
// Make newform 2880.2.t.b in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2880_t();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2880_t_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_2880_2_t_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_2880_2_t_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 := [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], [-5, 16, -24, 17, -11, 3, -1, 0], [-19, 77, -133, 155, -105, 60, -17, 5], [-23, 89, -152, 170, -115, 63, -18, 5], [-31, 126, -223, 256, -175, 98, -28, 8], [-33, 131, -236, 275, -190, 108, -31, 9], [-33, 141, -253, 290, -200, 111, -32, 9], [-43, 168, -285, 325, -220, 123, -35, 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_2880_t();"
function MakeCharacter_2880_t()
    N := 2880;
    order := 4;
    char_gens := [2431, 901, 641, 577];
    v := [4, 3, 4, 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_2880_t_Hecke();"
function MakeCharacter_2880_t_Hecke(Kf)
    N := 2880;
    order := 4;
    char_gens := [2431, 901, 641, 577];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0], [1, 1, 0, -1, -1, 1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0], [-1, 1, -1, 1, 0, 1, -1, 0], [-1, -1, 2, 0, -1, 0, 0, 1], [0, 0, -2, -2, -2, 0, 0, 2], [-3, 1, -2, 0, -3, 0, 0, -1], [-1, -1, 0, 0, 0, 1, -1, 0], [-1, -2, 0, -1, 1, -1, 0, -2], [0, 0, -4, -4, 4, -2, -2, -2], [0, 0, 0, -4, 0, 2, 0, 0], [0, -4, 1, -1, 0, -3, 3, 0], [0, 2, 0, 0, 0, -2, 0, 2], [1, 3, 0, 3, -1, 5, 0, 3], [-2, 1, -2, 0, -2, 0, -4, -1], [0, -2, 0, 0, 0, 0, 0, 2], [0, 0, 3, 3, -6, -1, -1, -2], [0, 0, 3, 3, -4, 1, 1, 0], [5, 1, 2, -2, 0, 1, -1, 0], [4, 2, 0, 0, 4, 0, -4, -2], [0, 0, -6, -6, -6, 2, 2, 0], [-6, -2, 1, -1, 0, 1, -1, 0], [4, 2, 0, -6, -4, 0, 0, 2], [0, 0, -5, -5, -10, 2, 2, -2], [0, 0, 0, -4, 0, 4, 0, 0], [2, 3, 0, 0, 2, 0, -6, -3], [3, -7, -3, 3, 0, -3, 3, 0], [10, 2, -5, 5, 0, 2, -2, 0], [1, -1, 7, 0, 1, 0, -3, 1], [0, 0, 3, 3, 7, -1, -1, -1], [4, 2, 0, -8, -4, -4, 0, 2], [-5, 1, 0, 2, 5, 4, 0, 1], [0, 0, 4, 4, -5, 1, 1, 1], [-7, 2, 5, 0, -7, 0, -3, -2], [-2, 0, -4, 0, -2, 0, -6, 0], [0, 0, 3, 3, -8, -1, -1, -4], [-5, 3, 12, 0, -5, 