
// Make newform 1960.2.q.y in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1960_q();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1960_q_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_1960_2_q_y();".
// 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_1960_2_q_y();".
// 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 := [196, 112, 162, 0, 51, -2, 11, -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], [169702, 19740, 20492, 28611, 4794, 2209, 154, 329], [204092, 351628, -200277, 122298, -21575, 32538, -8415, 3056], [8108, 1260, 1308, -353, 306, 141, -68, 21], [2058, -2878, 1071, -654, 712, -174, 45, 13], [543998, -238267, 283101, -172874, 84562, -45994, 11895, -3270], [-138894, -63840, -66272, -25401, -15504, -7144, 397, -1064]];
    Rf_basisdens := [1, 1, 84134, 588938, 3658, 1829, 294469, 42067];
    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_1960_q();"
function MakeCharacter_1960_q()
    N := 1960;
    order := 3;
    char_gens := [1471, 981, 1177, 1081];
    v := [3, 3, 3, 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_1960_q_Hecke();"
function MakeCharacter_1960_q_Hecke(Kf)
    N := 1960;
    order := 3;
    char_gens := [1471, 981, 1177, 1081];
    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], [0, 0, 0, -1, 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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, 0], [-3, 0, 1, 0, 1, 0, 0, -1], [2, -1, 0, -2, 0, 2, 0, 0], [0, 0, 0, 0, 1, 1, -1, 1], [-2, 2, 2, 2, 2, -1, -2, -1], [-1, 0, 1, 0, 3, 0, 0, 0], [-2, -2, 0, 2, 0, 1, 2, 0], [0, 0, 0, 0, 2, 1, -2, 1], [-2, 0, -2, 0, -1, 0, 0, -2], [-2, 0, 0, 0, 2, 0, 0, -2], [-1, 1, 1, 0, 1, 1, -1, 1], [0, 2, 0, 0, 0, 1, 2, 0], [2, 0, 0, -2, 0, 0, -5, 0], [-2, 2, 2, 6, -2, -2, 2, -2], [2, 0, 0, -2, 0, -1, -6, 0], [2, 0, -2, 0, 0, 0, 0, 4], [2, 4, 0, -2, 0, 1, 5, 0], [1, -1, -1, -6, 5, 0, -5, 0], [-10, 0, 2, 0, -1, 0, 0, 1], [0, 0, 0, 10, 3, -1, -3, -1], [-7, 0, 1, 0, -2, 0, 0, -2], [6, -4, 0, -6, 0, -2, 0, 0], [1, -1, -1, -4, -5, -1, 5, -1], [2, -2, -2, 4, 6, -2, -6, -2], [-4, 5, 0, 4, 0, 0, 1, 0], [0, 0, 2, 0, 4, 0, 0, -5], [-2, 0, 4, 0, 0, 0, 0, -1], [2, -2, -2, 2, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 