
// Make newform 2736.2.bm.p in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2736_bm();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2736_bm_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_2736_2_bm_p();".
// 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_2736_2_bm_p();".
// 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 := [169, 0, -104, 0, 51, 0, -8, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [1092, 0, -323, 0, 68, 0, -2, 0], [0, 923, 0, 85, 0, 17, 0, 6], [0, -1040, 0, 85, 0, 17, 0, -7], [-832, 0, 408, 0, -51, 0, 8, 0], [208, 0, 323, 0, -68, 0, 15, 0], [0, 13, 0, -38, 0, 8, 0, -1], [0, 91, 0, -38, 0, 8, 0, -1]];
    Rf_basisdens := [1, 663, 663, 663, 663, 663, 39, 39];
    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_2736_bm();"
function MakeCharacter_2736_bm()
    N := 2736;
    order := 6;
    char_gens := [1711, 2053, 1217, 1009];
    v := [3, 6, 6, 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2736_bm_Hecke();"
function MakeCharacter_2736_bm_Hecke(Kf)
    N := 2736;
    order := 6;
    char_gens := [1711, 2053, 1217, 1009];
    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], [1, 0, 0, 0, 1, 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, 1, 1, 0, 0, -1, -1], [0, -1, 0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 0, 1, 1], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, -1], [0, 5, 0, 0, 0, -3, 0, 0], [0, 0, -1, 0, 0, 0, -1, 0], [0, 0, -1, 1, 0, 0, -2, -1], [-6, 1, 0, 0, 0, 1, 0, 0], [1, 6, 0, 0, 2, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 2, 3, 0, 0], [0, 0, 2, 2, 0, 0, 0, -2], [0, 0, 2, 1, 0, 0, 1, -1], [0, 0, 1, 1, 0, 0, 1, 1], [3, 4, 0, 0, 3, -8, 0, 0], [-6, 3, 0, 0, -6, -6, 0, 0], [0, 0, 0, 0, 0, 0, -3, -3], [0, 12, 0, 0, 5, -6, 0, 0], [0, 10, 0, 0, -6, -5, 0, 0], [0, 0, -3, -1, 0, 0, 3, 2], [0, 0, 0, -3, 0, 0, 3, 3], [0, 0, 0, 0, 0, -6, 0, 0], [0, 0, -3, 1, 0, 0, 2, 1], [6, 5, 0, 0, 0, 5, 0, 0], [0, 0, 1, -5, 0, 0, 1, 4], [-8, 0, 0, 0, -4, -6, 0, 0], [0, 0, 1, 2, 0, 0, -1, 1], [0, -8, 0, 0, 0, 16, 0, 0], [0, 0, 0, 0, 0, 0, -1, 1], [0, 0, -1, 3, 0, 0, -2, 3], [-6, -1, 0, 0, 6, 0, 0, 0], [0, 