0, -6, -3], [-3, -1, -9, 0, -3, 0, 1, 1], [2, 1, 0, -8, -2, -2, 0, 1], [8, -4, -5, 5, 0, -5, 5, 0], [-4, 6, -4, 4, 0, 4, -4, 0], [-1, -3, 0, 6, 1, 0, 0, -3], [0, 0, -6, -6, 3, -5, -5, -3], [-10, 4, 0, 0, -10, 0, -4, -4], [-2, 2, -7, 7, 0, -2, 2, 0], [6, -4, 8, 0, 6, 0, 0, 4], [2, 5, 0, 6, -2, 0, 0, 5], [0, 0, -1, -1, 3, 5, 5, 3], [-4, 0, -9, 9, 0, -1, 1, 0], [16, -6, -4, 4, 0, -2, 2, 0], [-11, 1, 0, -1, 11, 1, 0, 1], [7, -7, 5, -5, 0, 1, -1, 0], [0, 0, -3, -3, 8, -3, -3, 0], [-9, 3, -2, 0, -9, 0, -4, -3], [-11, 5, 2, -2, 0, 3, -3, 0], [3, 4, 0, 5, -3, 5, 0, 4], [0, 0, 4, 4, -10, 0, 0, 4], [-10, 4, 0, -8, 10, 8, 0, 4], [5, -1, 0, 6, -5, -8, 0, -1], [10, -2, -8, 0, 10, 0, 4, 2], [0, 0, 5, 5, 0, -1, -1, -8], [0, 0, -2, -2, 0, -2, -2, -6], [5, -1, 10, 0, 5, 0, -4, 1], [-6, -4, 0, 10, 6, 2, 0, -4], [12, 0, 1, -1, 0, 5, -5, 0], [-8, 2, 0, 2, 8, 2, 0, 2], [-4, 5, 14, 0, -4, 0, -4, -5], [25, 3, 3, -3, 0, -1, 1, 0], [0, 0, -10, -10, -6, 4, 4, -2], [-8, -8, 13, -13, 0, -6, 6, 0], [9, -2, 0, 3, -9, -1, 0, -2], [5, 5, 0, 12, -5, 2, 0, 5], [-2, 6, 2, -2, 0, 2, -2, 0], [10, 6, 0, -2, -10, 0, 0, 6], [3, 2, 17, 0, 3, 0, -3, -2], [-4, 6, -4, 4, 0, -2, 2, 0], [0, 0, 6, 6, 14, -4, -4, -2], [-15, 1, 1, 0, -15, 0, 3, -1], [-4, 3, 0, -2, 4, -4, 0, 3], [-14, 6, -8, 8, 0, -2, 2, 0], [-4, 4, -5, 5, 0, 3, -3, 0], [0, 0, -6, -6, 5, -3, -3, -1], [2, -4, 0, 2, -2, -14, 0, -4], [-2, 4, -12, 12, 0, -2, 2, 0], [0, 0, 11, 11, 10, 1, 1, -6], [3, -3, -14, 0, 3, 0, 4, 3], [4, -8, 1, -1, 0, -10, 10, 0], [10, -4, 2, 0, 10, 0, -2, 4], [-2, 6, -3, 3, 0, -1, 1, 0], [0, 0, -5, -5, 6, 4, 4, 6], [-3, 7, 0, -11, 3, 11, 0, 7], [6, 4, 2, 0, 6, 0, 2, -4], [0, 0, 5, 5, -8, 7, 7, 8], [12, 6, -10, 0, 12, 0, -4, -6], [0, 0, -6, -6, 8, 4, 4, 2], [-10, 4, 0, 0, 10, 2, 0, 4], [-14, -5, 4, 0, -14, 0, 10, 5], [2, 2, 12, 0, 2, 0, 2, -2], [-11, -3, 4, 0, -11, 0, 6, 3], [-12, -2, -8, 0, -12, 0, 12, 2], [0, 0, 0, 0, -8, -6, -6, 2], [-4, -6, 0, 14, 4, -10, 0, -6], [-10, -10, -1, 1, 0, -5, 5, 0], [4, -4, 0, -2, -4, -6, 0, -4], [-11, 3, -11, 11, 0, 5, -5, 0], [0, 0, -8, -8, -10, -6, -6, -2], [0, 0, -2, -2, 12, 2, 2, 0], [-4, -8, 1, -1, 0, -4, 4, 0], [-11, -4, 0, -21, 11, -5, 0, -4], [0, 