
// Make newform 1287.2.b.c in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1287_b();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1287_b_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_1287_2_b_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_1287_2_b_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 := [49, 0, 511, 0, 1565, 0, 1695, 0, 835, 0, 201, 0, 23, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8491, 0, 16390, 0, 10009, 0, 2504, 0, 233, 0, -2, 0, -1], [0, -6265, 0, -29962, 0, -24931, 0, -7120, 0, -699, 0, 6, 0, 3], [413, 0, 954, 0, -885, 0, -1280, 0, -449, 0, -62, 0, -3, 0], [-21, 0, -1114, 0, -4951, 0, -4288, 0, -1375, 0, -186, 0, -9, 0], [315, 0, -1002, 0, -4951, 0, -4288, 0, -1375, 0, -186, 0, -9, 0], [0, -8757, 0, -66938, 0, -84519, 0, -44256, 0, -11023, 0, -1290, 0, -57], [-7399, 3213, -39914, -11418, -38521, -35989, -14224, -27528, -2485, -8305, -210, -1082, -7, -51], [0, -9863, 0, -48842, 0, -54725, 0, -25688, 0, -5861, 0, -642, 0, -27], [-7399, -3213, -39914, 11418, -38521, 35989, -14224, 27528, -2485, 8305, -210, 1082, -7, 51], [-117, 0, -714, 0, -1091, 0, -660, 0, -179, 0, -22, 0, -1, 0], [-14, 0, 138, 0, 1473, 0, 1392, 0, 456, 0, 62, 0, 3, 0], [0, 25207, 0, 135374, 0, 216869, 0, 136448, 0, 37957, 0, 4750, 0, 219]];
    Rf_basisdens := [1, 1, 784, 784, 56, 112, 112, 784, 784, 392, 784, 8, 14, 784];
    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_1287_b();"
function MakeCharacter_1287_b()
    N := 1287;
    order := 2;
    char_gens := [1145, 937, 496];
    v := [2, 2, 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1287_b_Hecke();"
function MakeCharacter_1287_b_Hecke(Kf)
    N := 1287;
    order := 2;
    char_gens := [1145, 937, 496];
    char_values := [[1, 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], [-1, 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, 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, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 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, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0], [2, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, -1, 