0, -3, -3, 0, 0, 1, 1], [-12, 4, 0, 0, 0, 4, 0, 0], [0, 12, 0, 0, -3, -6, 0, 0], [0, 5, 0, 0, 0, -5, 0, 0], [0, 0, 5, 2, 0, 0, -7, 2], [0, 0, -4, 4, 0, 0, 1, -1], [0, 0, 2, 5, 0, 0, 2, -7], [6, 12, 0, 0, -6, 0, 0, 0], [0, 0, -1, 2, 0, 0, 1, 3], [-2, 0, 0, 0, -1, -12, 0, 0], [0, 0, -1, 0, 0, 0, -1, 1], [-2, 3, 0, 0, 2, 0, 0, 0], [0, 10, 0, 0, -6, -5, 0, 0], [0, -2, 0, 0, 12, 1, 0, 0], [0, 0, -3, 0, 0, 0, -3, 3], [-9, -10, 0, 0, 0, -10, 0, 0], [0, 0, 0, 0, 0, 0, -5, -5], [0, 0, -7, -4, 0, 0, 7, 3], [3, 6, 0, 0, -3, 0, 0, 0], [0, 0, 0, -4, 0, 0, 4, 4], [0, 0, 2, 7, 0, 0, -5, -7], [0, 0, -4, 4, 0, 0, 3, -3], [0, 0, 1, -1, 0, 0, -4, 4], [-12, 0, 0, 0, -6, 12, 0, 0], [-18, -2, 0, 0, 0, -2, 0, 0], [0, 0, 1, 8, 0, 0, -7, -8], [8, 0, 0, 0, 4, -18, 0, 0], [0, 0, -4, -2, 0, 0, 4, 2], [0, 4, 0, 0, 24, -2, 0, 0], [0, 0, -8, -5, 0, 0, 8, 3], [6, -6, 0, 0, 6, 12, 0, 0], [0, 0, -1, 4, 0, 0, -5, -4], [0, -15, 0, 0, 0, -15, 0, 0], [14, 0, 0, 0, 7, 18, 0, 0], [0, 0, -3, 3, 0, 0, -2, 2], [23, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, -3, 0, 0, -4, 7], [0, 0, -6, 6, 0, 0, -4, 4], [6, 15, 0, 0, -6, 0, 0, 0], [-2, -24, 0, 0, -4, 24, 0, 0], [-6, -9, 0, 0, 0, -9, 0, 0], [0, 0, -5, -5, 0, 0, 10, 10], [0, 0, -8, -1, 0, 0, 9, -1], [0, 24, 0, 0, -5, -12, 0, 0], [0, 0, -1, 1, 0, 0, 4, -4], [-4, -30, 0, 0, 4, 0, 0, 0], [0, 0, 3, -4, 0, 0, -3, -7], [-12, 0, 0, 0, -6, 0, 0, 0], [0, 0, -2, -2, 0, 0, 4, -2], [-13, 0, 0, 0, 13, 0, 0, 0], [0, -18, 0, 0, -12, 9, 0, 0], [0, 0, 1, 1, 0, 0, 0, -1], [0, 0, 5, 7, 0, 0, -5, 2], [7, 6, 0, 0, 0, 6, 0, 0], [0, 0, 3, 3, 0, 0, 4, 4], [-10, 3, 0, 0, -20, -3, 0, 0], [0, 0, -4, -6, 0, 0, 4, -2], [0, 0, -5, -9, 0, 0, 4, 9], [-6, 6, 0, 0, 0, 6, 0, 0], [0, 0, 4, -4, 0, 0, 7, -7], [0, 0, 0, 0, 0, -35, 0, 0], [0, 0, 5, 9, 0, 0, -4, -9], [0, 0, 2, 4, 0, 0, -2, -4], [0, 0, -10, -5, 0, 0, 10, 5], [0, -1, 0, 0, 0, 2, 0, 0], [-5, -12, 0, 0, -5, 24, 0, 0], [12, 9, 0, 0, 12, -18, 0, 0], [0, 0, -7, -3, 0, 0, 10, -3], [0, 0, -5, 1, 0, 0, -5, 4], [0, 0, 2, -2, 0, 0, -2, -4], [12, 3, 0, 0, 24, -3, 0, 0], [6, 10, 0, 0, 0, 10, 0, 0], [0, 0, 13, -13, 0, 0, 3, -3], [0, 0, 0, -1, 0, 0, 1, -1], [0, 0, 6, -3, 