
// Make newform 2432.2.c.j in Magma, downloaded from the LMFDB on 06 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_2432_c();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2432_c_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_2432_2_c_j();".
// 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_2432_2_c_j();".
// 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 := [4096, 0, 0, 0, 95760, 0, 0, 0, 64168, 0, 0, 0, 6593, 0, 0, 0, 170, 0, 0, 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, 0, 0, 0], [13215776896, 0, 0, 0, 2552436256, 0, 0, 0, -60648551, 0, 0, 0, -4251522, 0, 0, 0, -29963, 0, 0, 0], [-4504397056, 0, 0, 0, -10707695292, 0, 0, 0, -1424870879, 0, 0, 0, -40138010, 0, 0, 0, -242999, 0, 0, 0], [-38172293120, 0, 0, 0, -17258379212, 0, 0, 0, -1898897707, 0, 0, 0, -51641634, 0, 0, 0, -309571, 0, 0, 0], [-3599744560, 0, 0, 0, -6173773922, 0, 0, 0, -653920303, 0, 0, 0, -16753088, 0, 0, 0, -98195, 0, 0, 0], [0, 0, 40140949280, 0, 0, 0, 38678132940, 0, 0, 0, 4277565505, 0, 0, 0, 112902174, 0, 0, 0, 669065, 0], [0, 34231972352, 0, 179515464352, 0, -67146520856, 0, 55438561884, 0, -8797725214, 0, 4508998129, 0, -242810436, 0, 107399710, 0, -1457982, 0, 615785], [0, 34231972352, 0, -179515464352, 0, -67146520856, 0, -55438561884, 0, -8797725214, 0, -4508998129, 0, -242810436, 0, -107399710, 0, -1457982, 0, -615785], [0, 0, -15653732560, 0, 0, 0, -9065609016, 0, 0, 0, -917926785, 0, 0, 0, -23585018, 0, 0, 0, -138593, 0], [0, -13822069824, 0, 68303003268, 0, 4078720304, 0, 36695011647, 0, 624991225, 0, 3622619113, 0, 17440896, 0, 92396535, 0, 104855, 0, 541737], [0, 13822069824, 0, 68303003268, 0, -4078720304, 0, 36695011647, 0, -624991225, 0, 3622619113, 0, -17440896, 0, 92396535, 0, -104855, 0, 541737], [0, 0, 263656409392, 0, 0, 0, 226468156432, 0, 0, 0, 23883688069, 0, 0, 0, 619264250, 0, 0, 0, 3648213, 0], [0, 0, -366908561792, 0, 0, 0, -238121531292, 0, 0, 0, -24471954775, 0, 0, 0, -631772570, 0, 0, 0, -3718111, 0], [0, 0, 256581837344, 0, 0, 0, 157489923452, 0, 0, 0, 15679810351, 0, 0, 0, 400216410, 0, 0, 0, 2346695, 0], [0, 321127594240, 0, 1513602899088, 0, 309425063520, 0, 1106257340504, 0, 34220524040, 0, 115363611333, 0, 903217392, 0, 2987313186, 0, 5352520, 0, 17595301], [0, 169169506816, 0, 802756029344, 0, 133297141176, 0, 564311386900, 0, 14260520262, 0, 58452837479, 0, 371332676, 0, 1510472018, 0, 2190262, 0, 8890847], [0, 321127594240, 0, -1513602899088, 0, 309425063520, 0, -1106257340504, 0, 34220524040, 0, -115363611333, 0, 903217392, 0, -2987313186, 0, 5352520, 0, -17595301], [0, 169169506816, 0, -802756029344, 0, 133297141176, 0, -564311386900, 0, 14260520262, 0, -58452837479, 0, 371332676, 0, -1510472018, 0, 2190262, 0, -8890847], [0, -587014522112, 0, -2789381653840, 0, -441726304160, 0, -1946870441368, 0, -45146114136, 0, -200898504009, 0, -1160261872, 0, -5185315850, 0, -6817080, 0, -30510473], [0, -587014522112, 0, 2789381653840, 0, -441726304160, 0, 1946870441368, 0, -45146114136, 0, 200898504009, 0, -1160261872, 0, 5185315850, 0, -6817080, 0, 30510473]];
    Rf_basisdens := [1, 2201812976, 8807251904, 8807251904, 1100906488, 17614503808, 35229007616, 35229007616, 3202637056, 4403625952, 4403625952, 17614503808, 17614503808, 8807251904, 70458015232, 35229007616, 70458015232, 35229007616, 70458015232, 70458015232];
    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_2432_c();"
function MakeCharacter_2432_c()
    N := 2432;
    order := 2;
    char_gens := [1407, 2053, 1921];
    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_2432_c_Hecke();"
function MakeCharacter_2432_c_Hecke( : Kf := false)
    N := 2432;
    order := 2;
    char_gens := [1407, 2053, 1921];
    char_values := [[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], [1, 0, 0, 0, 0, 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 := ISA(Type(Kf), Fld), 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]];