0], [2, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, -1, 1, 0], [0, 2, 1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 1, -2, -1, 0, 0, 0, 0, 1, 1, -1, 0, 0, -1], [0, -1, -2, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [3, 0, 0, 0, 2, -1, -1, 0, 0, 0, 0, 1, 0, 0], [0, -3, 0, 1, 0, 0, 0, 2, -1, 1, 1, 0, 0, 1], [-2, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 2, -1, 0], [0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, -2, -1, 1, 0, 0, 0, 2, -1, -4, 1, 0, 0, 0], [0, 1, 0, -5, 0, 0, 0, 0, 0, 3, 0, 0, 0, -1], [0, -4, 0, -5, 0, 0, 0, 2, 0, -2, 0, 0, 0, -1], [1, 0, 0, 0, -2, 1, -1, 0, -1, 0, -1, 1, 0, 0], [0, -1, -2, -4, 0, 0, 0, 1, -1, -1, 1, 0, 0, 1], [0, 1, 1, 6, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1], [0, 5, 0, 3, 0, 0, 0, -2, 2, 3, -2, 0, 0, 1], [-1, 0, 0, 0, 0, -3, 1, 0, 0, 0, 0, -1, 2, 0], [0, 0, 0, 0, -1, 3, -1, 0, 0, 0, 0, -2, 3, 0], [0, 0, 0, 0, 0, 6, 0, 0, -1, 0, -1, -2, 4, 0], [0, 4, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1], [-2, 0, 0, 0, 1, -3, 1, 0, 0, 0, 0, 2, 1, 0], [-2, 0, 0, 0, 2, 3, 1, 0, -1, 0, -1, -1, 1, 0], [2, 0, 0, 0, -2, 2, -2, 0, -2, 0, -2, 0, 0, 0], [0, -3, -1, 0, 0, 0, 0, 0, -1, -3, 1, 0, 0, 1], [0, 0, 0, 0, -2, 5, -3, 0, -2, 0, -2, 1, 3, 0], [0, -2, 0, -5, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1], [0, -5, 0, -7, 0, 0, 0, 3, -3, -1, 3, 0, 0, 0], [4, 0, 0, 0, 3, 2, -4, 0, 0, 0, 0, -2, -1, 0], [0, 3, -1, 6, 0, 0, 0, -2, -2, 1, 2, 0, 0, -1], [0, 2, -2, 4, 0, 0, 0, 0, 2, 2, -2, 0, 0, 2], [1, 0, 0, 0, 0, -1, 5, 0, 1, 0, 1, 3, -2, 0], [2, 0, 0, 0, 2, -5, -3, 0, 2, 0, 2, 2, 0, 0], [-4, 0, 0, 0, -1, 2, -4, 0, -2, 0, -2, 0, 5, 0], [2, 0, 0, 0, 3, -1, 3, 0, 0, 0, 0, 2, 1, 0], [0, 2, 0, -3, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1], [0, 1, 2, -3, 0, 0, 0, -3, 2, 3, -2, 0, 0, 2], [-8, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 4, 3, 0], [-5, 0, 0, 0, 0, 5, -3, 0, -4, 0, -4, -3, 6, 0], [0, -6, 1, -1, 0, 0, 0, -2, -3, 0, 3, 0, 0, 0], [0, -4, -4, 3, 0, 0, 0, 2, -3, -4, 3, 0, 0, 1], [0, 1, 2, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1], [4, 0, 0, 0, -2, -7, 1, 0, 0, 0, 0, 3, -1, 0], [0, 8, -2, -3, 0, 0, 0, -2, 3, 0, -3, 0, 