
// Make newform 1110.2.d.j in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1110_d();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1110_d_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_1110_2_d_j();".
// 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_1110_2_d_j();".
// 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, -72, 162, -170, 89, 0, 2, -2, 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], [-7524, 16897, -17653, 18711, 88, 209, -217, 198], [67844, -234110, 244926, -167761, -836, -2894, 2970, -1881], [56002, 74052, -166969, 176077, 2894, 968, -2057, 1969], [-2749, -13464, 30358, -32014, -361, -176, 374, -358], [328276, -1096418, 1516102, -811589, -4052, -14166, 17838, -9117], [-333748, 1151654, -1388536, 825197, 4116, 14318, -16344, 9261]];
    Rf_basisdens := [1, 1, 9085, 36340, 18170, 1817, 36340, 36340];
    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_1110_d();"
function MakeCharacter_1110_d()
    N := 1110;
    order := 2;
    char_gens := [371, 667, 631];
    v := [2, 1, 2];
    // 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_1110_d_Hecke();"
function MakeCharacter_1110_d_Hecke(Kf)
    N := 1110;
    order := 2;
    char_gens := [371, 667, 631];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 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, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0], [0, 0, -1, 1, 0, 0, -1, 1], [-1, 1, -1, 0, -1, 1, 0, 0], [0, 0, -1, 1, 0, 0, -1, 0], [0, -2, -1, -1, 0, 0, 1, 1], [3, 0, 0, 0, 2, 1, 0, 0], [0, -3, 0, -3, 0, 0, 3, 0], [-2, 1, -1, 0, 1, 0, 0, 0], [-4, 2, -2, 0, 1, 4, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [2, 1, -1, 0, -1, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 1, 6, 0, 0, 2, 0], [0, 1, -2, -7, 0, 0, -3, -1], [-2, 1, -1, 0, 0, 2, 0, 0], [0, 0, 0, 0, -3, 0, 0, 0], [0, 0, -2, 2, 0, 0, -2, -4], [0, 1, -1, 0, 4, 6, 0, 0], [0, 1, 2, -1, 0, 0, 1, 2], [0, -1, 1, 0, -2, -6, 0, 0], [0, -2, 3, -7, 0, 0, 5, -2], [-9, 1, -1, 0, 0, -1, 0, 0], [0, 1, 1, 0, 0, 0, 0, 3], [2, 0, 0, 0, 0, 0, 0, 0], [0, -1, -3, -4, 0, 0, -2, -2], [0, 4, -1, 7, 0, 0, -5, 0], [-1, -3, 3, 0, -3, -3, 0, 0], [0, -4, 0, -6, 0, 0, 4, 3], [0, 