
// Make newform 1950.2.bc.g in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1950_bc();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1950_bc_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_1950_2_bc_g();".
// 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_1950_2_bc_g();".
// 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 := [2704, 208, 8, 36, 185, 30, 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], [-320632, 258164, 5488658, 204731, -21770, -47714, 27304, -2225], [-62031216, 34618460, -5277648, -784473, -2370014, 800522, -125666, -1777], [2274116, -1640788, 360425, 80915, 84154, -39200, 7801, -299], [94417440, -18392236, -2633192, 3714597, 3350390, -318186, -71918, 43733], [-3328, -46500, 37828, -7135, -2554, -2018, 822, -151], [-117816036, 3493156, 7562729, -10547568, -5793110, -209286, 362933, -123974]];
    Rf_basisdens := [1, 1, 20561424, 6853808, 395412, 20561424, 51792, 10280712];
    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_1950_bc();"
function MakeCharacter_1950_bc()
    N := 1950;
    order := 6;
    char_gens := [1301, 1327, 301];
    v := [6, 6, 5];
    // 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_1950_bc_Hecke();"
function MakeCharacter_1950_bc_Hecke(Kf)
    N := 1950;
    order := 6;
    char_gens := [1301, 1327, 301];
    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, -1, 0, 0, -1, 0, 0], [1, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 1, 1, -1, 0, -1], [-1, 1, 1, 1, 0, 2, 1, 1], [1, 0, 0, 1, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, -4, 0], [-1, -1, -2, 1, 2, -1, 1, -2], [0, -1, 0, 0, -1, 0, 0, 0], [-2, 1, 2, -2, -1, 0, 2, 2], [1, 1, -1, 0, 1, 1, -4, 1], [-4, 1, -2, 1, 0, -1, -2, 1], [0, -2, 0, 0, 2, 0, 0, 0], [1, -1, 8, -1, 0, 3, -4, 0], [-2, 0, -3, 2, 0, 0, 4, -2], [-2, -2, -4, 1, 2, -6, 0, -1], [4, -1, -1, 1, 1, -2, -2, -1], [0, 0, -4, 0, 0, -2, -4, 0], [-2, 2, -2, 0, -2, -2, -2, 0], [-2, -2, 0, 2, 0, -4, 0, 0], [-4, 0, -2, -2, 0, 0, 8, 2], [-1, -3, -3, 0, 3, -3, 0, -3], [-4, 2, 4, 0, 2, 2, 4, 2], [5, 0, 1, -1, -1, 0, 3, -1], [4, -2, -2, 2, 2, -10, -2, -2], [2, -2, 0, 2, 0, -2, -2, -2], [10, 0, -2, -1, 0, -4, 0, -1], [10, 0, -4, 0, 0, 4, -10, 0], [4, -2, -4, -2, -2, -2, -4, 0], [-2, 3, 3, 3, -1, 4, -4, -1], [-8, -1, 3, 0, -1, -3, 8, 