0, 11, 11, 11, -3, -3, -9], [10, 8, 0, 0, -10, 12, 0, 8], [0, 0, 16, 16, 11, 3, 3, 1], [12, 6, 2, -2, 0, -4, 4, 0], [-4, 6, 8, 0, -4, 0, -6, -6], [0, 0, 5, 5, 4, 3, 3, 0], [-14, 2, -14, 0, -14, 0, -4, -2], [21, -1, 3, 0, 21, 0, 5, 1], [2, 1, 0, 18, -2, -8, 0, 1], [0, 16, 1, -1, 0, 1, -1, 0], [6, -6, 0, 14, -6, -4, 0, -6], [-6, -4, 0, 6, 6, 2, 0, -4], [1, -3, -26, 0, 1, 0, 4, 3], [2, -8, 2, 0, 2, 0, 12, 8], [-4, 5, 0, 2, 4, 12, 0, 5], [-2, -2, 6, -6, 0, 0, 0, 0], [0, 0, 13, 13, -6, -4, -4, -2], [-3, 0, -23, 0, -3, 0, 1, 0], [-4, -2, 18, 0, -4, 0, 10, 2], [0, 0, 0, 0, 10, 8, 8, 14], [7, 3, 6, -6, 0, 3, -3, 0], [-5, -6, 0, -9, 5, -9, 0, -6], [0, 0, 18, 18, -8, -4, -4, -6], [-26, 4, 8, -8, 0, 0, 0, 0], [-7, 3, 0, -2, 7, 8, 0, 3], [-16, 2, 0, 0, -16, 0, -2, -2], [11, -5, 8, 0, 11, 0, 10, 5], [0, 0, 4, 4, 2, -6, -6, 0], [13, 1, 0, -28, -13, -6, 0, 1], [-11, -7, 0, 2, 11, -8, 0, -7], [0, 0, 5, 5, -6, 8, 8, 2], [-4, -8, 0, 10, 4, 6, 0, -8], [-6, 5, -20, 0, -6, 0, 6, -5], [0, 0, 0, 0, 6, -6, -6, 2], [-9, 0, 0, -7, 9, -11, 0, 0], [0, 0, -5, -5, 5, -9, -9, -7], [-11, 9, 0, 8, 11, 2, 0, 9], [-16, -4, -15, 15, 0, -1, 1, 0], [3, -4, -3, 0, 3, 0, 5, 4], [-12, 2, 0, 0, 0, 8, -8, 0], [14, -4, -12, 0, 14, 0, -2, 4], [0, 0, 13, 13, 16, 5, 5, 0], [-14, -6, 0, -20, 14, -10, 0, -6], [-4, -8, 20, -20, 0, -4, 4, 0], [0, 0, 4, 4, 3, -9, -9, -11], [16, -10, 2, -2, 0, -4, 4, 0], [0, 0, 0, 0, -30, -4, -4, -8], [-12, 0, -14, 0, -12, 0, 4, 0], [-18, 2, 12, 0, -18, 0, 4, -2], [0, 0, 9, 9, -7, -3, -3, -15], [0, 0, -7, -7, 26, 8, 8, 6], [11, -9, 0, 5, -11, -1, 0, -9], [7, -3, -13, 13, 0, 5, -5, 0], [0, 0, 14, 14, -22, 2, 2, 2], [3, 7, -10, 10, 0, 1, -1, 0], [-5, 6, 0, -11, 5, 13, 0, 6], [-4, -4, -18, 18, 0, -6, 6, 0], [5, -3, 0, -4, -5, 2, 0, -3], [-11, 7, 0, 7, 11, -7, 0, 7], [0, -1, 8, 0, 0, 0, -6, 1], [0, 0, -24, -24, 12, 4, 4, 8], [0, 0, 18, 18, -24, -6, -6, -10], [-13, -13, 4, -4, 0, 1, -1, 0], [0, 0, -24, -24, 4, -8, -8, -6], [0, -2, 0, -4, 0, -8, 0, -2], [23, 5, 0, -2, -23, 12, 0, 5], [0, 0, -1, -1, -16, 0, 0, 12], [4, 7, -28, 0, 4, 0, -10, -7], [-2, 6, -3, 3, 0, 8, -8, 0], [3, 7, -5, 0, 3, 0, -7, -7], [5, -6, 0, -15, -5, -15, 