0, 1, 15, 0, 0, 1, 0], [-4, 3, -3, 0, -2, -4, 0, 0], [0, -1, -5, 2, 0, 0, -4, 4], [0, 4, -4, 0, 3, 8, 0, 0], [0, 2, -2, 0, -6, -2, 0, 0], [-7, 1, -1, 0, 0, 3, 0, 0], [0, 2, 2, 2, 0, 0, 0, 1], [0, -3, -2, -1, 0, 0, 1, 5], [0, -1, -4, 7, 0, 0, -3, 2], [0, 3, 0, -3, 0, 0, -3, -5], [-4, 6, -6, 0, 0, 6, 0, 0], [-10, -5, 5, 0, -4, -2, 0, 0], [-3, -2, 2, 0, 3, 1, 0, 0], [0, 4, 0, 10, 0, 0, -4, -4], [0, 1, 0, 7, 0, 0, -1, -4], [8, 0, 0, 0, 0, 0, 0, 0], [-2, 3, -3, 0, -3, 4, 0, 0], [0, -2, 2, -10, 0, 0, 4, -1], [0, -4, -6, -2, 0, 0, -2, 5], [-6, -1, 1, 0, 0, -2, 0, 0], [0, 4, 2, -6, 0, 0, -2, 2], [12, -2, 2, 0, -3, -4, 0, 0], [-8, 1, -1, 0, -2, -4, 0, 0], [-6, 6, -6, 0, -2, 8, 0, 0], [0, 4, 3, -3, 0, 0, -1, -6], [0, -3, -3, -8, 0, 0, 0, 1], [-3, 2, -2, 0, 2, 7, 0, 0], [0, -6, 6, 0, -2, -4, 0, 0], [0, 0, -1, 1, 0, 0, -1, 0], [-7, -5, 5, 0, -6, -7, 0, 0], [0, -7, 0, -7, 0, 0, 7, -4], [0, -3, -8, 3, 0, 0, -5, 1], [0, -3, 3, -4, 0, 0, 6, 6], [20, 0, 0, 0, -1, 4, 0, 0], [0, 11, 1, 6, 0, 0, -10, -2], [0, 8, 4, 6, 0, 0, -4, -3], [2, 2, -2, 0, 4, 0, 0, 0], [0, -1, 0, 11, 0, 0, 1, 8], [0, -7, 3, -12, 0, 0, 10, -2], [0, -5, 5, 0, 6, 0, 0, 0], [0, 6, 4, -4, 0, 0, -2, 1], [-10, -3, 3, 0, -4, -4, 0, 0], [0, 0, -5, 5, 0, 0, -5, -3], [0, -9, -3, -10, 0, 0, 6, 2], [-8, 5, -5, 0, -6, -6, 0, 0], [0, -3, 4, 9, 0, 0, 7, 4], [4, -2, 2, 0, -7, -12, 0, 0], [0, 12, 2, 4, 0, 0, -10, 0], [5, -1, 1, 0, -6, -11, 0, 0], [6, -7, 7, 0, 0, -6, 0, 0], [-7, -7, 7, 0, -2, -5, 0, 0], [-8, 2, -2, 0, -10, -4, 0, 0], [-3, 4, -4, 0, -9, -3, 0, 0], [0, -1, -2, 1, 0, 0, -1, 0], [-2, 3, -3, 0, -5, -4, 0, 0], [0, 10, 0, 6, 0, 0, -10, -6], [6, 2, -2, 0, -6, -8, 0, 0], [0, 2, 6, -6, 0, 0, 4, -7], [-4, 0, 0, 0, -1, 0, 0, 0], [0, -1, 5, -24, 0, 0, 6, -6], [0, 3, 7, -10, 0, 0, 4, -7], [-21, -6, 6, 0, 0, -5, 0, 0], [0, -2, -8, -6, 0, 0, -6, 0], [7, -1, 1, 0, 6, 1, 0, 0], [11, 12, -12, 0, -4, 13, 0, 0], [0, 6, -4, -6, 0, 0, -10, 2], [1, 6, -6, 0, 8, 11, 0, 0], [18, 3, -3, 0, 5, -2, 0, 0], [0, 2, 12, 2, 0, 0, 10, 0], [-11, 3, -3, 0, -4, -9, 0, 0], [0, -3, 0, 1, 0, 0, 3, -1], [0, -3, -1, -2, 0, 0, 2, 2], [0, 3, -11, 12, 0, 0, -14, 5], [-17, 3, -3, 0, -2, -5, 0, 0], [-2, 1, -1, 0, 5, 12, 0, 0], [0, 2, -6, -2, 