0, 0, -3, -3], [1, -18, 0, 0, 2, 18, 0, 0], [-30, 5, 0, 0, 0, 5, 0, 0], [0, 8, 0, 0, 0, -4, 0, 0], [0, 0, -1, 0, 0, 0, 1, 0], [-6, -5, 0, 0, -12, 5, 0, 0], [12, -23, 0, 0, -12, 0, 0, 0], [0, 0, -2, 2, 0, 0, -4, 4], [4, 0, 0, 0, 2, -39, 0, 0], [0, 0, -7, -3, 0, 0, 7, 4], [0, 0, -3, 7, 0, 0, -3, -4], [0, 0, -4, 5, 0, 0, -1, 5], [0, -24, 0, 0, 0, 0, 0, 0], [-21, -12, 0, 0, -42, 12, 0, 0], [0, 0, 4, -4, 0, 0, -4, -8], [0, 0, 7, -14, 0, 0, 7, 7], [-14, 12, 0, 0, -28, -12, 0, 0], [0, 0, 7, 7, 0, 0, -9, -9], [7, -18, 0, 0, 7, 36, 0, 0], [0, 0, -7, 7, 0, 0, -3, 3], [28, 0, 0, 0, 14, 9, 0, 0], [26, -6, 0, 0, 0, -6, 0, 0], [36, 0, 0, 0, 18, -5, 0, 0], [0, 0, -1, -1, 0, 0, 2, 2], [0, 7, 0, 0, 0, -14, 0, 0], [0, 28, 0, 0, 27, -14, 0, 0], [0, 0, -11, 14, 0, 0, -11, -3], [-21, -4, 0, 0, -21, 8, 0, 0], [0, 0, 2, 10, 0, 0, -8, -10], [30, 9, 0, 0, 0, 9, 0, 0], [0, 0, -3, 3, 0, 0, 3, 6], [0, 0, -2, 11, 0, 0, -2, -9], [24, -8, 0, 0, 24, 16, 0, 0], [0, 0, 1, 3, 0, 0, -4, 3], [-6, -32, 0, 0, 6, 0, 0, 0], [0, 0, -13, 11, 0, 0, 2, 11], [1, 6, 0, 0, 2, -6, 0, 0], [0, 0, -5, -5, 0, 0, -2, -2], [0, -24, 0, 0, 13, 12, 0, 0], [0, 0, 6, -6, 0, 0, 6, -6], [6, 1, 0, 0, -6, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, -6], [-42, 0, 0, 0, -21, 12, 0, 0], [0, 0, 0, -7, 0, 0, 0, 7], [-24, 5, 0, 0, 24, 0, 0, 0], [0, 0, -1, 2, 0, 0, -1, 2], [0, -36, 0, 0, 18, 18, 0, 0], [0, 0, 0, 6, 0, 0, 0, -6], [-18, -23, 0, 0, -36, 23, 0, 0], [0, 0, -7, -7, 0, 0, 9, 9], [-11, 6, 0, 0, -11, -12, 0, 0], [0, 0, -6, -6, 0, 0, 0, 6], [0, 0, -8, 8, 0, 0, 1, -1], [0, 0, -9, 9, 0, 0, 3, -3], [36, 0, 0, 0, 18, 23, 0, 0], [0, 0, -6, -6, 0, 0, 6, 6], [0, 0, -10, 4, 0, 0, 10, 14], [0, 0, 3, 3, 0, 0, -6, -6], [0, 30, 0, 0, 12, -15, 0, 0], [-9, 10, 0, 0, -9, -20, 0, 0], [16, 0, 0, 0, 8, -12, 0, 0], [0, 0, -4, -2, 0, 0, 6, -2], [0, 0, 0, 3, 0, 0, 0, -3], [-22, 0, 0, 0, -11, -12, 0, 0], [0, 0, 8, -8, 0, 0, -1, 1], [27, -12, 0, 0, 0, -12, 0, 0], [18, 3, 0, 0, 18, -6, 0, 0], [0, 0, 4, 2, 0, 0, -6, 2], [6, -25, 0, 0, -6, 0, 0, 0], [0, 0, -6, -6, 0, 0, 8, 8], [-24, 13, 0, 0, 0, 13, 0, 0], [0, -24, 0, 0, 17, 12, 0, 0], [-4, 12, 0, 0, 4, 0, 0, 0], [0, 0, -1, -7, 