8, 0], [-4, 0, -2, 0, -5, 0, 0, 0], [6, -6, -6, -10, -2, 2, 2, 2], [-6, 5, 0, 6, 0, -2, -5, 0], [6, 0, 0, -6, 0, -4, -2, 0], [4, -4, -4, 8, 8, -1, -8, -1], [9, 0, -5, 0, 3, 0, 0, -1], [-1, 1, 1, 10, 1, -3, -1, -3], [-12, 6, 0, 12, 0, -2, -2, 0], [4, 0, -8, 0, 0, 0, 0, 3], [5, -5, -5, 6, -7, 6, 7, 6], [0, -4, 0, 0, 0, 4, 0, 0], [2, 0, -2, 0, 2, 0, 0, 3], [-10, -2, 0, 10, 0, 1, -6, 0], [1, 0, 5, 0, 1, 0, 0, 4], [13, 0, 3, 0, -3, 0, 0, -3], [0, -5, 0, 0, 0, 4, 8, 0], [4, -4, -4, 0, 4, -1, -4, -1], [-8, 8, 8, 8, -4, -2, 4, -2], [-1, 0, 7, 0, -5, 0, 0, -2], [4, -4, 0, -4, 0, 4, 3, 0], [-8, 0, 6, 0, 7, 0, 0, -6], [2, -2, -2, 10, -3, 1, 3, 1], [16, 2, 0, -16, 0, 0, 6, 0], [0, 6, 0, 0, 0, -3, -14, 0], [4, -4, -4, -20, 4, 4, -4, 4], [12, 0, 0, -12, 0, 1, -4, 0], [-7, 0, -3, 0, 5, 0, 0, -2], [-8, 1, 0, 8, 0, 4, 4, 0], [3, 0, -1, 0, 13, 0, 0, 1], [7, 0, -7, 0, 2, 0, 0, -2], [8, 2, 0, -8, 0, 4, 6, 0], [3, -3, -3, -6, -6, 2, 6, 2], [0, 0, 0, 2, -10, 2, 10, 2], [-4, 4, 4, 2, 6, 4, -6, 4], [0, 0, 0, 0, -14, 0, 0, -1], [0, 4, 0, 0, 0, -3, 4, 0], [2, 0, 8, 0, -10, 0, 0, -2], [10, 3, 0, -10, 0, 4, 12, 0], [0, 0, 0, -8, -20, 0, 20, 0], [-8, 1, 0, 8, 0, 5, -7, 0], [-2, 2, 2, 10, -8, 4, 8, 4], [2, 0, -4, 0, 6, 0, 0, 2], [4, -4, -4, 8, -18, 4, 18, 4], [-8, -5, 0, 8, 0, 6, 11, 0], [1, -1, -1, -10, -5, -1, 5, -1], [-3, 3, 3, 4, -9, -4, 9, -4], [-2, -6, 0, 2, 0, 3, -11, 0], [-2, 0, 0, 0, -5, 0, 0, 2], [-5, 0, 1, 0, -15, 0, 0, -2], [2, -1, 0, -2, 0, 6, 13, 0], [0, 0, 2, 0, 13, 0, 0, -5], [-4, 4, 4, -18, 6, -3, -6, -3], [2, -2, -2, 12, -2, 2, 2, 2], [3, 0, -3, 0, 1, 0, 0, 8], [0, 0, 0, 14, -6, -3, 6, -3], [12, 0, -2, 0, -12, 0, 0, -2], [-12, 0, 0, 0, -8, 0, 0, 6], [-5, 5, 5, 12, 6, 4, -6, 4], [2, 0, 0, -2, 0, -1, 0, 0], [-6, -6, 0, 6, 0, 1, 10, 0], [15, 0, -5, 0, 3, 0, 0, -4], [15, -15, -15, -18, 1, 4, -1, 4], [7, 0, -3, 0, -5, 0, 0, 1], [6, -6, -6, 0, 10, -1, -10, -1], [-6, 10, 0, 6, 0, -3, -3, 0], [-2, 2, 2, -4, -1, -1, 1, -1], [7, -7, -7, -4, 5, 2, -5, 2], [-8, 0, 10, 0, 12, 0, 0, -8], [-6, -2, 0, 6, 0, 0, 12, 0], [20, -8, 0, -20, 0, 1, -1, 0], [2, -2, -2, -14, 2, 6, -2, 6], [-26, 8, 0, 26, 0, 0, 2, 0], [-2, 7, 0, 2, 0, -6, -6, 0], [-10, 0, -2, 0, 15, 0, 0, 3], [-5, 5, 5, -2, 12, -6, -12, -6], [-2, -3, 