
// Make newform 2960.2.a.bc in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2960_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_2960_2_a_bc();".
// 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_2960_2_a_bc();".
// 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 := [-44, -18, 60, 12, -16, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [500, 82, -304, 4, 25, -1], [-69, -115, 20, -8, -1, 2], [89, -211, -40, 65, 2, -4], [-87, -96, -11, 73, 3, -6]];
    Rf_basisdens := [1, 1, 98, 49, 49, 49];
    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_2960_a();"
function MakeCharacter_2960_a()
    N := 2960;
    order := 1;
    char_gens := [2591, 741, 1777, 2481];
    v := [1, 1, 1, 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;

function MakeCharacter_2960_a_Hecke(Kf)
    return MakeCharacter_2960_a();
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, -1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0], [0, 0, -1, 0, -1, 0], [2, -1, 0, 0, 1, 1], [1, 0, -1, -1, 0, -1], [1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 2, 0], [1, 1, -1, -1, 1, 0], [0, -1, 1, 1, 0, 2], [-1, 0, 0, 0, 0, 0], [2, -2, 1, -2, 1, 0], [1, -1, 3, 1, 1, 2], [-4, 1, 0, -1, -1, -2], [2, -2, 1, 0, 1, 0], [-1, 0, 0, -2, -1, -2], [1, -1, -1, -1, 1, 0], [1, 2, 0, 1, 2, 0], [-1, 1, 0, -1, 2, 0], [3, -3, 0, 1, 2, 0], [3, -2, 0, -2, 1, 0], [-2, 3, -2, 0, -2, -2], [4, 0, 0, 0, -4, -2], [5, 1, 1, 1, 1, -2], [3, 2, 0, 1, -3, -1], [0, -2, 2, -2, 2, 0], [-1, 2, 0, 0, 3, 2], [1, 1, -1, 1, -3, 2], [1, -2, 1, 1, 2, 1], [-6, 3, -2, 2, 0, 2], [1, 0, 2, -1, 2, 2], [10, 0, -2, 2, -2, 2], [7, 1, -3, -3, -1, -2], [3, 4, 0, -1, 1, -3], [-2, 2, 0, -2, -2, -2], [2, 4, -3, 2, -1, 0], [3, 3, -1, 1, -5, -2], [-6, -2, 2, 0, -4, 2], [-4, 0, 5, 2, -1, 2], [3, 0, 2, -1, 2, -4], [1, 0, -4, 1, -1, 3], [-2, 3, -1, -3, 2, 0], [-2, 0, 0, 4, -4, 0], [5, 5, 2, -1, 2, -2], [11, -2, -2, -1, 4, 2], [8, 0, 1, 0, 3, 2], [1, 4, -1, 3, 1, -2], [-1, -3, 1, 1, -1, 0], [3, 3, 0, -3, 0, 0], [-6, -4, -2, 0, -4, -2], [2, 3, 1, 0, -5, -2], [2, 0, -2, 2, -2, 2], [1, 0, 4, -1, 0, -2], [2, 3, 2, 0, -1, 1], [-3, -2, -1, -3, 1, -4], [-2, -3, -2, -2, 1, 1], [3, 1, 0, 1, 0, 0], [4, 3, 0, 4, 5, 3], [4, -2, 6, 0, 2, 2], [6, 4, -2, 2, 0, -4], [-7, 3, 1, -5, 3, 0], [10, -1, 6, -1, 3, 2], [4, -1, 3, 1, 4, 4], [-6, -6, -2, 0, -2, 2], [5, -5, 3, -3, -3, -2], [3, 4, 