
// Make newform 950.2.f.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_950_f();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_950_f_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_950_2_f_c();".
// 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_950_2_f_c();".
// 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 := [1, 0, 96, 0, 892, 0, 1960, 0, 1858, 0, 880, 0, 212, 0, 24, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -402, 0, -2743, 0, -4598, 0, -3369, 0, -1278, 0, -259, 0, -26, 0, -1], [215, 0, 255, 0, 6904, 0, 12887, 0, 8721, 0, 2603, 0, 334, 0, 15, 0], [-133, 0, 139, 0, 6904, 0, 12887, 0, 8721, 0, 2603, 0, 334, 0, 15, 0], [-1609, 0, 12564, 0, 84784, 0, 124547, 0, 75129, 0, 20922, 0, 2578, 0, 113, 0], [0, -3467, 0, -3820, 0, -12347, 0, -20160, 0, -12875, 0, -3664, 0, -455, 0, -20], [0, -2748, 0, -23711, 0, -45640, 0, -37029, 0, -15104, 0, -3211, 0, -332, 0, -13], [0, -4241, 0, -25792, 0, -45101, 0, -36892, 0, -15897, 0, -3604, 0, -393, 0, -16], [214, 2003, 2126, 22068, -1250, 46207, -6556, 40307, -4918, 17563, -1454, 3938, -182, 423, -8, 17], [1041, -8855, 19504, -110340, 47429, -231035, 43722, -201535, 19229, -87815, 4272, -19690, 453, -2115, 18, -85], [-1041, -8855, -19504, -110340, -47429, -231035, -43722, -201535, -19229, -87815, -4272, -19690, -453, -2115, -18, -85], [-214, 2003, -2126, 22068, 1250, 46207, 6556, 40307, 4918, 17563, 1454, 3938, 182, 423, 8, 17], [-407, 3293, -9439, 44275, -30397, 99318, -35219, 93501, -18511, 43847, -4695, 10479, -545, 1180, -23, 49], [-407, -3293, -9439, -44275, -30397, -99318, -35219, -93501, -18511, -43847, -4695, -10479, -545, -1180, -23, -49], [3095, 26987, 54930, 365058, 81885, 894358, 41830, 901744, 7555, 445013, -150, 110294, -155, 12716, -10, 536], [1935, -26987, 54930, -365058, 81885, -894358, 41830, -901744, 7555, -445013, -150, -110294, -155, -12716, -10, -536]];
    Rf_basisdens := [1, 40, 116, 116, 580, 232, 232, 232, 232, 1160, 1160, 232, 232, 232, 1160, 1160];
    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_950_f();"
function MakeCharacter_950_f()
    N := 950;
    order := 4;
    char_gens := [77, 401];
    v := [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_950_f_Hecke();"
function MakeCharacter_950_f_Hecke(Kf)
    N := 950;
    order := 4;
    char_gens := [77, 401];
    char_values := [[0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 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, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, -1, -1, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0], [2, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, -1, 1, 1, 1, 0, 0], [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 1], [0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, -1, 0, 0, 1, 1, 0, -2, 2, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0], [-2, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1], [-2, 2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 1, 1, -1, 0, 0, 1, 4, 0, 0, 2, 0, 0], [0, 0, 0, -2, 1, 0, 0, 0, 0, -1, 1, 0, 3, 3, 0, 0], [-4, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 1], [0, 0, 0, 0, -2, 2, 0, 0, 0, -2, 2, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 3, 1, 0, 0, 2, 2, 0, 1, -1, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2], [0, 0, 0, 4, -6, 0, 0, 0, 0, -5, 5, 0, -3, -3, 0, 0], [1, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 8, -8, 0, 1, 1, 0, 0], [0, 0, 0, 1, 1, -1, -1, 0, 0, 3, -1, 0, 2, 0, 0, 0], [3, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, -2], [0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 3, 0, 0, 3, 0, 0], [0, 0, 0, 2, -4, 4, -2, 0, 0, -6, 4, 0, -5, 0, 0, 0], [0, 0, 0, 5, 2, 0, 0, 0, 0, 4, -4, 0, -1, -1, 0, 0], [0, 0, 0, 1, 3, 3, 1, 0, 0, 3, -2, 0, 0, 5, 0, 0], [0, 0, 0, 4, 0, 0, -4, 0, 0, 2, 0, 0, -2, 0, 0, 0], [-6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0], [-2, 2, -4, 0, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, 0, 0], [-1, 6, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, -1], [-1, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 1, -1], [0, 0, 0, 0, 0, -2, -2, 0, 0, -7, -7, 0, 1, -1, 0, 0], [-2, 2, 6, 0, 0, 0, 0, -6, -2, 0, 0, 0, 0, 0, 2, 0], [5, 6, -2, 0, 0, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0, -1], [0, 0, 0, -2, -1, 1, 2, 0, 0, -2, 1, 0, -3, 0, 0, 0], [0, 0, 0, 3, -2, -2, 3, 0, 0, -2, 2, 0, 0, -2, 0, 0], [0, 0, 0, 6, -4, 0, 0, 0, 0, -4, 4, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 2, -2, 0, 0], [-6, 0, -5, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -2, 2, 2, -2, 0, 0, 2, -10, 0, 0, 6, 0, 0], [-5, 5, 6, 0, 0, 0, 0, -6, -3, 0, 0, 0, 0, 0, 5, 0], [0, 12, 0, 0, 0, 0, 0, 1, 3, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 12, 12, 0, -1, 1, 0, 0], [0, 0, 0, -1, 1, 1, -1, 0, 0, 1, 13, 0, 0, -2, 0, 0], [0, 0, 0, 0, 1, -1, 0, 0, 0, 7, -1, 0, 1, 0, 0, 0], [-4, -2, 0, 0, 0, 0, 0, -2, 4, 0, 0, 4, 0, 0, 4, -4], [-3, 1, -8, 0, 0, 0, 0, -8, 0, 0, 0, -6, 0, 0, 0, -4], [-1, 8, 0, 0, 0, 0, 0, -3, -1, 0, 0, -1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, -1, 1, 0, 0], [11, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 2, 2], [0, 0, 0, 6, 0, 0, -6, 0, 0, 9, 0, 0, -3, 0, 0, 0], [-12, -10, 3, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, -2], [0, 0, 0, 2, 2, 0, 0, 0, 0, -8, 8, 0, -2, -2, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0], [-2, 2, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, -3, 7, 0, 0, 2, 2, 0, 4, -4, 0, 0], [3, -3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 10, 0, 0, 0, 6], [0, 0, 0, -1, 5, 5, -1, 0, 0, 5, -6, 0, 0, 6, 0, 0], [0, 0, 0, 2, 4, -4, -2, 0, 0, -4, -4, 0, 0, 0, 0, 0], [7, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 3, 3], [1, -5, 4, 0, 0, 0, 0, 4, 0, 0, 0, -3, 0, 0, 0, 6], [0, 0, 0, -5, -1, 1, 5, 0, 0, 4, 1, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 1, -4, 0, 0, -2, -2, 0, -6, 6, 0, 0], [0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 0, 0, -5, 0, 0, 0], [6, -6, -2, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, -4, 0], [4, -12, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, -4, 4], [13, 9, -2, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 4], [3, -12, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, -3, 3], [16, -16, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, -2, -5, -5, -2, 