0, 2, 0, 4, 17, 0], [-12, 0, 10, 0, 5, 0, 0, -5], [-1, 1, 1, -12, 7, 5, -7, 5], [-6, 4, 0, 6, 0, -4, -16, 0], [-12, 0, 8, 0, 10, 0, 0, -5], [-6, 2, 0, 6, 0, -8, -17, 0], [11, 0, -1, 0, 5, 0, 0, -4], [14, 2, 0, -14, 0, 8, 6, 0], [-7, 0, -5, 0, -6, 0, 0, 12], [24, 4, 0, -24, 0, -4, -10, 0], [4, -4, -4, 6, 0, 8, 0, 8], [11, 0, 5, 0, 7, 0, 0, -2], [6, 6, 0, -6, 0, -2, 2, 0], [-4, 0, 0, 0, -12, 0, 0, 2], [-3, 3, 3, 14, -5, -1, 5, -1], [16, -12, 0, -16, 0, -2, 4, 0], [2, -2, -2, 24, 5, 5, -5, 5], [-5, 0, -3, 0, 11, 0, 0, -2], [-3, 3, 3, 0, 1, -4, -1, -4], [0, 0, 0, 14, -8, 5, 8, 5], [6, 0, -2, 0, -12, 0, 0, 2], [-5, 5, 5, -10, 3, -1, -3, -1], [-8, -5, 0, 8, 0, 10, 7, 0], [2, 0, -8, 0, 0, 0, 0, 7], [5, -5, -5, -2, 3, -2, -3, -2], [-16, 0, -10, 0, -10, 0, 0, -2], [8, -8, -8, 8, -7, -2, 7, -2], [-12, 0, -6, 0, -11, 0, 0, -3], [6, -19, 0, -6, 0, 5, 9, 0], [0, 1, 0, 0, 0, 0, 16, 0], [11, 0, -13, 0, -9, 0, 0, 3], [-2, 1, 0, 2, 0, -6, 11, 0], [-4, 0, -2, 0, 19, 0, 0, 4], [-19, 19, 19, 24, -1, -4, 1, -4], [30, -8, 0, -30, 0, -1, 2, 0], [4, 0, -2, 0, 8, 0, 0, -1], [-20, 20, 0, 20, 0, 1, -6, 0], [-6, 0, 4, 0, 0, 0, 0, -1], [-14, 0, -8, 0, 10, 0, 0, 2], [-10, 2, 0, 10, 0, 3, 1, 0], [2, -2, -2, 16, 9, -3, -9, -3], [0, 0, 0, 2, -14, 5, 14, 5], [-12, 12, 12, 2, 16, -8, -16, -8], [-22, 0, 8, 0, -17, 0, 0, 3], [0, 0, 0, 0, 24, 0, 0, 2], [-2, 2, 2, 32, 8, -2, -8, -2], [22, -14, 0, -22, 0, -1, 0, 0], [-24, 0, 16, 0, 12, 0, 0, -4], [-9, 9, 9, 18, 11, 8, -11, 8], [14, -14, -14, 4, -1, 2, 1, 2], [19, 0, -13, 0, -20, 0, 0, 4], [2, -6, 0, -2, 0, 4, -10, 0], [2, -2, -2, 24, 10, -1, -10, -1], [22, 0, -6, 0, 12, 0, 0, -7], [6, 0, -14, 0, 0, 0, 0, 0], [-4, 4, 4, 34, 7, 0, -7, 0], [-8, -10, 0, 8, 0, -2, -2, 0], [24, 1, 0, -24, 0, 1, 3, 0], [-16, -6, 0, 16, 0, 10, 0, 0], [30, -7, 0, -30, 0, 7, -11, 0], [1, 0, 1, 0, -19, 0, 0, 10], [2, -2, -2, 14, -8, 8, 8, 8], [-8, 2, 0, 8, 0, 8, -2, 0], [-26, 0, 4, 0, 6, 0, 0, 4], [-5, 5, 5, -6, -5, -6, 5, -6], [-18, 6, 0, 18, 0, 3, -16, 0], [8, -2, 0, -8, 0, 6, 8, 0], [-10, 0, 0, 0, 11, 0, 0, 1], [19, 0, -5, 0, 15, 0, 0, -2], [16, -11, 0, -16, 0, -4, -3, 0], [14, 0, 2, 0, -14, 0, 0, -4], [6, -6, -6, 2, -10, 10, 10, 10], [16, -16, -16, -24, 6, 2, -6, 2], [-34, 0, -6, 0, 