0, -3], [0, -3, 2, 8, 0, 0, 0, 1, 0, -1, 0, 0, 0, 3], [-2, 0, 0, 0, -3, 1, 1, 0, -2, 0, -2, -2, -1, 0], [8, 0, 0, 0, -1, -3, -3, 0, -2, 0, -2, 4, 3, 0], [2, 0, 0, 0, -2, -4, 2, 0, 1, 0, 1, -2, -4, 0], [-2, 0, 0, 0, -2, 4, -4, 0, -2, 0, -2, 0, 2, 0], [0, 0, 0, -1, 0, 0, 0, -2, -2, 0, 2, 0, 0, -1], [8, 0, 0, 0, 2, -8, 6, 0, 3, 0, 3, 0, -6, 0], [0, 0, 4, 3, 0, 0, 0, -2, -3, -2, 3, 0, 0, 1], [0, 0, 0, 0, -4, 1, -1, 0, 1, 0, 1, 1, 3, 0], [0, -3, 0, -3, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2], [0, -11, 0, 1, 0, 0, 0, 3, -3, -7, 3, 0, 0, 4], [-12, 0, 0, 0, -1, -6, 4, 0, 4, 0, 4, 2, 1, 0], [2, 0, 0, 0, 2, -5, 9, 0, 4, 0, 4, -2, -2, 0], [0, -3, 1, -18, 0, 0, 0, -2, -1, 1, 1, 0, 0, 3], [0, -5, -1, 4, 0, 0, 0, 2, -1, 3, 1, 0, 0, 3], [2, 0, 0, 0, 0, -2, -4, 0, 1, 0, 1, 2, -4, 0], [7, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, -2, -3, 0], [0, -9, -4, -2, 0, 0, 0, 9, -4, -3, 4, 0, 0, -1], [0, -8, 1, 1, 0, 0, 0, -4, 1, -2, -1, 0, 0, 0], [0, -8, -4, -5, 0, 0, 0, 4, -1, -4, 1, 0, 0, -5], [2, 0, 0, 0, -3, -1, 3, 0, 0, 0, 0, 4, 1, 0], [-2, 0, 0, 0, 4, -12, 4, 0, 2, 0, 2, -2, -2, 0], [0, 1, -5, -10, 0, 0, 0, -2, 2, -1, -2, 0, 0, -1], [0, 10, 4, -2, 0, 0, 0, -4, 5, 4, -5, 0, 0, 0], [-2, 0, 0, 0, -2, -2, -6, 0, 0, 0, 0, -2, 4, 0], [0, 11, 2, 11, 0, 0, 0, -2, 1, 7, -1, 0, 0, -3], [0, 4, 3, 9, 0, 0, 0, -4, 1, 2, -1, 0, 0, -2], [0, 2, 6, 7, 0, 0, 0, 2, 0, -4, 0, 0, 0, 1], [-4, 0, 0, 0, -4, 3, -3, 0, -2, 0, -2, 4, -2, 0], [0, 8, 6, 8, 0, 0, 0, -6, 3, 2, -3, 0, 0, 2], [0, -4, -2, 0, 0, 0, 0, 6, -4, -12, 4, 0, 0, 0], [-10, 0, 0, 0, -4, 8, -4, 0, -2, 0, -2, -4, 4, 0], [1, 0, 0, 0, 0, 7, -5, 0, 0, 0, 0, 1, 4, 0], [10, 0, 0, 0, 2, -2, -2, 0, 2, 0, 2, -2, 2, 0], [0, -2, -1, 9, 0, 0, 0, 2, -2, -6, 2, 0, 0, -2], [0, -8, -2, -16, 0, 0, 0, 2, 3, -2, -3, 0, 0, -2], [0, -1, 2, -5, 0, 0, 0, 1, -2, -3, 2, 0, 0, 4], [0, -9, 5, -6, 0, 0, 0, -2, -3, 3, 3, 0, 0, -1], [16, 0, 0, 0, 3, -12, 2, 0, 4, 0, 4, -2, -3, 0], [0, 0, 6, 9, 0, 0, 0, -2, 1, 4, -1, 0, 0, -3], [0, -5, -3, 18, 0, 0, 0, 4, -3, -1, 3, 0, 0, 1], [-5, 0, 0, 0, 0, 6, 0, 0, -1, 0, -1, -6, 5, 0], [0, 0, 1, -3, 0, 0, 0, 4, -4, -4, 4, 0, 0, 2], [-4, 0, 0, 0, -2, 0, -2, 0, 1, 0, 1, 6, -6, 