0, 0, -1, 8], [13, -12, 0, 0, -13, 0, 0, 0], [0, 0, -1, 1, 0, 0, 4, -4], [0, 0, -5, -3, 0, 0, 5, 2], [0, 0, 12, -10, 0, 0, 12, -2], [4, 54, 0, 0, -4, 0, 0, 0], [0, 22, 0, 0, -36, -11, 0, 0], [8, -18, 0, 0, 16, 18, 0, 0], [0, 0, 3, 8, 0, 0, -3, 5], [-11, 6, 0, 0, 11, 0, 0, 0], [0, 0, -6, -10, 0, 0, 4, 10], [-24, 9, 0, 0, 0, 9, 0, 0], [0, 0, 6, -6, 0, 0, -6, 6], [0, 0, 5, -12, 0, 0, 17, 12], [0, 0, 6, -6, 0, 0, 12, 6], [22, 6, 0, 0, 22, -12, 0, 0], [0, -24, 0, 0, 13, 12, 0, 0], [0, 0, 7, -9, 0, 0, 7, 2], [0, 0, 2, 0, 0, 0, -2, -2], [0, 0, 11, 4, 0, 0, 7, -4], [24, 10, 0, 0, 24, -20, 0, 0], [34, 0, 0, 0, 17, -24, 0, 0], [-2, 0, 0, 0, -1, -48, 0, 0], [0, 0, 13, -13, 0, 0, -5, 5], [0, 0, -10, 4, 0, 0, 6, 4], [-10, 36, 0, 0, 10, 0, 0, 0], [0, 0, 0, -6, 0, 0, 6, -6], [0, 0, 2, 2, 0, 0, -8, -8], [-42, 11, 0, 0, 0, 11, 0, 0], [0, 60, 0, 0, -3, -30, 0, 0], [0, 0, -9, 5, 0, 0, 4, 5], [-8, 3, 0, 0, -16, -3, 0, 0], [0, 0, -10, -7, 0, 0, 17, -7], [0, 0, 8, -13, 0, 0, 8, 5], [-9, 0, 0, 0, 9, 0, 0, 0], [12, 0, 0, 0, 6, -12, 0, 0], [0, 0, -3, -6, 0, 0, 3, -3], [0, 0, -9, 9, 0, 0, -9, 0], [0, 0, 15, 15, 0, 0, -14, -14], [11, -18, 0, 0, -11, 0, 0, 0], [6, -29, 0, 0, 0, -29, 0, 0], [0, 0, -5, 5, 0, 0, 14, -14], [60, 0, 0, 0, 30, -11, 0, 0], [0, 0, -2, -2, 0, 0, 4, 4], [-3, 14, 0, 0, -3, -28, 0, 0], [0, 0, 16, -4, 0, 0, -16, -20], [0, 0, -1, -1, 0, 0, -7, -7], [0, 20, 0, 0, 42, -10, 0, 0], [0, 0, 16, 6, 0, 0, -16, -10], [57, 4, 0, 0, 57, -8, 0, 0], [36, -5, 0, 0, 36, 10, 0, 0], [24, 14, 0, 0, 0, 14, 0, 0], [0, 0, -3, -3, 0, 0, 3, 0], [-6, -20, 0, 0, -12, 20, 0, 0], [0, 0, -11, 11, 0, 0, 6, -6], [49, -12, 0, 0, 0, -12, 0, 0], [0, 0, -4, 16, 0, 0, -4, -12], [0, 0, -20, 20, 0, 0, -8, 8], [0, 0, -4, -1, 0, 0, 5, -1], [0, 0, 3, 3, 0, 0, 6, 6], [-22, -36, 0, 0, -44, 36, 0, 0], [24, -15, 0, 0, -24, 0, 0, 0], [-3, -42, 0, 0, 3, 0, 0, 0], [0, 0, -3, 3, 0, 0, -9, 9], [0, 0, -1, 3, 0, 0, 1, 4], [12, 34, 0, 0, -12, 0, 0, 0], [0, 0, 21, -12, 0, 0, -9, -12], [0, 2, 0, 0, -30, -1, 0, 0], [0, 0, -8, 7, 0, 0, -15, -7], [3, 12, 0, 0, 0, 12, 0, 0], [0, 0, 11, 11, 0, 0, -5, -5], [0, 0, 15, 5, 0, 0, -15, -10], [20, -30, 0, 0, -20, 0, 0, 