7, 0, 0, 3], [22, 0, -8, 0, -20, 0, 0, 6], [-14, 14, 14, 10, -9, -7, 9, -7], [4, -8, 0, -4, 0, -2, 14, 0], [4, 14, 0, -4, 0, -1, 14, 0], [16, -18, 0, -16, 0, -3, -2, 0], [-4, 13, 0, 4, 0, -6, -24, 0], [11, -11, -11, 14, -3, 0, 3, 0], [12, -8, 0, -12, 0, 0, 2, 0], [-2, 2, 2, 22, 9, -5, -9, -5], [14, 0, -18, 0, 2, 0, 0, 6], [1, -1, -1, -6, 11, -12, -11, -12], [-4, 4, 4, 12, -8, 1, 8, 1], [-8, 0, 0, 8, 0, 2, 4, 0], [-10, 13, 0, 10, 0, -12, 2, 0], [-20, 3, 0, 20, 0, 4, -19, 0], [-14, 14, 14, -12, 4, 1, -4, 1], [-7, 0, -11, 0, 4, 0, 0, 6], [5, -5, -5, -8, 9, -5, -9, -5], [10, -2, 0, -10, 0, -6, 2, 0], [34, 0, -10, 0, 24, 0, 0, -4], [0, 0, 0, -10, -12, 8, 12, 8], [30, -2, 0, -30, 0, -11, -1, 0], [8, 0, -4, 0, -11, 0, 0, 11], [-14, 1, 0, 14, 0, -5, 5, 0], [12, -12, -12, 2, -16, 3, 16, 3], [18, -18, -18, -30, 0, 0, 0, 0], [-4, 0, -4, 0, 16, 0, 0, 8], [20, -18, 0, -20, 0, -1, 7, 0], [14, -14, -14, -8, 4, -5, -4, -5], [10, 0, -6, 0, -16, 0, 0, 15], [-18, 0, 4, 0, 0, 0, 0, -1], [7, -7, -7, -16, 18, -6, -18, -6], [12, -6, 0, -12, 0, 0, 30, 0], [12, -12, -12, -22, 11, 1, -11, 1], [2, 18, 0, -2, 0, -9, -12, 0], [-12, 2, 0, 12, 0, -6, -5, 0], [-6, 6, 6, -16, -22, 2, 22, 2], [-24, 0, -4, 0, 22, 0, 0, 3], [4, -4, -4, -6, -22, 14, 22, 14], [2, 0, 10, 0, 18, 0, 0, 0], [1, -1, -1, 32, -13, 0, 13, 0], [10, -10, -10, 4, 8, -2, -8, -2], [17, 0, -9, 0, 18, 0, 0, 2], [-2, 0, 0, 0, -22, 0, 0, -2], [-1, 1, 1, -22, 0, 0, 0, 0], [-2, -1, 0, 2, 0, 8, 13, 0], [-7, 7, 7, -20, -3, -5, 3, -5], [-4, 4, 4, 2, -2, -2, 2, -2], [-2, -10, 0, 2, 0, 10, -6, 0], [-32, -8, 0, 32, 0, -1, -11, 0], [46, 0, -2, 0, -16, 0, 0, 0], [16, 13, 0, -16, 0, 6, 27, 0], [-23, 0, 11, 0, -22, 0, 0, 8], [28, 1, 0, -28, 0, -7, -19, 0], [-6, 6, 6, 12, -21, -6, 21, -6], [6, -6, -6, -14, -12, 4, 12, 4], [-5, 0, 3, 0, -1, 0, 0, 6], [2, 0, -8, 0, -14, 0, 0, -3], [2, 2, 0, -2, 0, 6, -8, 0], [-18, 18, 18, -12, 9, -9, -9, -9], [-8, 13, 0, 8, 0, -7, -11, 0], [-18, 18, 18, 2, -2, -6, 2, -6], [-15, 0, 13, 0, 2, 0, 0, -6], [2, -2, -2, 0, -28, 2, 28, 2], [28, 0, 0, 0, -20, 0, 0, 8], [4, 8, 0, -4, 0, -7, -23, 0], [12, -19, 0, -12, 0, -2, 9, 0], [18, 0, 14, 0, -14, 0, 0, -14], [-22, 0, 4, 0, -14, 0, 0, 6], [6, -6, -6, 22, -7, 7, 7, 7], [-30, -12, 0, 30, 