
// Make newform 1232.2.q.o in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1232_q();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1232_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_1232_2_q_o();".
// 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_1232_2_q_o();".
// 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 := [36, 30, -65, -48, 87, -26, 10, -9, 1, -1, 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], [-166645188, -28179152, 200646585, -57379965, 19749496, -23214830, 1252650, -2291723, 2122814, -175931], [-12840162, 8565432, -1132357, -7882773, 4073080, -372550, 996486, -240025, 15964, -155541], [92028048, 118243028, -191378187, 108969915, -53645260, 23040746, -8349810, 4712021, -1615910, 1013393], [-25274400, 25557580, -36613935, -34920825, 33742060, 2989378, 6616590, -1671755, -737758, -1065671], [-131250, 4530313, -15167460, -3531393, 8490406, 2225113, 1491771, -612335, -372211, -276392], [38723880, -143152604, -43882995, 99152043, -21697700, 12029062, -9427146, 950941, -1178626, 1145905], [40428, -142600, -129855, 395715, -137080, 31478, -47178, 4601, -3458, 4793], [9226776, 8194516, 40792183, -65582787, 21055420, -6623314, 6820122, -904397, 685446, -673853], [-9415896, -33065602, 24370503, 69828225, -40881364, 425318, -9602418, 2850521, 725326, 1505423]];
    Rf_basisdens := [1, 41020284, 6836714, 41020284, 41020284, 10255071, 41020284, 144948, 13673428, 20510142];
    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_1232_q();"
function MakeCharacter_1232_q()
    N := 1232;
    order := 3;
    char_gens := [463, 309, 353, 673];
    v := [3, 3, 1, 3];
    // 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_1232_q_Hecke();"
function MakeCharacter_1232_q_Hecke(Kf)
    N := 1232;
    order := 3;
    char_gens := [463, 309, 353, 673];
    char_values := [[1, 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, 1, 0, 0], [1, 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, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [-1, 0, 0, 1, 1, 0, 0, 1, 1, 0], [1, 1, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [1, 1, 0, 1, -1, -1, 0, -1, 0, 1], [0, 0, 1, -1, 0, 1, -1, -1, 1, 2], [1, 1, 0, 1, 1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 1, -2, 1, 1, -1, -1], [3, 1, 2, 1, -2, -1, 1, -1, 0, 1], [1, 2, 1, 2, -1, 0, 2, 0, 1, 0], [-2, -1, 0, 2, 2, 2, -1, 1, 1, 1], [2, -2, 0, -2, 2, 1, 0, 2, 0, -1], [-2, 3, -2, 3, -3, -1, 0, -3, 0, 1], [3, 0, 0, 1, 1, -2, 0, -3, -1, -1], [-2, -4, -4, -2, 2, -1, -2, 2, -4, -2], [-2, -4, 