0], [0, 1, 5, -2, 0, 0, 0, 8, -2, -1, 2, 0, 0, -1], [-8, 0, 0, 0, 2, -10, 2, 0, 2, 0, 2, -4, 0, 0], [11, 0, 0, 0, -4, -3, -1, 0, -1, 0, -1, -7, 0, 0], [0, 8, -2, 6, 0, 0, 0, 2, -1, -2, 1, 0, 0, 0], [-8, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, -5, 3, 0], [0, 8, -2, 3, 0, 0, 0, -4, 3, 2, -3, 0, 0, -3], [-10, 0, 0, 0, 2, 6, -4, 0, 1, 0, 1, -4, -2, 0], [-5, 0, 0, 0, 2, 9, -5, 0, -5, 0, -5, -5, 10, 0], [-11, 0, 0, 0, 0, -3, 5, 0, 6, 0, 6, 3, -6, 0], [0, 2, 2, -2, 0, 0, 0, 6, -1, 0, 1, 0, 0, 0], [0, -6, -2, -4, 0, 0, 0, 4, -2, 2, 2, 0, 0, -2], [0, 3, -2, 5, 0, 0, 0, 1, 2, -3, -2, 0, 0, -2], [-6, 0, 0, 0, 1, -7, -3, 0, 2, 0, 2, 0, -3, 0], [-16, 0, 0, 0, 2, 2, 4, 0, -1, 0, -1, 4, 2, 0], [4, 0, 0, 0, 0, -3, -5, 0, -3, 0, -3, 1, 7, 0], [0, -4, -8, -13, 0, 0, 0, 4, -2, -2, 2, 0, 0, 1], [0, 4, -1, -9, 0, 0, 0, 4, 1, 6, -1, 0, 0, -4], [0, 11, -1, 16, 0, 0, 0, 0, 3, -1, -3, 0, 0, -7], [0, -1, 3, -16, 0, 0, 0, -2, 0, 1, 0, 0, 0, 5], [0, 0, 0, 0, 4, 6, -2, 0, 0, 0, 0, -2, 4, 0], [0, 6, 3, 5, 0, 0, 0, -10, 2, 2, -2, 0, 0, -2], [2, 0, 0, 0, -3, 1, -3, 0, -4, 0, -4, -6, 3, 0], [-6, 0, 0, 0, 5, -1, -1, 0, 2, 0, 2, 0, -1, 0], [-5, 0, 0, 0, 6, 8, 2, 0, 1, 0, 1, -4, 1, 0], [0, 10, 8, 8, 0, 0, 0, 0, 1, 0, -1, 0, 0, 2], [9, 0, 0, 0, 2, 4, -2, 0, -1, 0, -1, -6, 7, 0], [18, 0, 0, 0, 0, 7, -5, 0, -4, 0, -4, -3, 1, 0], [0, 17, 4, 13, 0, 0, 0, -6, 2, 7, -2, 0, 0, -5], [0, 5, -1, -2, 0, 0, 0, 4, -3, -7, 3, 0, 0, -1], [-5, 0, 0, 0, 0, -1, -3, 0, 5, 0, 5, -1, -4, 0], [0, 1, -4, 9, 0, 0, 0, 2, 3, 1, -3, 0, 0, -7], [14, 0, 0, 0, -2, -2, 6, 0, 4, 0, 4, 0, -4, 0], [8, 0, 0, 0, 2, -4, -4, 0, -4, 0, -4, -6, 0, 0], [0, -6, -2, 3, 0, 0, 0, 2, 0, -8, 0, 0, 0, 5], [0, 0, 4, 1, 0, 0, 0, 4, -2, 4, 2, 0, 0, 3], [0, 9, 0, -22, 0, 0, 0, 3, 1, 1, -1, 0, 0, -1], [2, 0, 0, 0, 7, -3, 5, 0, 2, 0, 2, 0, -1, 0], [-12, 0, 0, 0, -3, 0, -2, 0, 4, 0, 4, 0, -9, 0], [0, 9, 6, -3, 0, 0, 0, -3, 2, 15, -2, 0, 0, -2], [0, 6, 0, -16, 0, 0, 0, 2, -1, -8, 1, 0, 0, 0], [0, -1, 3, -12, 0, 0, 0, -4, 2, 5, -2, 0, 0, 3], [0, 10, 4, -21, 0, 0, 0, 0, 4, 6, -4, 0, 0, -3], [0, 0, 0, 0, -3, -7, 1, 0, 0, 0, 0, 12, -3, 0], [-15, 0, 0, 0, -4, -1, 1, 0, 1, 0, 1, -3, -8, 0], [0, -1, 2, -1, 0, 0, 0, -3, 