0, 3, -6, 0], [-10, 0, -8, 0, 1, 0, 0, 1], [-22, 8, 0, 22, 0, -6, -12, 0], [9, -9, -9, -14, -9, 16, 9, 16], [-38, 10, 0, 38, 0, -12, 12, 0], [4, -8, 0, -4, 0, 13, 11, 0], [-17, 0, -9, 0, 5, 0, 0, -1], [-13, 13, 13, 22, 14, -4, -14, -4], [16, -14, 0, -16, 0, 4, -20, 0], [-28, 0, -16, 0, -8, 0, 0, 3], [52, 4, 0, -52, 0, 1, 6, 0], [35, 0, 7, 0, 5, 0, 0, -5], [26, -18, 0, -26, 0, 5, 13, 0], [2, -2, -2, -38, -5, 12, 5, 12], [-29, 0, 17, 0, 25, 0, 0, -4], [28, 0, 10, 0, -1, 0, 0, -1], [-18, 0, 8, 0, -2, 0, 0, -9], [-18, -20, 0, 18, 0, 4, 4, 0], [-12, 12, 12, 28, 0, 5, 0, 5], [40, 10, 0, -40, 0, 5, 18, 0], [-18, 9, 0, 18, 0, 12, -6, 0], [-18, 18, 18, 44, 2, 0, -2, 0], [0, 0, -18, 0, -15, 0, 0, 3], [7, -7, -7, -44, -5, 7, 5, 7], [-14, 14, 14, 26, -12, -4, 12, -4], [34, 6, 0, -34, 0, 8, 14, 0], [-11, 11, 11, -6, -9, 6, 9, 6], [24, -24, -24, -36, 7, 13, -7, 13], [-4, 13, 0, 4, 0, 5, -3, 0], [-30, -19, 0, 30, 0, -6, -19, 0], [-8, 0, 12, 0, 2, 0, 0, -14], [18, 0, -2, 0, 24, 0, 0, 1], [17, -17, -17, -4, -16, 14, 16, 14], [-1, 1, 1, -34, 9, 2, -9, 2], [-2, 16, 0, 2, 0, 6, 0, 0], [14, 0, 0, 0, -2, 0, 0, 2], [-6, 6, 0, 6, 0, -5, 34, 0], [22, 0, -6, 0, 19, 0, 0, -18], [20, -9, 0, -20, 0, 4, 25, 0], [4, -27, 0, -4, 0, 12, 14, 0], [-6, 6, 6, -44, 0, -1, 0, -1], [34, 0, -4, 0, -13, 0, 0, 10], [22, 0, -12, 0, 6, 0, 0, 6], [-28, 8, 0, 28, 0, 9, 8, 0], [-12, 12, 12, 6, 2, -11, -2, -11], [-13, 0, 3, 0, 3, 0, 0, -1], [22, -22, -22, -32, -11, -7, 11, -7], [37, 0, -9, 0, -24, 0, 0, 10], [-3, 3, 3, 10, -2, 4, 2, 4], [0, 0, 0, -32, 2, 3, -2, 3], [50, 7, 0, -50, 0, -4, -17, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1960_q_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1960_2_q_y();".
// 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_1960_2_q_y(:prec:=8)
    chi := MakeCharacter_1960_q();
    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_1960_2_q_y();".
// 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_1960_2_q_y( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1960_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![196, 112, 162, 0, 51, -2, 11, -2, 1]>,<11,R![16, 80, 356, 236, 165, 18, 15, 2, 1]>,<13,R![-124, -52, 19, 10, 1]>],Snew);
    return Vf;
end function;