
// Make newform 3072.2.d.f in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_3072_d();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_3072_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_3072_2_d_f();".
// 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_3072_2_d_f();".
// 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, 6, -7, 2, -1, 0, 0, 0], [4, -12, 19, -15, 10, -3, 1, 0], [-5, 16, -24, 17, -11, 3, -1, 0], [31, -126, 223, -256, 175, -98, 28, -8], [-42, 166, -285, 325, -220, 123, -35, 10], [-43, 168, -285, 325, -220, 123, -35, 10], [109, -440, 774, -890, 610, -342, 98, -28]];
    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_3072_d();"
function MakeCharacter_3072_d()
    N := 3072;
    order := 2;
    char_gens := [2047, 2053, 1025];
    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_3072_d_Hecke();"
function MakeCharacter_3072_d_Hecke(Kf)
    N := 3072;
    order := 2;
    char_gens := [2047, 2053, 1025];
    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, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0], [-1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 1, 1], [0, 0, 0, 0, -2, 0, 1, 1], [0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 1, -1], [0, 0, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 2, 1, 0], [3, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 2, -1, 1], [0, -1, 3, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, -3, -1], [0, 0, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 2, 1, 0], [0, 0, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, -4, -2, -1, 1], [0, 0, 0, 0, 4, 2, 2, 2], [2, -2, 0, 0, 0, 0, 0, 0], [2, 2, 4, 0, 0, 0, 0, 0], [3, 1, 4, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, -5, -3, 1], [2, -2, 6, 2, 0, 0, 0, 0], [0, 2, 6, -2, 0, 0, 0, 0], [0, 0, 0, 0, 5, 0, -1, -2], [-1, 1, 0, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, 0, -4], [0, 0, 0, 0, -6, 0, -1, -1], [-2, 0, 4, -4, 0, 0, 0, 0], [3, 1, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, -2, 2, 2], [0, -1, 3, 3, 0, 0, 0, 0], [0, 0, 0, 0, -4, 6, 2, 2], [0, 0, 0, 0, 7, -4, -1, 0], [-1, 1, -8, -4, 0, 0, 0, 0], [0, 0, 0, 0, -8, 4, -1, -3], [0, 0, 0, 0, 0, 1, -1, -3], [10, 2, -2, 4, 0, 0, 0, 0], [0, 0, 0, 0, -9, -6, 1, 2], [0, 0, 0, 0, 0, -2, 6, -2], [0, 0, 0, 0, 6, 2, -1, 3], [-10, 2, 6, 0, 0, 0, 0, 0], [-4, -6, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 9, 2, -3, 0], [-7, -1, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 4, 10, -2, -2], [-3, -1, -8, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, -5, -3, 1], [0, 0, 0, 0, -2, 6, 5, -3], [2, 6, 2, -2, 0, 0, 0, 0], [-14, 2, -10, -4, 0, 0, 0, 0], [-4, 4, -2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, -3, -5, 