0, -7, 4, -2], [3, 1, 4, -5, 0, 0], [-2, 6, -6, -4, -2, -4], [-6, -3, 6, 2, 5, 1], [-5, 5, -7, 3, 1, 0], [-1, -1, 2, 1, 2, 0], [4, -3, 3, 2, -1, 6], [-1, -3, 6, -1, -2, 0], [9, 7, -2, -3, 2, -6], [-20, -6, 2, 0, -2, 2], [3, 3, 1, -1, -1, -6], [-5, -1, -2, -3, 0, 0], [-2, 0, 0, 0, 8, 4], [4, 4, -2, 4, -4, -4], [9, 1, -2, 3, -2, 0], [-8, -4, 0, 6, -2, 2], [-8, 7, 7, 1, 2, -2], [7, -9, -2, -1, 4, 6], [8, 3, -3, 4, -1, 4], [-6, 5, 2, 1, 5, 2], [-2, 6, -8, 4, 0, 0], [-5, 11, -3, 3, -7, -6], [7, -3, 1, 3, -1, -2], [-10, -4, 2, -2, 6, 6], [-9, 1, 3, -5, 3, -4], [-3, -2, 2, -3, -4, 2], [-16, 2, 4, 2, 0, 0], [0, -2, 4, 2, 8, 6], [21, -4, -2, -2, 1, 0], [-12, 2, -2, 0, 2, 2], [-5, 1, -4, -1, -2, 2], [0, -5, 3, -6, 2, -5], [2, -4, -2, -4, -4, -6], [-10, -10, 4, -2, 2, 0], [11, -1, -1, 1, -3, -4], [6, -3, -8, 2, -3, 3], [-1, -3, 1, 7, -9, 2], [6, -4, 0, 4, 2, 2], [0, -2, -3, 4, -3, 8], [-6, 7, -2, -4, 3, -3], [-1, 3, 3, 1, -3, -4], [-3, 5, -4, -3, 0, -4], [-13, 7, -6, 3, 0, 0], [-17, 0, 1, -5, -4, -5], [-6, 0, -4, -4, -2, 2], [2, 0, -5, -2, 3, -2], [3, 5, 0, 1, 0, 2], [10, -2, -1, 2, -3, -2], [-4, -3, 3, 4, 1, 4], [6, 9, 1, -6, 2, -1], [7, -9, 3, 5, 3, 6], [-12, -8, 6, 4, 4, 4], [-8, 2, 0, -2, 0, -4], [-7, -9, 2, -3, 0, 4], [7, -3, -3, 3, -3, 0], [-1, 13, 2, -5, 0, -2], [-1, 1, 6, 5, 8, 8], [-9, -1, 1, -1, 5, 8], [19, -1, 3, 7, 3, -2], [4, 0, 4, 0, 0, -2], [3, 1, -9, 3, 1, 2], [-17, 1, 4, -1, -4, -6], [0, 0, -2, -6, 6, -8], [-2, 0, 11, 4, 5, 2], [6, 2, 3, 0, -5, 2], [-15, -6, 1, -2, 0, 2], [9, -5, 4, 1, 0, 2], [14, -4, -4, 0, 0, 0], [4, 2, 3, 6, -3, 2], [0, 2, 6, 0, 8, 4], [-8, 8, -1, 0, -9, -10], [4, -5, 10, -5, 5, -6], [-14, 1, 2, -6, -1, -9], [6, 4, -4, 2, -6, 4], [11, 7, 2, -1, 2, -2], [23, -3, 0, 3, 2, 2], [-5, 6, -2, 2, -3, 8], [-7, -9, -3, -1, 3, 0], [21, -1, -9, -7, -5, -4], [8, -12, 4, 0, 0, -4], [10, 6, -6, -8, -6, -6], [17, -7, 9, 1, 1, 2], [17, -2, -4, 4, 1, 0], [-22, 1, 7, -4, -1, -6], [-3, -9, -5, 1, -7, -2], [9, 8, -9, -3, -8, -3], [3, 5, 1, -7, 7, -4], [-19, -4, -3, 4, -4, 4], [10, 8, -2, 0, -10, 0], [1, 6, 0, 2, -7, 6], [-7, -2, 4, 2, -7, -2], [-1, 7, 1, 1, -9, -6], [23, 7, 2, -3, -2, 2], [-10, -7, -6, 4, -9, -3], [-9, 9, 1, 1, -1, 4], [3, 13, -8, 5, -8, -2], [4, -6, -6, 6, 2, 4], [-3, 5, -5, 9, -7, 0], [-13, 7, 7, -5, -1, -6], [-3, 6, -3, 5, -9, 4], [14, 3, -3, 4, -5, 6], [4, -10, 6, -2, 2, 0], [14, 1, -1, -4, -2, -5], [-8, -4, -2, -6, 