, 0, 0, 24], [1, 0, 0, 0, 10, 19, 10, 0], [0, 10, 16, 6, -14, 6, 16, 10], [21, -4, 41, -16, 41, -4, 21, 0], [2, -6, 40, -6, 2, 0, 0, 6], [-30, 0, 0, 20, 20, 2, 20, 20], [0, 11, 15, -4, 6, -4, 15, 11], [0, 27, -22, 1, -49, 1, -22, 27], [-8, 0, 0, -10, -28, -8, -28, -10], [10, 4, 10, 0, 0, -14, 26, -14], [0, 19, 11, 24, 2, 24, 11, 19], [0, 41, -4, 29, 1, 29, -4, 41], [14, -16, -4, -16, 14, 0, 0, 6], [-22, 18, -22, 0, 0, 16, 12, 16], [9, 0, 0, -28, 18, -24, 18, -28], [0, -27, 23, -14, 22, -14, 23, -27], [-26, 0, 0, 5, -13, 19, -13, 5], [3, 12, -8, 12, 3, 0, 0, 20], [0, -48, -10, -50, -4, -50, -10, -48], [-23, 0, 0, -20, 4, 6, 4, -20], [-22, 32, 8, 32, -22, 0, 0, 10], [-7, -18, -7, 0, 0, -26, 33, -26], [0, 2, 39, -5, -1, -5, 39, 2], [0, 10, -6, -22, -6, 10, 0, 0], [5, 9, 16, 9, 5, 0, 0, 17], [-33, 0, -45, -21, -45, 0, -33, 0], [0, 0, 5, -17, 3, -17, 5, 0], [0, -27, 2, -11, -11, -11, 2, -27], [-2, 20, 21, 20, -2, 0, 0, 8], [2, 12, -13, -8, -13, 12, 2, 0]];
    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_b();".
// 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_b(: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_b();".
// 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_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1148_n();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-1, -2, 1]>],Snew);
    return Vf;
end function;