5, -1, -5, 0, 0, -2], [0, -4, 0, 15, 0, 0, 0, 0, -5, -6, 5, 0, 0, 3], [6, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, -4, -6, 0], [0, -6, 4, -17, 0, 0, 0, -6, -1, -2, 1, 0, 0, 5], [-6, 0, 0, 0, 2, 2, -6, 0, 0, 0, 0, -4, -6, 0], [0, -10, 4, 14, 0, 0, 0, 4, -2, 6, 2, 0, 0, 6], [0, -2, -2, 2, 0, 0, 0, 2, -1, -8, 1, 0, 0, 0], [-4, 0, 0, 0, -8, -7, 7, 0, 1, 0, 1, 9, 1, 0], [-2, 0, 0, 0, 0, 10, -6, 0, -2, 0, -2, 0, -2, 0], [0, 0, -4, -4, 0, 0, 0, 0, 1, 6, -1, 0, 0, 2], [0, 7, 8, 4, 0, 0, 0, -1, 2, 9, -2, 0, 0, 3], [20, 0, 0, 0, 6, -6, 2, 0, -2, 0, -2, 2, -2, 0], [10, 0, 0, 0, 5, -3, -3, 0, -2, 0, -2, 2, 7, 0], [5, 0, 0, 0, 2, -6, 14, 0, 6, 0, 6, 4, -7, 0], [-10, 0, 0, 0, 1, -5, 3, 0, 2, 0, 2, -4, -7, 0], [10, 0, 0, 0, 1, -3, -7, 0, -4, 0, -4, -14, 3, 0], [-18, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 9, -1, 0], [0, -1, -5, -6, 0, 0, 0, -2, 0, -11, 0, 0, 0, 7], [5, 0, 0, 0, 2, -12, 0, 0, 6, 0, 6, 6, -3, 0], [0, -1, -4, 3, 0, 0, 0, -3, 2, -7, -2, 0, 0, -2], [0, -11, -2, -5, 0, 0, 0, 0, -4, 3, 4, 0, 0, 9], [-8, 0, 0, 0, 2, 5, -11, 0, -2, 0, -2, 9, -3, 0], [0, -9, -8, 9, 0, 0, 0, 7, -3, -13, 3, 0, 0, -4], [-10, 0, 0, 0, -1, -4, 2, 0, 0, 0, 0, 2, 7, 0], [0, -13, 3, -6, 0, 0, 0, 6, -3, -1, 3, 0, 0, -3], [0, 2, -8, 6, 0, 0, 0, -6, 2, 6, -2, 0, 0, -4], [10, 0, 0, 0, 2, -2, 6, 0, 0, 0, 0, 4, 0, 0], [8, 0, 0, 0, -2, -14, 0, 0, 3, 0, 3, 6, -12, 0], [0, 2, 0, 5, 0, 0, 0, -2, 4, 8, -4, 0, 0, 5], [-26, 0, 0, 0, -3, 3, -1, 0, 0, 0, 0, 4, -1, 0], [0, -3, 12, -6, 0, 0, 0, -1, -1, 1, 1, 0, 0, 3], [0, 1, -12, 15, 0, 0, 0, 0, -2, -5, 2, 0, 0, -1], [7, 0, 0, 0, -4, 10, 6, 0, 0, 0, 0, -12, 5, 0], [0, 3, -2, 18, 0, 0, 0, -7, -2, -3, 2, 0, 0, -3], [-6, 0, 0, 0, 3, -1, 7, 0, 2, 0, 2, -2, -7, 0], [22, 0, 0, 0, -3, -7, -3, 0, 6, 0, 6, 4, -5, 0], [0, 0, -8, 15, 0, 0, 0, -4, 2, 8, -2, 0, 0, 1], [0, 9, -5, 4, 0, 0, 0, -2, 5, -3, -5, 0, 0, -1], [7, 0, 0, 0, -6, 3, 7, 0, -4, 0, -4, 7, 2, 0], [-2, 0, 0, 0, 6, 6, -10, 0, 2, 0, 2, -2, 4, 0], [0, 14, 3, 5, 0, 0, 0, -14, 2, 6, -2, 0, 0, 2], [26, 0, 0, 0, -2, 18, 0, 0, -3, 0, -3, -4, 6, 0], [0, 0, 0, 0, -5, -2, 0, 0, 0, 0, 0, 6, -1, 0], [0, 13, -4, 5, 0, 0, 0, -3, 6, 11, -6, 0, 0, -8], [0, -3, -4, 3, 