0, 0, -8, 4], [0, -6, 4, -2, 0, 0, 10, 7], [0, 0, 8, -4, 0, 0, 8, 4], [-6, 7, -7, 0, 6, 12, 0, 0], [19, -6, 6, 0, 3, -7, 0, 0], [0, -16, -2, -2, 0, 0, 14, 2], [0, 0, 6, -4, 0, 0, 6, -3], [0, -1, 7, 2, 0, 0, 8, 0], [-4, -11, 11, 0, 5, -10, 0, 0], [-18, 0, 0, 0, -3, -2, 0, 0], [14, -4, 4, 0, 1, -4, 0, 0], [0, 3, -10, -3, 0, 0, -13, 1], [0, 3, 0, 7, 0, 0, -3, 2], [0, -4, 2, -20, 0, 0, 6, 0], [-20, 2, -2, 0, -4, -16, 0, 0], [9, 9, -9, 0, 1, 15, 0, 0], [0, 3, 4, -1, 0, 0, 1, -8], [0, 5, 8, -13, 0, 0, 3, 0], [0, -1, -1, -6, 0, 0, 0, -7], [-6, -11, 11, 0, 5, -16, 0, 0], [20, -4, 4, 0, -2, -8, 0, 0], [-13, 5, -5, 0, 1, 13, 0, 0], [-12, 1, -1, 0, -10, -14, 0, 0], [0, 5, -11, 14, 0, 0, -16, 0], [0, -8, -10, 12, 0, 0, -2, -3], [-4, 6, -6, 0, -1, 8, 0, 0], [0, -5, -7, 6, 0, 0, -2, 9], [12, -2, 2, 0, 8, 0, 0, 0], [0, -6, 7, -21, 0, 0, 13, -12], [-12, 2, -2, 0, -7, -6, 0, 0], [-28, 5, -5, 0, -4, 4, 0, 0], [0, -3, 8, 7, 0, 0, 11, 9], [0, 4, 2, -6, 0, 0, -2, -6], [0, 3, -5, -20, 0, 0, -8, 0], [-1, 3, -3, 0, 8, 7, 0, 0], [-32, -4, 4, 0, 4, -4, 0, 0], [-5, 6, -6, 0, 0, -7, 0, 0], [0, 6, 1, 1, 0, 0, -5, 4], [0, 11, -1, -2, 0, 0, -12, -13], [-1, 1, -1, 0, 1, 21, 0, 0], [-4, -1, 1, 0, 6, 14, 0, 0], [0, 14, -1, 11, 0, 0, -15, -6], [0, -8, -1, -11, 0, 0, 7, -1], [9, 0, 0, 0, -6, -9, 0, 0], [0, 11, -1, 4, 0, 0, -12, -9], [0, -1, -15, 18, 0, 0, -14, 3], [26, 6, -6, 0, -7, 16, 0, 0], [0, -19, -8, -23, 0, 0, 11, 7], [0, -2, -12, -24, 0, 0, -10, 1], [0, 15, 0, 15, 0, 0, -15, -8], [8, 0, 0, 0, 0, -4, 0, 0], [0, 7, -7, 0, 2, 14, 0, 0], [4, -4, 4, 0, -3, -2, 0, 0], [0, 4, -8, -16, 0, 0, -12, -4], [0, -12, 12, 0, -4, -6, 0, 0], [0, 7, -1, -14, 0, 0, -8, -13], [0, -13, -5, -10, 0, 0, 8, -4], [0, -9, 7, 10, 0, 0, 16, 12], [-12, -10, 10, 0, 3, -24, 0, 0], [0, 4, 5, -29, 0, 0, 1, -7], [0, 6, -8, 20, 0, 0, -14, 13], [-10, 6, -6, 0, -1, 10, 0, 0], [0, -6, -3, -15, 0, 0, 3, 4], [2, 6, -6, 0, -3, -12, 0, 0], [0, 0, -6, 36, 0, 0, -6, 4], [10, -11, 11, 0, 4, -10, 0, 0], [-10, 0, 0, 0, 5, 10, 0, 0], [6, 18, -18, 0, -1, 14, 0, 0], [0, 9, -12, 1, 0, 0, -21, -4], [15, 3, -3, 0, -2, 5, 0, 0], [12, -6, 6, 0, -10, -10, 0, 0], [-16, 4, -4, 0, 4, 10, 0, 0], [-11, 10, -10, 0, -10, 3, 0, 