0, -6], [0, 0, 9, 9, 19, 3, 3, -1], [-22, 2, 10, -10, 0, -2, 2, 0], [10, -6, 0, 14, -10, -20, 0, -6], [-1, 4, 21, 0, -1, 0, -3, -4], [4, -6, 4, 0, 4, 0, 4, 6], [0, 0, -16, -16, -4, 2, 2, 18], [0, 8, -19, 19, 0, 9, -9, 0], [4, 6, -24, 24, 0, 4, -4, 0], [10, -2, 0, 20, -10, -4, 0, -2], [-2, 8, -12, 0, -2, 0, -8, -8], [7, 1, 38, 0, 7, 0, -8, -1], [-2, 10, -4, 0, -2, 0, 4, -10], [0, 0, -5, -5, -21, -3, -3, -1], [-6, 10, -2, 2, 0, 16, -16, 0], [1, -10, 5, 0, 1, 0, -7, 10], [19, 1, 5, -5, 0, 1, -1, 0], [0, 0, -16, -16, -14, 4, 4, 2], [4, -4, 38, 0, 4, 0, 8, 4], [35, 7, 10, -10, 0, 3, -3, 0], [35, -2, 0, -15, -35, 1, 0, -2], [2, -2, 30, -30, 0, 0, 0, 0], [7, 7, 0, 7, -7, 9, 0, 7], [9, 7, -18, 0, 9, 0, -12, -7], [-15, 1, 2, -2, 0, 9, -9, 0], [24, 10, -2, 0, 24, 0, -6, -10], [0, 0, 4, 4, -16, -12, -12, -2], [-27, -3, 0, -6, 27, -4, 0, -3], [4, -2, 30, -30, 0, 2, -2, 0], [5, 11, 0, -2, -5, 16, 0, 11], [0, 0, 11, 11, 6, 2, 2, 6], [20, -4, 0, -2, -20, -10, 0, -4], [0, 0, -7, -7, 22, -11, -11, -6], [0, 0, 14, 14, -24, -6, -6, -4], [8, -8, -3, 3, 0, 6, -6, 0], [-2, 4, 6, -6, 0, 0, 0, 0], [0, 0, -10, -10, 2, 2, 2, 6], [-13, -9, 0, 0, -13, 0, 6, 9], [-6, -13, 0, -10, 6, -8, 0, -13], [0, 0, -8, -8, 17, -9, -9, -17], [-2, 16, 14, -14, 0, 4, -4, 0], [-32, -4, 13, -13, 0, 2, -2, 0], [-2, 0, -18, 0, -2, 0, 2, 0], [-4, 1, 0, -28, 4, 2, 0, 1], [0, 0, 25, 25, 9, -1, -1, -3], [-26, 6, -8, 8, 0, 6, -6, 0], [0, 0, 11, 11, -20, -18, -18, -16], [5, -5, 0, 5, -5, -21, 0, -5], [-15, -2, 29, 0, -15, 0, 9, 2], [-1, 7, -8, 0, -1, 0, -2, -7], [13, -15, -12, 12, 0, -11, 11, 0], [0, 0, -8, -8, -30, -4, -4, -4], [10, -8, 0, -28, -10, 2, 0, -8], [-6, 14, 0, 0, 0, 2, -2, 0], [-6, -10, -2, 2, 0, 0, 0, 0], [8, -8, 0, -34, -8, 8, 0, -8], [23, -13, 0, 25, -23, -13, 0, -13], [0, 0, 1, 1, -6, 5, 5, 2], [-16, 2, -22, 0, -16, 0, -18, -2], [30, 0, 0, -10, -30, 14, 0, 0], [0, 0, -9, -9, 10, 8, 8, 14], [24, 1, -2, 0, 24, 0, 4, -1], [-11, 7, -17, 17, 0, -1, 1, 0], [0, 0, 11, 11, 6, 3, 3, 2], [-4, 8, 3, -3, 0, 4, -4, 0], [-13, -11, 15, 0, -13, 0, 13, 11], [24, 6, 0, 2, -24, 2, 0, 6], [16, 0, -7, 7, 0, -5, 5, 0], [5, -6, -21, 0, 5, 0, 15, 6], [0, -10, -10, 10, 0, 6, -6, 