0, 0, 0, 6, -1, -11, 1, 0, 0, -1], [-14, 0, 0, 0, 1, 11, -1, 0, 0, 0, 0, 8, -1, 0], [19, 0, 0, 0, -4, -20, 6, 0, 9, 0, 9, -2, -5, 0], [0, 9, -1, 2, 0, 0, 0, 0, -2, -5, 2, 0, 0, -3], [0, -1, 12, 0, 0, 0, 0, -5, 0, 5, 0, 0, 0, 3], [0, -5, 8, 24, 0, 0, 0, 5, -7, -1, 7, 0, 0, 3], [4, 0, 0, 0, -3, 24, -2, 0, -8, 0, -8, 0, 7, 0], [0, -4, 4, 14, 0, 0, 0, -8, 2, 0, -2, 0, 0, -2], [22, 0, 0, 0, -3, -11, -3, 0, 0, 0, 0, 4, -3, 0], [0, 5, -1, 4, 0, 0, 0, 8, -2, -1, 2, 0, 0, -9], [-6, 0, 0, 0, -2, 14, -2, 0, -4, 0, -4, 4, 8, 0], [0, 0, 0, 0, 5, -11, 13, 0, 4, 0, 4, -4, -11, 0], [0, -22, 0, 8, 0, 0, 0, 2, -5, -4, 5, 0, 0, 0], [0, 0, 0, 0, 3, -15, 1, 0, 2, 0, 2, 8, -1, 0], [0, 6, -2, 21, 0, 0, 0, -4, 5, 8, -5, 0, 0, 3], [5, 0, 0, 0, 4, -10, 0, 0, 1, 0, 1, -4, -3, 0], [0, 2, -14, 9, 0, 0, 0, 6, 3, 0, -3, 0, 0, -3], [-8, 0, 0, 0, 2, 5, 7, 0, 1, 0, 1, -7, 5, 0], [0, -6, 6, -12, 0, 0, 0, 2, -1, -4, 1, 0, 0, -6], [-9, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 1, 0], [0, -15, -6, -13, 0, 0, 0, 10, -4, -5, 4, 0, 0, -5], [6, 0, 0, 0, 2, 10, -10, 0, -2, 0, -2, 0, -2, 0], [0, -17, -3, -26, 0, 0, 0, 6, -2, -7, 2, 0, 0, 9], [10, 0, 0, 0, 2, -12, -6, 0, -1, 0, -1, -4, 2, 0], [0, 12, 0, 15, 0, 0, 0, 4, 3, 2, -3, 0, 0, -1], [-14, 0, 0, 0, 3, 3, -9, 0, 0, 0, 0, -2, 1, 0], [5, 0, 0, 0, -6, 8, 6, 0, -3, 0, -3, -10, -1, 0], [6, 0, 0, 0, -8, -12, -4, 0, 2, 0, 2, 2, -2, 0], [-2, 0, 0, 0, -1, 17, -3, 0, -2, 0, -2, -2, 5, 0], [0, -8, -4, 20, 0, 0, 0, 0, -4, -8, 4, 0, 0, 4], [0, 24, -2, 11, 0, 0, 0, -6, 3, 8, -3, 0, 0, -5], [0, -21, 4, 1, 0, 0, 0, -4, -1, -1, 1, 0, 0, 3], [-1, 0, 0, 0, 4, -5, -9, 0, -6, 0, -6, -9, 8, 0], [4, 0, 0, 0, 8, -15, -5, 0, 1, 0, 1, -13, -1, 0], [0, 3, -6, -9, 0, 0, 0, 4, -3, -1, 3, 0, 0, -1], [0, 4, -5, 3, 0, 0, 0, 0, 4, -4, -4, 0, 0, 2], [10, 0, 0, 0, 2, -18, 10, 0, 6, 0, 6, 8, -10, 0], [0, 1, -2, 25, 0, 0, 0, 5, -5, -7, 5, 0, 0, 0], [0, 16, 9, -5, 0, 0, 0, -12, 3, 18, -3, 0, 0, 2], [0, -22, 5, -5, 0, 0, 0, 0, -1, 0, 1, 0, 0, 2], [-3, 0, 0, 0, -2, 16, -6, 0, -7, 0, -7, 4, 7, 0], [-14, 0, 0, 0, -2, -6, 12, 0, 1, 0, 1, -2, -2, 0], [24, 0, 0, 0, -2, 10, -10, 0, -2, 0, -2, -4, 0, 0], [-14, 0, 0, 0, 3, -9, 7, 0, 2, 0, 2, 2, 1, 0], [-21, 