0, 0, -5, -6, 0, 0, 0, 0, 0], [0, 0, 0, -2, -3, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, -3, 0, 0, 0, -3, 0, 0, 0, -9, 0, 0], [2, 3, 0, 0, 0, 0, 0, 3, -2, 0, 0, -2, 0, 0, -2, 2], [3, -3, 3, 0, 0, 0, 0, -3, -8, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, -1, 5, 0, 0, 7, 7, 0, -7, 7, 0, 0], [0, 0, 0, 1, -3, 0, 0, 0, 0, 1, -1, 0, -6, -6, 0, 0], [6, -11, 0, 0, 0, 0, 0, 7, 3, 0, 0, 3, 0, 0, -6, 6], [0, 0, 0, 0, 0, -6, -7, 0, 0, -11, -11, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 5, -5, 0, 0, 2, 2, 0, -3, 3, 0, 0], [0, 0, 0, 4, -2, -2, 4, 0, 0, -2, 9, 0, 0, -3, 0, 0], [0, 0, 0, -1, -3, 0, 0, 0, 0, 11, -11, 0, 3, 3, 0, 0], [0, 1, 5, 0, 0, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, -1], [0, 0, 0, 2, -8, 0, 0, 0, 0, -9, 9, 0, -3, -3, 0, 0], [-7, 7, -4, 0, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, -4, 0], [21, 0, 7, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0], [-6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -8], [-6, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0], [4, 0, 0, 0, 0, 0, 0, 14, 6, 0, 0, 6, 0, 0, -4, 4], [0, 0, 0, -2, 2, -2, 2, 0, 0, -2, -2, 0, 6, 0, 0, 0], [-8, 0, -9, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -7, -7], [-4, -7, 0, 0, 0, 0, 0, -5, -3, 0, 0, -3, 0, 0, 4, -4], [-1, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 10, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, -9, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, -4, 8, 0, 0, -17, -17, 0, 3, -3, 0, 0], [0, 0, 0, -2, -1, -1, -2, 0, 0, -1, -7, 0, 0, 5, 0, 0], [15, 0, 5, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, 0, 6, 6], [0, 0, 0, -4, -3, 3, 4, 0, 0, 1, 3, 0, -4, 0, 0, 0], [1, -1, 1, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, -6, 0, 0, -6, 0, 0, 0, -6, 0, 0, -4, 0, 0], [0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0], [9, 0, 9, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0], [-15, 15, 2, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 2, 0], [4, -4, -6, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, -5, 0], [8, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0, 2], [0, 0, 0, 9, 1, 0, 0, 0, 0, -8, 8, 0, -6, -6, 0, 0], [0, 0, 0, 0, 0, 1, -7, 0, 0, -17, -17, 0, 3, -3, 0, 0], [0, 0, 0, 5, 5, -5, -5, 0, 0, -9, -5, 0, 4, 0, 0, 0], [-17, -20, 1, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 3], [-11, 11, -2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 6, 0], [2, 1, 0, 0, 0, 0, 0, -7, 1, 0, 0, 1, 0, 0, -2, 2], [-9, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -9, -9], [0, 0, 0, 0, 0, -1, -5, 0, 0, 11, 11, 0, -3, 3, 0, 0], [-4, -10, -4, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 6], [-14, 14, 7, 0, 0, 0, 0, -7, -4, 0, 0, 0, 0, 0, 5, 0], [-2, -14, 8, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 12], [0, 0, 0, -4, -5, 0, 0, 0, 0, 3, -3, 0, -4, -4, 0, 0], [0, 0, 0, 0, 0, -2, -1, 0, 0, 10, 10, 0, 5, -5, 0, 0], [0, 0, 0, 8, 0, 0, 8, 0, 0, 0, -4, 0, 0, -4, 0, 0], [0, 0, 0, 0, 3, -3, 0, 0, 0, -6, -3, 0, -6, 0, 0, 0], [0, 0, 0, 6, -8, -8, 6, 0, 0, -8, 8, 0, 0, -14, 0, 0], [-17, 0, 6, 0, 0, 0, 0, 0, -7, 0, 0, 7, 0, 0, 1, 