0], [-8, 1, 2, 1, -1, 3, 0, 2], [-12, 1, 1, -1, -1, 8, 6, 1], [-1, 1, 0, 1, 0, 1, -7, 0], [-6, 1, -1, -1, 1, 2, 4, -1], [-2, 2, 2, -2, 2, 2, 0, 4], [-3, -1, 5, -1, 1, 11, 0, -2], [-1, 1, -2, -1, 2, 5, 2, -2], [-6, -2, 9, 0, 2, 9, -6, 0], [2, -1, 5, -1, -1, 1, -6, -1], [-8, -1, 6, 0, -1, -6, 8, 0], [-8, -2, 2, 0, 2, 6, 0, -2], [-2, 2, -12, 2, 0, -4, 4, 0], [0, -2, -10, -2, 0, -12, -4, -2], [2, -1, -9, 0, 1, -9, 2, 0], [2, -2, -8, -2, 0, -6, -2, 0], [-7, 2, -3, -1, 1, 4, 7, 1], [-8, 1, 5, 2, 1, 7, -4, 2], [20, 0, 0, 0, 0, -2, -10, 0], [0, -2, 12, -2, -2, -2, 4, 0], [-10, -2, -5, 3, 2, -8, 0, 1], [-10, 4, -6, 6, 4, 4, 12, -2], [-2, 0, -4, 0, 4, -8, 3, -4], [5, -2, 13, -2, -3, 3, -1, -3], [-2, -1, 6, -2, -3, -4, 2, 2], [6, 2, -3, -4, -2, 7, -6, 4], [4, 0, -12, 0, -4, -8, 0, -4], [14, 0, 5, -1, -1, 4, 12, -1], [1, 0, -11, 0, -1, -6, -6, -1], [4, 0, -6, 2, 0, 0, -8, -2], [-10, 2, -1, -1, 1, 2, 10, 1], [-14, -1, 1, 1, -1, 7, 6, 1], [-2, 0, 8, -4, 0, 0, 4, 4], [2, -6, -4, 2, 6, -2, 0, -4], [8, -4, 0, -2, 4, 4, 0, -6], [-2, 4, -4, 5, 4, 4, -4, -1], [6, 6, 4, -6, -4, 10, -2, 4], [0, 8, 10, -4, -8, 12, 0, 4], [2, -2, 12, -2, 0, 4, -10, 0], [10, 0, 2, 0, 0, 2, 10, 0], [6, 0, 20, -2, -2, 18, 2, -2], [-4, 0, -12, -2, 0, 0, 8, 2], [0, -4, 4, 2, -2, -6, 0, -2], [-1, -3, -12, -3, 4, -7, 2, 4], [-1, -8, -1, -1, 7, -2, -3, -1], [-6, 3, 1, -3, -1, -8, 4, 1], [6, -8, -11, 3, 8, -14, 0, -5], [-1, 0, -3, 0, 3, -6, 2, -3], [-3, -4, 11, 1, 5, 12, -1, 1], [-3, -7, -6, 7, 6, 1, 1, -6], [4, -2, 0, 4, 2, -4, -4, -4], [6, -2, 16, 2, -2, -2, -8, -4], [0, 2, 14, 2, 0, 16, 4, 2], [-6, 4, 18, 4, 2, 14, 0, 2], [-20, 2, -2, 4, 6, -2, 20, -4], [-2, 4, 2, 2, -4, 0, 0, 6], [29, -1, 0, 1, 0, 3, -15, 0], [10, -8, 0, -4, 4, -4, 2, -4], [20, 1, 1, -1, -1, 4, -10, 1], [-4, 0, 18, -2, 0, 0, 8, 2], [-2, 0, 4, -2, 0, 8, 0, -2], [-6, 4, 10, 0, -4, 10, -6, 0], [10, 1, -1, -1, 1, -13, -4, -1], [-5, 4, 11, -5, -1, -6, 5, 5], [2, 0, -2, -2, 0, 0, -4, 2], [6, -3, -5, -3, -3, -7, -22, -3], [-2, 1, 14, 0, -1, 14, -2, 0], [18, -1, 5, 0, 1, 11, 0, -1], [4, 0, -15, 3, 3, 12, -4, -3], [8, -4, 12, -6, -4, -4, -8, 2], [-8, 0, 16, 2, 0, 32, 0, 2], [14, -5, 1, -6, -1, -5, 2, -6], [-4, 0, 16, 0, 4, 10, 2, 4], [-15, 0, 1, -3, -3, 2, 15, 3], [4, 3, 1, -2, -3, -1, 0, 1], [0, -2, -4, -10, -2, -2, 4, 8], [-4, 