2, 6], [7, -2, 6, 0, -3, 8], [-11, -3, -5, 1, 11, 0], [18, -5, 5, -2, 3, -4], [5, -3, 12, 1, 4, 8], [-5, 5, 12, -3, 4, -4], [0, -2, 8, -12, 6, -4], [5, 2, -6, 0, 1, 2], [-2, 3, 6, 4, -7, -5], [-15, -10, 3, -2, 6, 6], [-28, 4, -4, 4, -6, 2], [26, 0, -4, -4, 10, -2], [3, 14, -2, 1, -2, -10], [22, 7, 2, -2, -7, 1], [-7, -3, -3, 1, 13, -2], [0, 13, -7, -9, 0, -6], [9, 1, -4, -5, -4, -8], [4, 4, -5, 4, 1, 0], [-15, -3, 3, 5, -1, 4], [30, 0, -2, -6, 6, -6], [21, -13, -6, -1, 0, 2], [12, -7, -2, -8, -3, -11], [-25, 4, 8, -3, 2, -6], [9, -2, 2, -8, 3, -4], [3, 1, 4, -1, -2, 2], [16, 1, -6, 5, -7, 8], [3, -5, 6, 7, 8, 14], [14, 2, -4, 4, 0, 0], [-16, -3, 0, -4, -1, 1], [-21, 15, 2, 5, 0, 4], [-2, 6, -4, 0, -6, -10], [-6, -2, -4, 10, 2, 0], [25, 1, -2, 1, -6, 6], [5, 7, -13, 7, -5, 2], [-4, -5, -1, 4, 4, 7], [3, -7, 7, -5, 1, -4], [-8, 3, 0, 2, -13, -5], [-18, -12, 10, 10, -4, 10], [23, -10, -2, 0, 11, 8], [4, 8, -4, -4, -8, -2], [12, -8, 1, 6, 5, 10], [9, -12, 9, -3, 4, 7], [15, -3, -1, -7, 9, -4], [-4, 4, -2, -4, -4, -8], [-1, 2, 10, 5, 8, -2], [6, -7, -5, 14, -11, 4], [-14, 1, 9, -10, 6, -13], [22, 4, 6, -2, 2, -10], [-4, -8, 10, -4, -10, -6], [28, 4, -14, 4, -14, 2], [-9, 5, -7, -7, 1, -10], [23, 2, 0, -5, -1, -5], [11, -3, -6, 3, -4, 0], [-14, 1, -3, 10, -10, 7], [-22, -4, -6, 2, -6, -2], [-2, -13, 10, -8, 6, -2], [28, 6, -4, 0, 6, -4], [0, -4, -6, -4, -2, -6], [-9, 9, -4, -3, -2, -6], [35, -10, -1, 2, 0, 2], [3, 0, 12, 5, 4, -2], [-2, -4, 13, 8, -7, 4], [1, -3, -10, -3, 0, -4], [-7, 5, -6, -7, 4, -4], [17, 7, -2, -7, 8, -6], [4, 3, 2, -9, -5, 0], [-1, 4, 7, -5, -11, -4], [-2, 6, -6, 2, 0, 2], [18, -9, 4, 8, -3, 1], [-15, -4, -2, 9, -6, 4], [29, -16, -8, 0, 5, 4], [-9, -9, 7, -9, 3, 0], [13, 2, -12, -8, -3, -8], [-6, -3, -10, 6, -4, 2], [15, -5, 1, -1, 1, 4], [-6, -16, 4, 8, 4, 4], [8, -5, 3, -3, -6, -6], [-6, -16, 12, -2, -2, 0], [-11, -8, 8, 6, 5, 2], [12, -10, -7, 2, -1, 4], [6, 4, -2, 4, -6, 0], [10, 7, -6, -6, -11, -11], [-14, -3, 6, 10, 1, 5], [-18, 11, 7, 2, -1, -8], [-8, 2, -2, 2, -4, 2], [-2, -4, -4, -4, 4, 8], [-28, 0, 5, 6, 9, 6], [7, -1, 18, 5, 2, 4], [11, -12, 2, 11, 0, 8], [-10, 6, 1, -8, -7, 0], [-3, -1, 1, 13, 1, 4], [30, 0, 8, 2, 4, -2], [4, -6, 10, -2, -8, -6], [10, -20, 4, -4, 12, 12], [1, 5, 7, -9, 13, 4], [-46, 7, -6, -2, -3, -3], [36, 2, -3, -6, -7, -2], [11, -2, 2, -7, 3, 3], [18, 2, -10, 