1], [1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 1, 1], [1, -2, 0, 0, 0, 0, 0, -4, -3, 0, 0, -3, 0, 0, -1, 1], [-4, -4, 0, 0, 0, 0, 0, -1, 5, 0, 0, 5, 0, 0, 4, -4], [8, -8, 1, 0, 0, 0, 0, -1, 8, 0, 0, 0, 0, 0, 7, 0], [1, 9, -5, 0, 0, 0, 0, -5, 0, 0, 0, 2, 0, 0, 0, -8], [-2, 13, 0, 0, 0, 0, 0, -11, -1, 0, 0, -1, 0, 0, 2, -2], [0, 0, 0, -2, -3, -3, -2, 0, 0, -3, 16, 0, 0, -5, 0, 0], [0, 0, 0, 0, 0, 11, -3, 0, 0, -6, -6, 0, -3, 3, 0, 0], [1, -1, 5, 0, 0, 0, 0, -5, -8, 0, 0, 0, 0, 0, 8, 0], [-19, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2], [-2, -9, 0, 0, 0, 0, 0, -18, -8, 0, 0, -8, 0, 0, 2, -2], [0, 0, 0, 10, 1, 1, 10, 0, 0, 1, 6, 0, 0, -6, 0, 0], [0, 0, 0, -2, 0, 0, 2, 0, 0, -34, 0, 0, 1, 0, 0, 0], [0, 0, 0, 7, -1, 1, -7, 0, 0, -8, 1, 0, 0, 0, 0, 0], [-6, 11, 0, 0, 0, 0, 0, -4, -1, 0, 0, -1, 0, 0, 6, -6], [0, 0, 0, 0, 0, -5, 10, 0, 0, -4, -4, 0, 1, -1, 0, 0], [-9, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 5, 0, 0, -1, -1], [-9, -16, 2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 7], [0, 0, 0, 2, 4, -4, -2, 0, 0, -4, -4, 0, -11, 0, 0, 0], [0, 0, 0, 9, -10, 0, 0, 0, 0, -1, 1, 0, -9, -9, 0, 0], [0, 0, 0, -4, 0, 0, 0, 0, 0, 5, -5, 0, 3, 3, 0, 0], [9, 5, -1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 4], [0, 0, 0, -5, 3, -3, 5, 0, 0, -7, -3, 0, -2, 0, 0, 0], [-1, 11, 0, 0, 0, 0, 0, 1, -8, 0, 0, -8, 0, 0, 1, -1], [0, 0, 0, -7, -2, -2, -7, 0, 0, -2, -17, 0, 0, -1, 0, 0], [0, 0, 0, 9, -5, 5, -9, 0, 0, -2, 5, 0, -16, 0, 0, 0], [-6, 0, -12, 0, 0, 0, 0, 0, 13, 0, 0, -13, 0, 0, -6, -6], [-6, -2, -10, 0, 0, 0, 0, -10, 0, 0, 0, -16, 0, 0, 0, -4], [0, 0, 0, 0, 11, -11, 0, 0, 0, 14, -11, 0, 13, 0, 0, 0], [0, 0, 0, 14, -1, 1, -14, 0, 0, 21, 1, 0, -13, 0, 0, 0], [0, 0, 0, 0, 0, 6, 2, 0, 0, 7, 7, 0, 5, -5, 0, 0], [-6, 6, 0, 0, 0, 0, 0, -11, -11, 0, 0, -11, 0, 0, 6, -6], [-4, -5, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, -4], [8, -8, 4, 0, 0, 0, 0, -4, 9, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, -6, 9, 0, 0, -9, -9, 0, 5, -5, 0, 0], [4, -4, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 4, 0], [0, 0, 0, 5, -11, -11, 5, 0, 0, -11, -20, 0, 0, -5, 0, 0], [-18, 18, -10, 0, 0, 0, 0, 10, 14, 0, 0, 0, 0, 0, -6, 0], [0, 0, 0, 0, 0, -16, 0, 0, 0, -6, -6, 0, 10, -10, 0, 0], [0, 0, 0, 8, -12, 12, -8, 0, 0, -5, 12, 0, -21, 0, 0, 0], [0, 0, 0, 11, -3, -3, 11, 0, 0, -3, 17, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -7, 1, 0, 0, -28, -28, 0, 1, -1, 0, 0], [13, -13, -4, 0, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, -11, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_950_f_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_950_2_f_c();".
// 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_950_2_f_c(:prec:=16)
    chi := MakeCharacter_950_f();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(997) - 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_950_2_f_c();".
// 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_950_2_f_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_f();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![50625, 0, 0, 0, 41356, 0, 0, 0, 4710, 0, 0, 0, 140, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;