    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, 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, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 2, 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, 1, 0], [0, 0, -1, -1, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [2, 0, 2, 1, 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, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, -2, 0], [0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -1, -2, 0, 0, -1, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1], [0, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0], [2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, -3, 1, 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, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1], [0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0], [-2, 2, -2, 3, 2, 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, 0, 0, 0, 3, 1, 0, 1], [0, 0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 2, -3, -1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -3, 0, 0, -3, 0], [0, 0, 0, 0, 0, 2, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 5, 0], [0, 0, 0, 0, 0, 3, 0, 0, -10, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 4, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 5, 0, 3], [-4, 1, 3, -4, -3, 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, -4, 0, 0, 0, -5, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -3, 4, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, -2, -2, 0, -4], [0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, -5, 2, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0], [-4, 2, 2, -2, -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, -2, 0, 0, 0, 0, 0, 0, 0, -7, 0, -1], [2, 2, 4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 12, 0, 0, 2, 3, -1, 0, 0, 0, 0, 0, 0], [4, 3, -1, 3, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 4], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -3, 2, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 3, 4, 0, 0, 1, 0], [2, -2, -8, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -5, 0, 0, 4, 0, 0, -2, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -3, 0], [0, 0, 0, 0, 0, -3, 0, 0, -10, 0, 0, -1, -2, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, -1], [2, -2, -3, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 3, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0], [0, -3, 5, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, -5, 0, 0, 0, 0], [-2, 0, -3, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, -1, 0, -3], [0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, 0, -2, 3, 0, 3], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 6, -2, 0, 0, -5, 0], [0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, -4, -8, 0, -4], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, -6, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -2, 0, 0, 0, 1, -4, 0, 0, -5, 0], [-4, -3, 3, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 3, -5, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, -6, 0, 0, -3, 5, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 5, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0], [-6, 2, 8, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, -7, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, -1, 4, 0, 0, 0, 0, 0, 0, 0], [-10, 2, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, -1, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, -1, -2, 0, 0, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0], [0, 0, 0, 0, 0, -3, 0, 0, -8, 0, 0, 4, -7, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, -6, -3, 0, -3], [0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1], [0, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, -2, 2, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, -4, 0, 0, -2, 3, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, 0, -6], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, -4, 1, 0, 0, -1, 0], [14, 0, -2, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0, -22, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 6, 5, 0, 0, -2, 0], [0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 8, 1, 0, 0, 2, 0], [0, 0, 0, 0, 0, -5, 0, 0, -10, 0, 0, -1, 6, 1, 0, 0, 0, 0, 0, 0], [4, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 10, 0, 0, 1, -3, -5, 0, 0, 0, 0, 0, 0], [8, 0, -5, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 1, -6, 0, 0, 0, 0, 0, 0, 0], [14, -4, 8, -2, 2, 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, 0, 0, 0, -5, 3, 0, 3], 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0, 1, 0, 0, 0, 0, 0, 0, 6, 6, 0, 2], [-8, 1, -19, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 0, 0, -24, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4, 0, -12, 0, 0, 0, 0, 0, 0, 8, 5, 0, 3], [16, 0, 4, -2, 1, 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, -2, 0, 0, 0, 9, 6, 0, 0, 5, 0], [0, 0, 0, 0, 0, -17, 