0], [0, 0, -10, -10, -18, 0, 0, -6], [0, 0, -2, -2, -16, -16, -16, -18], [24, -2, -16, 0, 24, 0, 6, 2], [-1, 5, -17, 0, -1, 0, -3, -5], [10, -1, 0, 8, -10, 18, 0, -1], [6, -8, 0, 20, -6, 4, 0, -8], [-12, -6, 0, 8, 12, -10, 0, -6], [0, 0, -7, -7, -4, -9, -9, -12], [6, 6, -5, 5, 0, 8, -8, 0], [10, -2, 6, 0, 10, 0, -10, 2], [8, -5, 0, 42, -8, -4, 0, -5], [-5, -6, -19, 0, -5, 0, -3, 6], [15, 13, 17, -17, 0, -1, 1, 0], [8, 2, -2, 0, 8, 0, 6, -2], [0, 12, 18, 0, 0, 0, -16, -12], [0, 0, 4, 4, 36, 4, 4, 10], [-6, -8, 0, 20, 6, -18, 0, -8], [12, -8, 0, 30, -12, -12, 0, -8], [-14, -3, 8, 0, -14, 0, 2, 3], [-34, -2, -20, 0, -34, 0, 0, 2], [0, 0, -24, -24, 0, 0, 0, -14], [13, -15, -8, 8, 0, -1, 1, 0], [-20, 10, 6, -6, 0, 10, -10, 0], [0, 0, -3, -3, -6, 4, 4, 34], [4, -2, 0, 28, -4, -8, 0, -2], [4, -7, 38, 0, 4, 0, -8, 7], [0, 0, 6, 6, 2, -4, -4, -18], [23, 1, 9, 0, 23, 0, 3, -1], [10, 14, 8, -8, 0, 10, -10, 0], [0, 0, -22, -22, 7, 11, 11, 13], [0, 0, 29, 29, 20, -5, -5, 0], [-12, 11, 0, -40, 12, 18, 0, 11], [-18, 18, 0, -12, 18, 14, 0, 18], [0, 16, 19, -19, 0, 15, -15, 0], [6, -12, -6, 6, 0, -6, 6, 0], [-10, -6, 0, -14, 10, -8, 0, -6], [0, 0, 20, 20, -29, -3, -3, 5], [-16, -2, -4, 4, 0, 4, -4, 0], [10, 2, -14, 0, 10, 0, -20, -2], [-18, -2, -2, 0, -18, 0, 2, 2], [0, 0, 35, 35, -11, -3, -3, 1], [11, -7, 0, -1, -11, -7, 0, -7], [-21, 12, 7, 0, -21, 0, -17, -12], [7, 9, -26, 0, 7, 0, -12, -9], [-37, 7, -18, 18, 0, -5, 5, 0], [2, -4, 0, -36, -2, -6, 0, -4], [-31, -3, 0, 23, 31, 9, 0, -3], [-10, -14, 12, 0, -10, 0, 2, 14], [0, 0, -10, -10, -12, 14, 14, 6], [0, 8, -10, 0, 0, 0, -12, -8], [1, 9, 26, -26, 0, -1, 1, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2880_t_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2880_2_t_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_2880_2_t_b(:prec:=8)
    chi := MakeCharacter_2880_t();
    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_2880_2_t_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_2880_2_t_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2880_t();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![2, 0, 1]>],Snew);
    return Vf;
end function;