3], [10, 2, 2, -2, 0, 0, 0, 0], [16, 4, 4, -4, 0, 0, 0, 0], [0, 0, 0, 0, 5, 8, -1, 6], [13, -1, 8, 4, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 1, 5], [-10, 2, -2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 12, 4, 0, 0], [0, 0, 0, 0, 1, -6, 5, 8], [0, 0, 0, 0, 4, 2, -6, 2], [4, 0, 12, -4, 0, 0, 0, 0], [4, -6, -4, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -8, 1, 6], [0, 0, 0, 0, 12, 6, 2, -6], [10, -2, 0, -4, 0, 0, 0, 0], [0, 0, 0, 0, -16, -9, 1, -3], [0, 0, 0, 0, 8, -2, 5, 7], [-2, -2, -6, 6, 0, 0, 0, 0], [6, -6, -4, -8, 0, 0, 0, 0], [7, -3, -12, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 5, -5], [0, 0, 0, 0, 0, -3, 7, 1], [-10, -6, 10, 0, 0, 0, 0, 0], [0, 0, 0, 0, -11, 10, -1, 2], [0, 0, 0, 0, 8, -4, 3, 1], [0, -5, -5, -5, 0, 0, 0, 0], [-4, 6, -2, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, -7, 7, 3], [0, 0, 0, 0, -2, 6, -7, 1], [-4, -8, -10, 4, 0, 0, 0, 0], [4, 0, -8, 0, 0, 0, 0, 0], [-11, -5, 12, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, -13, 5, 1], [-16, -1, -1, -5, 0, 0, 0, 0], [16, 2, -2, -2, 0, 0, 0, 0], [0, 0, 0, 0, 5, 10, 3, -2], [-9, -3, 12, 0, 0, 0, 0, 0], [0, 0, 0, 0, 16, -9, 9, 5], [-6, 2, -4, -12, 0, 0, 0, 0], [-19, 3, -4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 0, 0, 4], [0, 0, 0, 0, -12, 0, -4, -4], [18, -2, 12, 8, 0, 0, 0, 0], [0, 0, 0, 0, 19, -2, -5, -4], [0, -1, -17, 3, 0, 0, 0, 0], [0, 0, 0, 0, -8, -15, -1, 1], [0, 0, 0, 0, 2, -10, -9, -1], [0, 0, 0, 0, 0, 7, -3, 7], [0, 0, 0, 0, 9, -8, -3, 4], [0, 0, 0, 0, 16, -13, -3, -3], [16, -1, 3, 7, 0, 0, 0, 0], [0, 0, 0, 0, -4, 12, 0, 0], [-2, -2, -16, -4, 0, 0, 0, 0], [0, 0, 0, 0, 20, -10, 2, -2], [-2, 8, -12, -4, 0, 0, 0, 0], [12, -4, -14, 0, 0, 0, 0, 0], [2, -2, -4, 0, 0, 0, 0, 0], [-1, 5, -8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 1, 3], [6, -8, -4, 4, 0, 0, 0, 0], [0, 0, 0, 0, 12, 0, 0, 8], [-15, -1, 16, 0, 0, 0, 0, 0], [8, 1, -11, -3, 0, 0, 0, 0], [0, 0, 0, 0, -8, 7, -7, -5], [-12, -4, 2, 8, 0, 0, 0, 0], [0, 0, 0, 0, -3, 10, -1, -6], [0, 0, 0, 0, -20, 4, -4, 0], [0, 0, 0, 0, -16, 0, 3, 1], [-12, 4, -12, -4, 0, 0, 0, 0], [0, 0, 0, 0, -9, -20, 3, -4], [0, 0, 0, 0, -16, -7, -1, 3], [0, 0, 0, 0, 8, 5, 3, -7], [0, 0, 0, 0, -3, -4, 7, -2], [0, 0, 0, 0, -18, -6, -5, 7], [-10, -10, 8, 4, 0, 0, 0, 0], [1, 7, -8, 4, 0, 0, 0, 0], [0, 0, 0, 0, 10, -10, 9, -3], [0, 0, 0, 0, 4, -4, 8, 0], [22, -6, -2, 0, 0, 0, 0, 0], [-3, -1, -4, -12, 0, 0, 0, 0], [0, 0, 0, 0, 2, -10, 11, 3], [-8, 5, -11, 1, 0, 0, 0, 0], [12, -2, 8, 12, 0, 0, 0, 0], [0, 0, 0, 0, -7, 24, -1, 2], [0, 0, 0, 0, -8, 9, 3, 5], [0, 0, 0, 0, 3, 8, 7, 12], [8, 5, 1, -11, 0, 0, 0, 0], [0, 0, 0, 0, -8, 3, 1, -9], [0, 0, 0, 0, 7, 4, 