0, 0, 6, 0, 0, -5, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 5, 0, 0, 0, 0, 0, 0, -5, -11, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -10, 14, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 18, 0, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 7, 0, 10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -16, 0, 0, -1, 0], [4, 1, -1, 14, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, -5, -9, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 7, -3, 0, -10], [0, 0, 0, 0, 0, -1, 0, 0, -14, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -6, 0, 0, -8, 0, 0, -10, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, -10, 0, 0, 0, 0, 0, 0, 4, -1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, -7, 0], [-8, -2, 5, -3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 0, -2, 0, 0, 0, 0, 0, 0, -1, 11, 0, 6], [-10, -2, -4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 8, 0, 0, 0, 3, 12, 0, 0, -1, 0], [0, 0, 0, 0, 0, 11, 0, 0, -10, 0, 0, -13, 5, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, -6, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, -30, 0, 0, 5, -4, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 13, 0, 0, 0, 8, 0], [2, 2, 10, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 2, -4, 0, 8], [0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 4, 6, -6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, -11, 0, 0, -12, 0], [0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, -2, 0, 0, -11, 0], [12, 0, -12, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, -6, 2, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 1, 0, 0, 0, -3, 1, 0, 0, 0, 0], [-4, -4, -7, 5, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 7, 2, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, -6, 13, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 3, 19, 0, 0, 4, 0], [0, 0, 0, 0, 0, 5, 0, 0, -12, 0, 0, 2, 8, -2, 0, 0, 0, 0, 0, 0], [-28, 2, 1, 1, 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, -6, 0, 0, 0, 0, 0, 0, -8, -1, 0, 5], [-2, 0, 8, 3, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3, 0, 8, 0, 0, 0, 0, 0, 0, 5, 1, 0, 8], [0, 0, 0, 0, 0, 22, 0, 0, 26, 0, 0, 7, 4, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -5, -1, 0, 0, 8, 0], [-12, -1, 7, -7, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0, -26, 0, 0, -7, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 0, -2, 0, 0, 0, 0, 0, 0, 1, 7, 0, 7], [0, 0, 0, 0, 0, 0, 0, -1, 0, -6, 0, 0, 0, 0, 0, 0, 9, 5, 0, -2], [0, 0, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, -12, -15, 0, -5], [0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 20, 2, 0, 0, 3, 0], [0, 0, 0, 0, 0, -12, 0, 0, 6, 0, 0, -7, -2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -3, 15, 0, 18], [24, 2, 11, -3, 3, 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, 2, 0, 0, 0, 2, -9, 0, 0, -7, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 8, 1, 0, -1], [-48, 1, -1, 7, -3, 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, -10, 0, 0, 0, -7, -5, 0, 0, -13, 0], [0, 0, 0, 0, 0, -6, 0, 0, -34, 0, 0, 1, 4, 6, 0, 0, 0, 0, 0, 0], [-38, 4, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 16, 0, 0, 32, 0, 0, -2, 14, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 6, 0, 0, 0, 6, -9, 0, 0, -5, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 10, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, -5, 0, 2, 0, 0, 0, 0, 0, 0, 3, -3, 0, -1], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 12, 3, 0, 0, 12, 0], [0, 0, 0, 0, 0, 13, 0, 0, 20, 0, 0, 2, 4, -8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -7, 0, 0, -12, 0, 0, 10, -1, -3, 0, 0, 0, 0, 0, 0], [0, -2, 2, 2, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -6, 0, 0, 0, 4, 6, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -1, 0, 9]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2432_c_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2432_2_c_j();".
// 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_2432_2_c_j(:prec:=20)
    chi := MakeCharacter_2432_c();
    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_2432_2_c_j();".
// 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_2432_2_c_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2432_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![64, 0, 388, 0, 428, 0, 157, 0, 22, 0, 1]>,<7,R![-200, 0, 3689, 0, -3112, 0, 694, 0, -48, 0, 1]>],Snew);
    return Vf;
end function;