6, 0, 2, -4, 2, 0, 2], [6, -2, -1, 1, -2, -2, -8, -3], [-12, 2, 0, 6, -2, -2, 0, 8], [1, -4, -10, 2, -2, 8, -1, -2], [0, -3, -3, -3, 3, -3, 0, 3], [0, -7, 4, -5, 2, -1, -10, -5], [8, -5, -1, 5, 1, 2, -6, -1], [-14, 1, -5, -2, 1, 1, 26, 3], [-6, 2, 0, -2, 0, 6, 4, 0], [-3, 1, 6, 1, 2, 5, -1, 2], [-2, 2, 4, -2, -4, -30, 0, 4], [-2, 1, -5, -4, -3, 9, 2, 4], [-2, -3, -21, 4, 1, 17, 2, -4], [2, -5, -25, -5, 3, -16, 20, 3], [-18, 2, -4, 0, -2, -4, -18, 0], [4, -4, 4, 0, -4, -4, -4, 0], [2, 2, 8, -2, -2, 14, 0, 0], [2, -2, 0, 2, 0, 2, -2, 0], [-5, 2, 33, 1, -1, 34, -3, 1], [-2, 6, 5, 3, -6, 4, 0, 9], [-14, 0, 2, 0, -2, -4, 6, 2], [0, 0, 32, 0, 0, 16, -16, 0], [-4, 2, 8, 3, -2, 14, 0, 5], [0, 0, -2, 3, 0, 0, 0, -3], [-1, 8, -15, 5, -3, -10, 9, 5], [0, -7, 12, -2, 5, 10, -4, -2], [-20, -2, 1, 5, 3, -6, 20, -5], [-16, 9, 9, -8, 1, -1, 16, 8], [15, -7, -4, 7, 4, 5, -9, -4], [8, 2, -11, -3, -5, -14, 2, -3], [-14, 1, 3, -1, -3, 11, 6, 3], [31, -1, 0, 1, 0, -21, -16, 0], [-16, 12, 4, 12, 4, 16, 8, 4], [10, 4, 0, -4, 0, 4, -10, 4], [8, 3, 5, 2, 3, 3, -22, 1], [-10, 3, 18, 4, 1, 22, -2, 4], [-4, 7, 3, 7, -3, 7, 0, -3], [-18, 2, 14, -2, 2, 2, 32, 4], [2, -4, -20, 6, 2, 14, -2, -6], [-22, -4, -2, 4, 2, -14, 10, -2], [1, 1, 15, 4, 1, 1, -4, -3], [6, -6, 9, 5, 6, 24, 0, -1], [6, -1, -3, 2, 1, -5, 0, 1], [-18, 6, 15, 5, 6, 6, 24, 1], [-9, -1, -4, 1, 4, -21, 6, -4], [-3, -2, -1, 3, 1, -2, 3, -3], [13, 5, -11, -2, -5, -27, 0, 3], [6, 0, 7, 8, 8, -15, -6, -8], [-12, 0, -13, 5, 5, 8, 12, -5], [16, -4, -10, 2, 4, -16, 0, -2], [8, -6, 18, -6, -2, 2, -4, -2], [24, -4, 4, 4, -4, 20, -16, 4], [2, 0, 12, 4, 0, 24, 0, 4], [-4, 0, -14, 6, 0, 0, 8, -6], [-14, 2, -4, 8, 6, 4, 2, 8], [10, -7, 21, -7, -3, 2, 12, -3], [-2, 6, 14, 11, 6, 6, -8, -5], [1, -1, -20, -1, 0, -11, 9, 0], [-18, 7, -8, 8, 1, 0, -2, 8], [-14, 4, 17, 6, 4, 4, 20, -2], [-6, 6, 11, -9, -3, -2, 6, 9], [-2, 1, 3, 1, 1, 3, -24, 1], [5, 2, 18, -4, 2, 2, -14, 6], [-2, 10, 2, -8, -10, -6, 0, 2], [-16, 2, 18, 4, 2, 2, 28, -2], [-34, 2, 4, -2, -4, 8, 16, 4], [-8, 6, 26, 6, 2, 20, -6, 2], [-20, -4, 4, 4, -4, -32, 6, 4], [13, -5, -17, 0, 5, -29, 0, -5], [-5, 9, -16, 9, -4, -1, 17, -4], [-14, 2, -34, 2, 0, -32, -10, 2], [4, 0, 30, -10, 0, 0, -8, 10], [-24, -6, -18, 12, 6, 6, 24, -12], [-4, 6, -12, 2, 8, 10, 4, -2], [14, -2, 