4, -8, 2], [-20, 7, -10, 0, 2, -8], [-34, 7, -10, 2, -3, -3], [-10, -4, 4, -6, -12, -6], [7, -9, 5, -9, 11, 2], [24, -7, 2, 6, 3, 1], [0, 21, 5, -1, -6, -10], [24, 10, -8, 6, -10, 2], [-30, -3, -1, -5, 10, 0], [9, -6, 6, 3, 4, 10], [22, 0, 4, 0, 2, -6], [0, -4, -1, 0, 7, -8], [11, 10, -4, -4, -3, -6], [16, -9, -4, 1, -9, -8], [-2, -9, -11, -4, -13, -2], [10, 3, 7, -11, 6, -2], [-29, -3, 8, -5, -18, -6], [24, 6, -10, 12, -4, 8], [7, -5, 0, -9, 2, 0], [5, 8, -7, -3, 0, -1], [-5, -11, 15, -11, 5, -4], [-29, -4, 4, 0, -9, 0], [16, -20, 0, -6, 0, -4], [3, -1, 5, -1, -1, -10], [-18, 20, -2, -8, -8, -10], [25, 1, 4, 3, -12, -10], [-36, 12, -1, -10, -1, -10], [22, 6, -7, -2, -5, -8], [-25, -3, -18, -1, 0, 2], [1, 3, 8, 1, 4, 2], [18, 10, -16, -18, 4, -14], [-11, -4, 10, -2, -13, -6], [32, 11, 0, 2, -4, -10], [-9, -7, 3, 3, -9, 0], [-1, -15, 14, -11, 8, 4], [-31, 13, 6, 5, -8, -8], [20, -8, 10, 0, 4, 4], [-13, -2, -6, 8, -17, -6], [7, 14, -5, -7, -4, -9], [-1, 9, -3, 9, 1, -2], [12, 2, 0, 10, -6, -10], [1, 9, -12, -5, 2, -2], [18, -19, 4, 4, 7, 7], [4, -3, 0, 15, -7, 4], [-15, 4, -8, -5, -7, -13], [16, -9, 17, 4, 2, 7], [-28, 11, -8, -9, -7, -8], [-12, -2, 2, 2, 4, -2], [2, -8, -6, -6, 12, -8], [-6, 2, -7, 8, -7, -2], [9, 10, 2, 3, 0, 4], [27, -15, -4, 9, 0, 6], [-26, -12, 6, -4, -8, 6], [-13, 14, 0, 4, -1, 12], [-11, 1, 2, -11, 20, 6], [5, -7, 5, -1, 9, 18], [-38, -3, -1, 7, -2, 0], [9, -1, 12, -13, 6, -4], [6, 8, -4, 2, 20, 10], [7, 1, -9, 5, 11, 8], [-25, -1, -7, 3, 7, -2], [10, -14, 14, -6, 12, 12], [9, -3, -7, -3, 7, -6], [5, 21, -8, -1, 0, -4], [0, 4, 10, 2, 2, 2], [-4, -7, -5, -2, -3, 6], [4, -14, -2, 6, 4, -6], [1, 0, 4, 17, 12, 4], [5, 16, -14, -2, 1, -6], [19, 7, -14, 5, -10, 0], [-19, 5, 12, -5, 10, 0], [22, -2, -8, -10, 10, -12], [11, -6, -6, -14, -7, -4], [31, -7, 6, 1, -8, 0], [17, 11, -6, -5, -8, -8], [-18, 2, 4, -2, 12, -2], [-18, -11, 7, 2, 1, -4], [32, -6, -2, 6, 14, 4], [-13, 4, 4, -2, 5, 0], [-7, -17, 2, 5, 0, 14], [18, -3, -2, 9, -7, 14], [20, 15, -5, -3, 0, -4], [10, -12, 9, 4, 1, -4], [7, -3, 3, 13, -5, 8], [1, 9, 4, -1, 2, -8], [9, 3, -5, -7, -1, 0], [-16, -10, -6, 8, -4, 0], [4, -13, 12, -6, 5, 5], [4, -16, 14, 4, -6, 2], [-16, -7, 9, -5, -12, -4], [-9, -4, -4, 7, -16, 8], [3, 15, -2, -1, -6, -24], [-4, 8, -10, -20, -6, -10], [-22, 11, 4, -4, 1, -7], [1, 13, 4, 3, -8, 8], [-2, 0, -12, -6, 6, 4], [-13, -2, -2, -7, -10, -14], [-4, -7, 