0, 0, 0, 2, 9, 3, 0, 3, 0, 3, -5, 0, 0], [0, -13, 8, -22, 0, 0, 0, 7, -5, -5, 5, 0, 0, 3], [-8, 0, 0, 0, 2, -6, -2, 0, -2, 0, -2, 0, 0, 0], [-19, 0, 0, 0, 2, -5, -5, 0, -2, 0, -2, -1, -4, 0], [0, -15, -6, -3, 0, 0, 0, 3, -1, 5, 1, 0, 0, 2], [-4, 0, 0, 0, -2, 11, -13, 0, -2, 0, -2, 3, -5, 0], [16, 0, 0, 0, -1, -17, 7, 0, 6, 0, 6, -6, -9, 0], [0, 0, -4, -16, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4], [0, 30, 12, 16, 0, 0, 0, -16, 5, 12, -5, 0, 0, -2], [0, -17, 2, -15, 0, 0, 0, 11, -6, -11, 6, 0, 0, 4], [-8, 0, 0, 0, -4, -15, 3, 0, 10, 0, 10, -2, -12, 0], [-20, 0, 0, 0, 1, 24, -10, 0, -6, 0, -6, -10, 15, 0], [0, -16, 0, -32, 0, 0, 0, 2, -5, -2, 5, 0, 0, 4], [8, 0, 0, 0, -8, -19, 11, 0, 5, 0, 5, 13, -13, 0], [8, 0, 0, 0, 0, -10, 2, 0, 0, 0, 0, 8, -4, 0], [0, 6, -4, -30, 0, 0, 0, 6, -1, -8, 1, 0, 0, 2], [0, -3, -2, 25, 0, 0, 0, -3, -2, 3, 2, 0, 0, 2], [-11, 0, 0, 0, -8, -10, 2, 0, -4, 0, -4, 8, -9, 0], [0, 1, 3, -12, 0, 0, 0, -2, -1, -3, 1, 0, 0, 7], [0, 9, -8, 5, 0, 0, 0, -14, 3, 5, -3, 0, 0, -3], [0, 18, 2, 17, 0, 0, 0, 4, 2, 2, -2, 0, 0, -7], [-13, 0, 0, 0, 0, 28, -6, 0, -7, 0, -7, -4, 7, 0], [0, -9, -2, -6, 0, 0, 0, 7, -2, 1, 2, 0, 0, -9], [0, 5, 2, 7, 0, 0, 0, 3, 6, -9, -6, 0, 0, 2], [0, 17, -14, 9, 0, 0, 0, 0, -1, -3, 1, 0, 0, -7], [-6, 0, 0, 0, -10, 9, 3, 0, -2, 0, -2, 12, 4, 0], [4, 0, 0, 0, 14, -7, 1, 0, -2, 0, -2, 1, 5, 0], [0, -6, -2, 37, 0, 0, 0, 6, -7, -10, 7, 0, 0, -3], [-16, 0, 0, 0, -2, 25, -5, 0, -4, 0, -4, 6, -4, 0], [0, 3, 2, -17, 0, 0, 0, 1, 7, -1, -7, 0, 0, -2], [14, 0, 0, 0, 4, 2, 6, 0, -4, 0, -4, 0, 0, 0], [0, -5, 8, 8, 0, 0, 0, 5, -4, 9, 4, 0, 0, -3], [-14, 0, 0, 0, 8, 23, -13, 0, 0, 0, 0, -15, 7, 0], [-19, 0, 0, 0, 2, 2, -4, 0, 3, 0, 3, 8, -1, 0], [0, 21, 8, -6, 0, 0, 0, -3, 6, 11, -6, 0, 0, -13], [-14, 0, 0, 0, -8, 16, -4, 0, -4, 0, -4, 6, -2, 0], [0, -15, -9, -2, 0, 0, 0, 0, 3, 1, -3, 0, 0, -5], [-12, 0, 0, 0, -4, 28, -4, 0, -6, 0, -6, 2, 6, 0], [0, 22, 5, -17, 0, 0, 0, -2, 7, 8, -7, 0, 0, -12], [0, 2, -9, -29, 0, 0, 0, -6, 7, -4, -7, 0, 0, 2], [0, -5, 4, -3, 0, 0, 0, 9, -3, -5, 3, 0, 0, -6], [16, 0, 0, 0, -12, -11, 11, 0, 5, 0, 5, 9, -3, 0], [-8, 0, 0, 0, -7, 15, -5, 0, -6, 0, -6, -2, 3, 