5, -6], [25, 7, 12, -8, 0, 0, 0, 0], [0, 0, 0, 0, -16, 6, -2, 2], [0, 0, 0, 0, 18, 16, -1, 7], [14, -2, 4, -12, 0, 0, 0, 0], [0, 0, 0, 0, 16, 12, 5, 7], [8, -3, -7, -7, 0, 0, 0, 0], [0, 0, 0, 0, -32, 9, -1, -3], [-6, -10, -10, 8, 0, 0, 0, 0], [0, 0, 0, 0, -8, 22, -5, -7], [2, -10, -2, 10, 0, 0, 0, 0], [0, 0, 0, 0, -8, -11, 7, 5], [-8, -8, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, -32, 13, 3, 1], [2, 2, 6, -12, 0, 0, 0, 0], [-19, 3, 0, -8, 0, 0, 0, 0], [8, 1, 1, -3, 0, 0, 0, 0], [-10, 0, 0, -16, 0, 0, 0, 0], [0, 0, 0, 0, -11, -14, 7, 2], [0, 0, 0, 0, 8, -2, -10, 6], [8, -1, -9, 3, 0, 0, 0, 0], [23, 1, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 11, 5, 1], [-16, -3, -3, 9, 0, 0, 0, 0], [12, -8, 0, -4, 0, 0, 0, 0], [5, 7, 4, -12, 0, 0, 0, 0], [0, 0, 0, 0, -4, 6, 15, 1], [-12, 2, 10, -6, 0, 0, 0, 0], [0, 0, 0, 0, 5, -2, -9, 2], [0, 0, 0, 0, 20, 16, 8, -4], [0, 0, 0, 0, -12, 12, 17, 7], [-10, -2, -6, 4, 0, 0, 0, 0], [-22, -4, -12, -4, 0, 0, 0, 0], [-3, 7, 8, 4, 0, 0, 0, 0], [-26, -2, 18, -2, 0, 0, 0, 0], [0, 0, 0, 0, 28, 8, -4, -4], [0, 0, 0, 0, 11, -20, 7, 4], [-15, -9, 8, -4, 0, 0, 0, 0], [0, 0, 0, 0, 16, -6, 13, -1], [-5, 1, 12, -4, 0, 0, 0, 0], [0, 0, 0, 0, 24, 15, -7, 5], [0, 0, 0, 0, 18, -4, -7, -11], [-10, -2, -6, 14, 0, 0, 0, 0], [-14, -2, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, -11, -10, 3, 14], [0, 0, 0, 0, -6, -2, 11, -5], [0, 0, 0, 0, -4, -20, -8, 0], [4, 0, 34, 6, 0, 0, 0, 0], [24, -8, -8, -8, 0, 0, 0, 0], [-6, 0, -4, -20, 0, 0, 0, 0], [0, 0, 0, 0, -24, 16, 12, 4], [0, 0, 0, 0, -28, -16, 4, 4], [0, 0, 0, 0, 3, 10, -3, -6], [0, 0, 0, 0, -4, 2, -2, -2], [-18, -4, -16, 16, 0, 0, 0, 0], [-2, 10, -4, 0, 0, 0, 0, 0], [0, 0, 0, 0, -42, 6, -1, -5], [-14, -2, 10, 6, 0, 0, 0, 0], [-8, 0, -4, 16, 0, 0, 0, 0], [0, 0, 0, 0, 13, 16, 1, 12], [1, 3, -4, 8, 0, 0, 0, 0], [0, 0, 0, 0, 2, 4, -3, -7], [10, -6, 4, 8, 0, 0, 0, 0], [0, 0, 0, 0, 8, 3, -19, -3], [0, 0, 0, 0, 5, -18, -11, 4], [21, -1, 4, 4, 0, 0, 0, 0], [0, 0, 0, 0, -32, 7, 9, 1], [18, 8, 20, -4, 0, 0, 0, 0], [0, 0, 0, 0, -8, 1, 11, 9], [-12, -6, 12, -8, 0, 0, 0, 0], [0, 0, 0, 0, 23, -4, 3, -4], [25, -1, 8, 12, 0, 0, 0, 0], [0, 0, 0, 0, 32, 0, 4, 4], [-30, 6, -8, -8, 0, 0, 0, 0], [16, 4, 8, -8, 0, 0, 0, 0], [-25, 5, 8, 0, 0, 0, 0, 0], [-8, -9, 3, -9, 0, 0, 0, 0], [-38, -2, 14, 0, 0, 0, 0, 0], [0, 0, 0, 0, -35, 4, -7, 4], [0, 0, 0, 0, 42, 0, -7, 5], [-3, 3, -12, -8, 0, 0, 0, 0], [-8, -1, 35, 3, 0, 0, 0, 0], [11, -7, -8, -20, 0, 0, 0, 0], [0, 0, 0, 0, -32, -1, 9, -3], [0, 0, 0, 0, 4, 4, -7, -17], [-6, 8, 0, 8, 0, 0, 0, 0], [2, -2, 4, 8, 0, 0, 0, 0], [15, 1, -4, -8, 0, 0, 0, 0], [0, 0, 0, 0, -20, 8, -8, -4], [0, 0, 0, 0, -10, 24, 3, -1], [0, 0, 0, 0, 8, -33, -11, -1], [-17, -3, -20, 