10, 9, -3, 4], [-11, -3, 3, 5, 7, 14], [-10, 9, 8, 0, -9, -5], [4, -14, -2, 20, -8, 8], [-20, 0, 16, 4, 6, 0], [-11, -4, 10, 17, -2, 12], [-33, -8, 10, 6, -11, 2], [-2, 3, -3, -4, -11, -22], [-36, -17, 16, 8, 7, 13], [18, 11, 3, -7, 8, -2], [8, 2, -11, -2, -15, -12], [-18, -6, 8, 0, 12, 6], [15, 3, -14, 3, 2, 2], [20, 10, -14, 8, -12, -4], [-20, -4, 12, 12, 6, 12], [-13, -7, 0, 11, -10, 18], [-21, -21, -9, 5, -15, 0], [14, -19, 18, -4, 1, 3], [-22, 6, 8, 4, 4, 12], [-18, -2, -8, -2, -8, 6], [13, 4, 6, 6, -19, -12], [-7, 10, 7, 7, 1, 14], [7, 5, -10, -11, -6, -4], [4, 8, -20, -6, -8, -14], [-21, 3, 1, -3, 11, 8], [-4, 12, -10, 20, -10, -2], [-30, 0, 7, 16, -19, 10], [-40, 8, 4, 14, -8, 10], [-23, -4, 4, -5, -8, -10], [1, 19, -7, -1, -1, -12], [19, 7, -20, -13, -8, -14], [48, 10, 4, 0, 0, -10], [9, 6, -4, 6, 11, 8], [22, -2, -5, -6, -5, -16], [10, -12, 17, 4, 5, -2], [8, 12, -20, 8, -2, -2], [7, -4, 6, 5, -15, 9], [-33, 21, -5, -1, -5, 0], [-14, 0, -4, -10, 12, -2], [6, -4, -4, -8, 0, -12], [-34, -8, 20, 8, 12, 12], [7, -1, -14, -9, -2, -10], [-16, -14, 14, 10, 2, 8], [55, -1, -3, -11, -1, -2], [-5, -10, -2, 8, 7, 0], [-32, 16, -17, -14, 1, -4], [-1, -11, 0, 7, 8, -8], [-2, 2, -9, -8, -5, -8], [-1, 3, -13, -7, -9, 2], [-9, 2, 8, -7, -8, 2], [-17, -9, -13, -5, -13, -14], [18, -3, -2, 4, 15, 5], [-8, 6, 0, 20, -2, 2], [-13, -8, -9, 7, 1, 8], [-26, 10, -12, 6, 0, 6], [-30, 12, 12, 6, -12, -6], [-4, -2, 0, 0, -2, -4], [-10, -4, 4, 12, -20, 8], [-11, 12, -10, 8, -13, -6], [6, 2, 11, 8, -3, 0], [-12, 2, 0, 6, -6, -10], [6, -18, 13, 14, 9, 18], [5, 4, -12, 3, -6, -2], [38, 16, -15, 0, 7, -6], [-14, -22, -4, 8, 0, 2], [60, 11, 1, -2, -1, -10]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2960_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2960_2_a_bc();".
// 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_2960_2_a_bc(:prec:=6)
    chi := MakeCharacter_2960_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 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_2960_2_a_bc();".
// 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_2960_2_a_bc( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2960_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-44, 18, 60, -12, -16, 1, 1]>,<7,R![302, 138, -144, -76, 7, 8, 1]>,<13,R![384, -648, -260, 180, 4, -10, 1]>],Snew);
    return Vf;
end function;