0], [0, 12, -10, 0, 0, 0, -22, 1], [6, -7, 7, 0, -6, -10, 0, 0], [0, 4, 20, 4, 0, 0, 16, -8], [-2, -9, 9, 0, 10, -6, 0, 0], [0, 8, -7, 3, 0, 0, -15, 8], [0, -14, 0, -12, 0, 0, 14, 13], [0, 7, 3, -12, 0, 0, -4, 7], [-29, 4, -4, 0, -2, 1, 0, 0], [0, 3, -11, -6, 0, 0, -14, -3], [0, -17, -6, -11, 0, 0, 11, 5], [-42, 1, -1, 0, 2, 2, 0, 0], [0, 0, 0, 0, -2, 16, 0, 0], [0, -2, -2, 14, 0, 0, 0, 12], [0, 10, -6, 4, 0, 0, -16, 6], [-17, 2, -2, 0, 16, 9, 0, 0], [23, -6, 6, 0, 0, 5, 0, 0], [0, 0, 0, -12, 0, 0, 0, -16], [0, 6, 2, 24, 0, 0, -4, 6], [4, 0, 0, 0, 10, 6, 0, 0], [0, -12, 0, 6, 0, 0, 12, 0], [0, 1, 3, -20, 0, 0, 2, 8], [0, 9, 4, 9, 0, 0, -5, 0], [26, 4, -4, 0, 6, 6, 0, 0], [-25, -5, 5, 0, -2, -19, 0, 0], [0, 4, -8, -22, 0, 0, -12, -7], [10, -6, 6, 0, -19, -20, 0, 0], [-10, -6, 6, 0, -3, -10, 0, 0], [0, -2, -10, 2, 0, 0, -8, 12], [33, 3, -3, 0, -4, 7, 0, 0], [0, 0, -1, 11, 0, 0, -1, 14], [21, 5, -5, 0, -16, 13, 0, 0], [-16, 5, -5, 0, -3, -14, 0, 0], [0, 2, 4, -16, 0, 0, 2, 1], [-6, 6, -6, 0, 9, 26, 0, 0], [0, -10, 10, 20, 0, 0, 20, 4], [0, 6, -3, -21, 0, 0, -9, 6], [21, 4, -4, 0, 3, 1, 0, 0], [7, 2, -2, 0, 9, 17, 0, 0], [0, -6, -16, 14, 0, 0, -10, 2], [22, 10, -10, 0, 0, 4, 0, 0], [0, 7, 2, -23, 0, 0, -5, 4], [0, -9, -6, -9, 0, 0, 3, 5], [14, 0, 0, 0, 12, 12, 0, 0], [13, 5, -5, 0, -2, 15, 0, 0], [-28, -4, 4, 0, 3, -6, 0, 0], [0, -10, -4, 14, 0, 0, 6, 16], [0, 2, 6, -24, 0, 0, 4, -6], [27, 3, -3, 0, 4, 9, 0, 0], [0, 9, 15, -12, 0, 0, 6, -6], [4, -8, 8, 0, -8, -28, 0, 0], [0, -8, 0, 6, 0, 0, 8, 3], [4, 2, -2, 0, -2, 10, 0, 0], [0, -22, 0, -20, 0, 0, 22, -5], [18, -1, 1, 0, 2, 4, 0, 0], [-35, 9, -9, 0, -12, -17, 0, 0], [16, 19, -19, 0, 6, 12, 0, 0], [0, 5, 13, -34, 0, 0, 8, 8], [0, -12, -2, -4, 0, 0, 10, 13], [-39, -6, 6, 0, 0, -13, 0, 0], [0, 9, -11, 8, 0, 0, -20, -4], [10, 6, -6, 0, 14, 20, 0, 0], [-34, -4, 4, 0, 4, -6, 0, 0], [0, -8, -22, 10, 0, 0, -14, 1], [-5, -2, 2, 0, 12, -3, 0, 0], [0, 26, -5, 3, 0, 0, -31, -12], [3, 25, -25, 0, -5, 25, 0, 0], [0, -17, 5, -24, 0, 0, 22, -2], [-21, 2, -2, 0, 9, -5, 0, 0], [0, -20, 2, -2, 0, 0, 22, -4], [-30, 10, -10, 0, -12, 0, 0, 0], [32, -2, 2, 0, -15, -4, 0, 0], [0, -9, -4, 7, 0, 0, 5, -8], [0, -6, -7, -27, 0, 