0, -2, -2, -2, -24, 0], [-8, 1, -8, -5, -1, -17, 0, -4], [-23, -9, 5, 5, 9, 19, 0, -4], [18, -2, -7, -1, -2, -2, -32, -1], [18, 0, 23, 0, 0, 23, 18, 0], [4, -1, -31, -1, -3, -18, -22, -3], [-35, -5, -3, 7, 5, -1, 0, 2], [3, -3, 35, -8, -3, -3, 0, 5], [3, -8, -6, 2, 10, -4, 7, 2], [12, -2, -6, 2, 6, 10, -4, -6], [14, -8, 2, -8, -6, -10, -10, -6], [16, 6, 10, -6, -10, 2, -10, 10], [-28, -1, -19, 6, 1, -37, 0, 5], [-16, -1, 6, -2, -1, 4, -20, -2], [12, -10, 2, -10, -2, -10, 20, -2], [26, 4, 14, -10, -6, -4, -26, 10], [-1, 3, -7, -6, 3, 3, -4, 9], [-3, 2, 35, 2, 1, 20, 18, 1], [-2, -2, -3, -5, -2, -2, 8, 3], [6, -4, -21, -1, 4, -38, 0, -5], [-2, 12, 10, -12, -10, -10, 2, 10], [-7, 1, -14, 1, 6, -3, 6, 6], [8, -2, -30, -4, -2, -34, 0, -4], [-8, -5, 11, 4, 5, 27, 0, -1], [-21, 12, 17, 7, -5, 24, -7, 7], [4, -2, 2, 2, 0, -4, -4, -2], [-6, 2, -46, 8, 2, 2, 8, -6], [-18, 14, -8, 14, 4, 12, 10, 4], [-5, -6, -11, 3, 9, -8, 1, 3], [1, -3, -6, -3, 2, -5, 5, 2], [10, -4, 2, 0, -4, -2, -10, 0], [22, 12, 9, -3, -12, 6, 0, 9], [0, 1, -23, -6, -5, 29, 0, 6], [-28, 2, -2, -2, 2, -6, 16, -2], [18, -4, -6, 4, 6, -32, -8, -6], [7, -10, 26, -4, -10, -10, 6, -6], [6, -2, -18, -6, 2, -34, 0, -8], [9, -9, 12, -9, 0, -3, -19, 0], [22, -11, 5, -10, 1, -5, 2, -10], [2, 4, -38, 7, 4, 4, -12, -3], [18, -2, 4, 6, 4, -10, -18, -6], [-2, -2, 22, 6, -2, -2, 8, -8], [6, -1, 5, 8, -1, -1, -10, -9], [4, -12, -16, 12, 16, -24, 0, -16], [-24, 2, -12, 10, 12, 2, 24, -10], [10, 4, -12, -6, -4, -28, 0, -2], [-36, 1, -12, 8, 9, 4, 36, -8], [-6, 2, 4, 2, 4, 6, 30, 4], [-16, 8, 4, 8, 8, 14, 20, 8], [-26, 3, -4, 3, 3, 3, 46, 0], [14, -3, 24, -7, -10, -17, -14, 7], [1, -12, -11, 15, 3, -4, -1, -15], [-18, 2, 42, 0, -2, 42, -18, 0], [8, 9, 7, -8, -9, 5, 0, 1], [-13, -1, -1, 4, 1, -1, 0, 3], [4, -2, -16, -3, -2, -2, -4, 1], [-1, 1, 6, -1, -6, 17, -2, 6], [-12, -2, -20, 2, 4, -18, -8, 2], [-5, -3, -12, -3, 8, -5, -17, 8], [-2, -4, -26, 6, 2, 20, 2, -6], [8, -6, 34, 0, 6, 34, 8, 0], [-24, 2, 12, -4, -2, -8, 24, 4], [-2, 1, -1, 1, 1, 1, 8, 1], [12, -10, -32, -2, 8, -34, 8, -2], [-24, -8, -16, 8, 16, 2, 16, -16], [10, 4, 8, 2, -4, 12, 0, 6], [-4, 0, 4, 0, -4, -28, 0, 4], [1, 0, -9, 1, 1, -8, 3, 1], [-9, -3, -4, 3, 4, -53, 5, -4], [-6, 4, 7, -12, -8, 5, 6, 12], [12, -4, -7, -1, 3, -8, 10, -1], [15, 