0], [0, 2, 5, -15, 0, 0, 0, 0, 3, 4, -3, 0, 0, -4], [0, 8, 10, 12, 0, 0, 0, -6, 0, -8, 0, 0, 0, 0], [12, 0, 0, 0, -4, -1, 11, 0, 2, 0, 2, -1, 7, 0], [-12, 0, 0, 0, -8, -4, -14, 0, -1, 0, -1, -10, 6, 0], [0, 17, 5, 24, 0, 0, 0, -8, 8, 3, -8, 0, 0, 5], [0, 1, 16, -9, 0, 0, 0, -2, -4, 7, 4, 0, 0, 13], [0, 20, 10, 23, 0, 0, 0, -10, 6, 2, -6, 0, 0, 1], [0, -18, -4, 35, 0, 0, 0, -6, -6, -8, 6, 0, 0, -5], [-17, 0, 0, 0, 2, 10, -22, 0, -4, 0, -4, 0, 3, 0], [21, 0, 0, 0, -2, -6, 8, 0, -5, 0, -5, -6, -3, 0], [0, 11, -1, -6, 0, 0, 0, -2, -3, -9, 3, 0, 0, -11], [9, 0, 0, 0, -6, 12, 0, 0, -4, 0, -4, 8, 1, 0], [0, -4, 2, -25, 0, 0, 0, -2, -4, 6, 4, 0, 0, 5], [0, -5, 2, 31, 0, 0, 0, -3, 3, -13, -3, 0, 0, 2], [-16, 0, 0, 0, 4, 32, -8, 0, -4, 0, -4, -4, 4, 0], [0, 0, 0, 0, 10, -2, -2, 0, 0, 0, 0, -4, 8, 0], [0, -24, -8, -1, 0, 0, 0, 12, -7, -14, 7, 0, 0, -5], [0, -7, -13, -32, 0, 0, 0, 16, -6, -5, 6, 0, 0, 3], [28, 0, 0, 0, 8, -11, 9, 0, 8, 0, 8, -1, -11, 0], [18, 0, 0, 0, -5, -3, 1, 0, -6, 0, -6, 10, -5, 0], [24, 0, 0, 0, -5, -8, 2, 0, -2, 0, -2, 10, -3, 0], [0, -18, 10, -15, 0, 0, 0, 4, -7, -4, 7, 0, 0, 3], [0, 10, -8, -5, 0, 0, 0, 0, -1, 14, 1, 0, 0, -1], [15, 0, 0, 0, -2, -8, -2, 0, 3, 0, 3, -8, -5, 0], [29, 0, 0, 0, 6, -9, -5, 0, 0, 0, 0, 7, 2, 0], [6, 0, 0, 0, 6, -4, 0, 0, 4, 0, 4, -4, 4, 0], [18, 0, 0, 0, -9, 9, 5, 0, -8, 0, -8, -4, 5, 0], [3, 0, 0, 0, 2, 8, -6, 0, -5, 0, -5, 10, -13, 0], [0, 5, 14, -35, 0, 0, 0, -7, 5, 13, -5, 0, 0, 4], [24, 0, 0, 0, -2, -8, 6, 0, -1, 0, -1, 0, -6, 0], [0, -1, 8, 3, 0, 0, 0, -3, 4, -3, -4, 0, 0, 6], [-16, 0, 0, 0, -6, 27, -9, 0, -2, 0, -2, 1, 7, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1287_b_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1287_2_b_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_1287_2_b_c(:prec:=14)
    chi := MakeCharacter_1287_b();
    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_1287_2_b_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_1287_2_b_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1287_b();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![49, 0, 511, 0, 1565, 0, 1695, 0, 835, 0, 201, 0, 23, 0, 1]>],Snew);
    return Vf;
end function;