0, -1, -2], [4, 3, -3, 0, -10, -16, 0, 0], [0, -16, 6, 16, 0, 0, 22, 15], [2, 7, -7, 0, -2, -10, 0, 0], [0, 5, -3, 0, 0, 0, -8, -8], [24, 2, -2, 0, -15, 12, 0, 0], [2, 6, -6, 0, 10, 12, 0, 0], [0, -3, 15, -8, 0, 0, 18, 4], [0, -3, 0, -29, 0, 0, 3, -7], [0, 1, 7, -6, 0, 0, 6, -7], [0, -19, 13, 6, 0, 0, 32, 12], [0, 12, 4, 12, 0, 0, -8, -12], [44, -4, 4, 0, 8, 10, 0, 0], [0, -13, -5, -8, 0, 0, 8, 17], [0, 6, -11, -19, 0, 0, -17, -14], [34, 2, -2, 0, 1, -2, 0, 0], [21, 22, -22, 0, -8, 23, 0, 0], [6, -14, 14, 0, 10, 0, 0, 0], [0, -19, 11, -4, 0, 0, 30, 8], [0, 2, -6, -50, 0, 0, -8, -2], [-1, 21, -21, 0, -8, 17, 0, 0], [0, -3, -4, -19, 0, 0, -1, 17], [0, 5, -1, -10, 0, 0, -6, -6], [-10, 10, -10, 0, -1, 10, 0, 0], [0, 7, -10, 37, 0, 0, -17, 2], [0, 10, -3, -11, 0, 0, -13, -7], [0, -6, -15, -29, 0, 0, -9, 2], [18, 8, -8, 0, 14, 2, 0, 0], [-37, -8, 8, 0, -1, -23, 0, 0], [14, 1, -1, 0, 16, 2, 0, 0], [0, 2, 6, -26, 0, 0, 4, -6], [-4, 7, -7, 0, 9, 14, 0, 0], [0, 4, -6, 4, 0, 0, -10, -11], [8, -6, 6, 0, -16, -6, 0, 0], [0, 0, 10, -18, 0, 0, 10, -16], [-28, -9, 9, 0, -10, -10, 0, 0], [0, 5, -1, -18, 0, 0, -6, -7], [0, -2, 2, 6, 0, 0, 4, 9], [-6, -1, 1, 0, 10, 0, 0, 0], [7, -5, 5, 0, 10, 7, 0, 0], [14, -21, 21, 0, 5, -8, 0, 0], [0, -1, 3, -22, 0, 0, 4, 14], [0, -17, -1, 2, 0, 0, 16, 14], [21, -1, 1, 0, 23, 23, 0, 0], [0, 11, 17, 14, 0, 0, 6, -15], [36, 2, -2, 0, 4, -6, 0, 0], [33, -11, 11, 0, 10, -5, 0, 0], [0, 3, -22, -9, 0, 0, -25, 8], [4, -4, 4, 0, -6, 6, 0, 0], [0, 16, 8, 28, 0, 0, -8, -22], [0, -12, -10, -16, 0, 0, 2, 3], [0, -4, 0, 6, 0, 0, 4, 16], [34, -12, 12, 0, 2, 2, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1110_d_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1110_2_d_j();".
// 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_1110_2_d_j(:prec:=8)
    chi := MakeCharacter_1110_d();
    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_1110_2_d_j();".
// 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_1110_2_d_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1110_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![2500, 0, 2525, 0, 579, 0, 43, 0, 1]>,<11,R![4, -7, -11, 5, 1]>],Snew);
    return Vf;
end function;