0], [0, 0, 17, 17, 0, 0, -11, -11], [0, 0, 7, 3, 0, 0, 4, -3], [25, 0, 0, 0, 25, 0, 0, 0], [-30, 23, 0, 0, 0, 23, 0, 0], [0, 0, 14, -14, 0, 0, 4, -4], [15, 30, 0, 0, 15, -60, 0, 0], [0, 15, 0, 0, 0, -30, 0, 0], [0, 0, 11, 11, 0, 0, -1, -1], [0, -12, 0, 0, 17, 6, 0, 0], [-14, 0, 0, 0, -7, -24, 0, 0], [0, 0, 2, 1, 0, 0, -3, 1], [6, -5, 0, 0, 0, -5, 0, 0], [0, 0, 3, 3, 0, 0, -3, 0], [0, 0, 12, -2, 0, 0, 12, -10], [-42, 11, 0, 0, -42, -22, 0, 0], [0, 0, -4, 0, 0, 0, 4, 0], [-21, -6, 0, 0, -42, 6, 0, 0], [-24, 26, 0, 0, 0, 26, 0, 0], [0, 8, 0, 0, 6, -4, 0, 0], [-18, 28, 0, 0, -36, -28, 0, 0], [9, 36, 0, 0, -9, 0, 0, 0], [72, 0, 0, 0, 36, -11, 0, 0], [0, 0, -4, 2, 0, 0, 4, 6], [-42, 0, 0, 0, -21, -30, 0, 0], [-23, 18, 0, 0, 23, 0, 0, 0], [0, 0, -16, -22, 0, 0, 6, 22], [0, 0, -8, 7, 0, 0, -8, 1], [-36, 2, 0, 0, -72, -2, 0, 0], [0, 0, -6, -13, 0, 0, 7, 13], [3, -42, 0, 0, 6, 42, 0, 0], [-40, 0, 0, 0, -20, 24, 0, 0], [0, 0, -15, -19, 0, 0, 4, 19], [21, -28, 0, 0, 0, -28, 0, 0], [0, 0, -5, -10, 0, 0, 5, 10], [24, 0, 0, 0, 12, -47, 0, 0], [0, 0, -11, -1, 0, 0, 11, 10], [0, 0, 2, -12, 0, 0, 2, 10], [0, 0, 13, -8, 0, 0, -13, -21], [0, 0, -11, -19, 0, 0, 8, 19], [0, 0, 4, 10, 0, 0, 4, -14], [30, 0, 0, 0, 15, 18, 0, 0], [0, 0, 1, -6, 0, 0, 1, 5], [0, 32, 0, 0, 0, -64, 0, 0], [0, 0, -3, -3, 0, 0, 4, 4], [0, 0, 15, 15, 0, 0, -18, -18], [6, -29, 0, 0, 12, 29, 0, 0], [0, -8, 0, 0, -24, 4, 0, 0], [0, 0, 10, -10, 0, 0, 2, -2], [22, 9, 0, 0, -22, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2736_bm_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2736_2_bm_p();".
// 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_2736_2_bm_p(:prec:=8)
    chi := MakeCharacter_2736_bm();
    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_2736_2_bm_p();".
// 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_2736_2_bm_p( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2736_bm();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![2704, 0, 1040, 0, 348, 0, 20, 0, 1]>,<7,R![1, 0, 1]>,<11,R![52, 0, 20, 0, 1]>,<23,R![2704, 0, -2288, 0, 1884, 0, -44, 0, 1]>,<31,R![33, 12, 1]>],Snew);
    return Vf;
end function;