4, 13, -5, -9, 8, 5, -5], [10, -8, -23, -8, -8, -8, -4, 0], [8, -8, 5, -5, -13, 0, -8, 5], [26, 10, 6, -9, -10, 2, 0, 1], [-31, -1, -4, 1, 4, -21, 17, -4], [4, -2, 26, -2, -2, 10, -12, -2], [18, 8, 4, 4, -4, 8, 26, 4], [14, -2, 4, -9, 2, 10, 0, -11], [40, -4, 4, 4, -4, 26, -24, 4], [0, 14, 10, -1, -14, 6, 0, 13], [4, -2, -4, 8, 6, -4, -4, -8], [6, 2, -28, 6, 2, 2, -16, -4], [28, -12, -10, 6, -6, 4, -28, -6], [-6, -15, -17, 15, 17, -2, 4, -17], [2, -6, 20, -6, 4, 6, -12, 4], [-26, -8, -18, 8, 18, 6, 18, -18], [18, -1, 45, -8, -1, -1, -34, 7], [-19, -7, -12, 7, 12, 9, 12, -12], [14, -12, 6, -12, -2, -10, -4, -2], [-8, -2, -10, -8, 2, -18, 0, -10], [11, 5, -1, 0, 5, 5, -32, 5], [14, -2, -28, 2, 4, -26, 18, 2], [7, -5, -6, -5, -2, -9, -28, -2], [-8, 8, 8, 8, 0, 12, -24, 0], [-12, 0, -16, -4, -4, -20, -20, -4], [28, 8, 4, -8, -4, 10, -12, 4], [14, 4, 12, 8, 4, 4, -36, -4], [25, -1, 2, 1, -2, -5, -14, 2], [-2, 3, 35, 3, -1, 20, 28, -1], [10, -7, 7, -4, -11, -3, -10, 4], [18, -4, -25, -3, 1, -28, 12, -3], [14, -12, -21, 3, 12, -30, 0, -9], [20, 0, 4, -8, -8, -4, 4, -8], [13, -1, -11, -6, -1, -1, -24, 5], [-20, 4, -8, -2, -4, -20, 0, 2], [14, 4, 2, 2, -4, 0, 0, 6], [-10, 0, -8, 3, 0, 0, 20, -3], [15, -3, 6, 3, -6, 29, -12, 6], [9, -3, 30, -3, -6, 9, 5, -6], [-20, 3, -10, 0, 3, 10, 20, 0], [10, -10, -8, -10, 0, -14, 32, 0], [32, -3, 28, -6, -3, 22, 20, -6], [5, 6, 3, -6, -3, -7, -1, 3], [-14, 10, 20, 10, 4, 22, 28, 4], [-38, -2, -17, 3, 2, -32, 0, 1], [11, 21, 17, -16, -21, 13, 0, 5], [18, -3, 3, 0, -3, -3, -18, 0], [24, 5, -10, -4, 1, 14, -24, 4], [10, -12, 1, -5, 7, -4, 0, -5], [2, -2, -40, -2, 0, -22, 24, 0], [-10, 2, -24, 8, 2, 2, 16, -6], [38, 0, 11, 1, 1, -12, -38, -1]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1950_bc_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1950_2_bc_g();".
// 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_1950_2_bc_g(:prec:=8)
    chi := MakeCharacter_1950_bc();
    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_1950_2_bc_g();".
// 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_1950_2_bc_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1950_bc();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![2704, 1248, -900, -504, 389, 0, -21, 0, 1]>],Snew);
    return Vf;
end function;