8, 0, 0, 0, 0], [-18, 18, 14, -6, 0, 0, 0, 0], [0, 0, 0, 0, 16, 1, 19, -7], [50, 2, 0, 4, 0, 0, 0, 0], [-8, -10, 18, -6, 0, 0, 0, 0], [0, 0, 0, 0, 51, -8, -5, 0], [0, 0, 0, 0, -16, 17, -17, 3], [8, -8, 10, 8, 0, 0, 0, 0], [0, 0, 0, 0, -32, 3, -3, 5], [0, 0, 0, 0, 20, -22, 10, 2], [13, -5, -4, 4, 0, 0, 0, 0], [0, 0, 0, 0, -8, -4, 13, -9], [26, -4, 0, 16, 0, 0, 0, 0], [-10, 10, 12, 8, 0, 0, 0, 0], [21, -9, -8, -12, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, -4], [0, 0, 0, 0, 4, 10, -6, -6], [20, 4, 4, -16, 0, 0, 0, 0], [0, 0, 0, 0, -10, -8, -11, -3], [-2, -12, -8, 16, 0, 0, 0, 0], [-24, -8, 10, -8, 0, 0, 0, 0], [-6, -8, 20, 4, 0, 0, 0, 0], [0, 0, 0, 0, -17, 18, 3, 0], [0, 0, 0, 0, 16, 22, -2, 10], [0, 0, 0, 0, 18, -4, 11, 11], [0, 0, 0, 0, -28, 0, 16, 0], [0, 0, 0, 0, 19, -10, 7, 16], [4, 0, 8, -16, 0, 0, 0, 0], [-15, 11, -8, -8, 0, 0, 0, 0], [0, 0, 0, 0, -8, 0, 4, -4], [0, 0, 0, 0, -2, -4, 15, 11], [0, 0, 0, 0, -48, 0, -7, 3], [8, 1, -3, 1, 0, 0, 0, 0], [0, 0, 0, 0, 4, -6, -14, 10], [0, 0, 0, 0, 11, -24, -5, -8], [10, -4, -8, -16, 0, 0, 0, 0], [0, 0, 0, 0, 0, 15, 13, 3], [0, 0, 0, 0, 35, 20, 7, -4], [0, 0, 0, 0, -20, -18, -7, 15], [0, 0, 0, 0, 28, -12, 4, -4], [-26, 0, -12, 4, 0, 0, 0, 0], [-15, -5, 8, 8, 0, 0, 0, 0], [6, 8, 8, 8, 0, 0, 0, 0], [-11, -5, -12, 0, 0, 0, 0, 0], [0, 0, 0, 0, 24, 7, -7, 1], [0, 0, 0, 0, 40, 12, 3, 1], [-14, 2, 8, 20, 0, 0, 0, 0], [0, 0, 0, 0, -8, 22, 6, 10], [-6, 14, 12, -16, 0, 0, 0, 0], [21, 3, 12, -20, 0, 0, 0, 0], [-16, -8, -22, 8, 0, 0, 0, 0], [0, 0, 0, 0, 16, -24, 5, -1], [0, 0, 0, 0, 40, 7, -3, 3], [24, 16, -20, 8, 0, 0, 0, 0], [20, 4, -10, 18, 0, 0, 0, 0], [0, 0, 0, 0, 13, 8, -11, 0], [-1, -7, 16, -8, 0, 0, 0, 0], [-10, 10, 22, -6, 0, 0, 0, 0], [0, 0, 0, 0, -11, -10, 15, 2], [0, 0, 0, 0, 8, -10, -2, -18], [-30, -8, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, -48, 2, -6, 2], [0, 0, 0, 0, -24, 18, 11, 1], [0, 0, 0, 0, 37, 6, 11, -10], [-9, 5, 16, -4, 0, 0, 0, 0], [0, 0, 0, 0, 21, 8, 11, 10], [0, 0, 0, 0, -8, 21, 3, -5], [0, 0, 0, 0, 8, 13, -9, -23], [36, -10, -28, -8, 0, 0, 0, 0], [0, 0, 0, 0, -25, 2, 5, -2], [37, 15, -16, 4, 0, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_3072_d_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_3072_2_d_f();".
// 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_3072_2_d_f(:prec:=8)
    chi := MakeCharacter_3072_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_3072_2_d_f();".
// 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_3072_2_d_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_3072_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![64, 0, 320, 0, 160, 0, 24, 0, 1]>,<7,R![4, -24, -8, 4, 1]>],Snew);
    return Vf;
end function;