0, 0, 2, 1, 0, 3, 0, 2], [-2, -2, 0, -2, -2, 2, -2, 0, 1, 1], [-1, -2, 4, -1, 1, 0, -1, 0, 4, 0], [-4, -3, -2, -3, 4, 0, -1, 3, 0, 0], [-2, -4, 3, -2, 2, 0, -2, -3, 3, 0], [-2, 0, 0, -3, -3, 4, 0, 2, 1, 2], [3, 0, 5, 0, 1, -3, -1, 0, 0, 3], [-8, 1, 0, 1, 1, 0, 1, 9, 3, 0], [3, 1, 4, 1, -3, -1, 2, -1, 0, 1], [0, 0, 1, 5, 0, -3, 5, -6, 1, -6], [4, 1, 0, 3, 3, -2, 1, -3, 1, -1], [-5, 0, 0, 5, 5, -4, 0, 5, 1, -2], [1, 2, 0, 6, -1, -1, 6, 3, 0, -2], [-1, -4, -4, -4, 5, 2, -1, 4, 0, -2], [-9, 0, -2, 0, 0, -1, 0, 0, 0, 1], [2, -2, 0, 3, 3, 2, -2, -4, 4, 1], [3, 6, -1, -1, -3, 0, -1, -1, -1, 0], [7, 4, 1, 4, 0, 1, -4, -4, 0, -1], [-5, 2, 0, 0, 0, 2, 2, 7, -5, 1], [4, 8, -3, 8, -4, -2, 8, -2, -3, -4], [2, 4, 3, 2, -2, 1, 2, -5, 3, 2], [-7, -1, 0, -2, -2, 10, -1, 6, 1, 5], [0, 2, 1, 2, -3, 0, 1, -2, 0, 0], [-2, 5, 0, -4, -4, 2, 5, 7, 2, 1], [0, 0, -2, -2, 0, 3, -2, 3, -2, 6], [2, -5, 0, -5, 7, 1, -2, 5, 0, -1], [-7, -2, 0, 4, 4, -10, -2, 5, 1, -5], [0, 0, 4, -6, 0, 1, -6, 6, 4, 2], [-8, 0, -7, 0, 3, 1, -3, 0, 0, -1], [2, 4, -2, -1, -2, -1, -1, -8, -2, -2], [-5, 1, 3, 1, -1, 5, 0, -1, 0, -5], [-4, -3, 2, -3, 7, 2, -4, 3, 0, -2], [1, 2, 2, 4, -1, 3, 4, 1, 2, 6], [5, 0, 0, 0, 0, -2, 0, -5, -3, -1], [3, 3, 0, -4, -4, -4, 3, 0, -14, -2], [-2, 0, 7, 0, -7, 2, 7, 0, 0, -2], [2, 4, 7, 8, -2, -2, 8, -7, 7, -4], [7, 2, -5, 2, -1, -1, -1, -2, 0, 1], [-16, -3, 0, -1, -1, 6, -3, 13, -4, 3], [-1, -2, -12, -4, 1, -4, -4, -4, -12, -8], [-1, -2, 1, -6, 1, 0, -6, -10, 1, 0], [-7, 1, 0, -4, -4, 6, 1, 8, 9, 3], [-1, -2, 5, -1, 1, 0, -1, 1, 5, 0], [5, 4, -5, 4, -3, 2, -1, -4, 0, -2], [1, 2, -1, 0, -1, -5, 0, -4, -1, -10], [-1, -4, -5, -4, 6, -1, -2, 4, 0, 1], [-1, 2, -9, 2, 1, 2, -3, -2, 0, -2], [-2, -4, 3, -3, 2, -2, -3, 1, 3, -4], [-11, 0, 0, -1, -1, 8, 0, 11, 0, 4], [-15, -3, 0, 2, 2, 2, -3, 12, 8, 1], [3, 3, 0, -6, -6, -2, 3, 0, -11, -1], [8, 3, 0, 3, 0, -2, -3, -3, 0, 2], [-2, -4, 6, 5, 2, -1, 5, -10, 6, -2], [5, 2, 1, 2, 2, 1, -4, -2, 0, -1], [5, 10, 5, 11, -5, -2, 11, -16, 5, -4], [4, -1, 0, -5, -5, 12, -1, -5, 0, 6], [2, 4, -2, 11, -2, -1, 11, -8, -2, -2], [5, 4, 0, -4, -4, 0, 4, -1, 0, 0], [-8, 7, -1, 7, -4, -1, -3, -7, 0, 1], [-8, 0, 0, 4, 4, 2, 0, 8, 8, 1], [0, 0, 14, -1, 0, 3, -1, 8, 14, 6], [-2, 4, 0, -2, -2, 4, 4, 6, -8, 2], [-5, -1, 0, -4, -4, 4, -1, 4, 7, 2], [-4, -8, -6, -3, 4, 1, -3, -4, -6, 2], [5, -2, -1, -2, -4, 3, 6, 2, 0, -3], [-2, 4, 4, 4, -11, -2, 7, -4, 0, 2], [3, 6, -17, 3, -3, -1, 3, -3, -17, -2], [20, -2, 6, -2, -2, 0, 4, 2, 0, 0], [-10, -3, 0, 7, 7, 4, -3, 7, 10, 2], [-3, -5, 0, -5, -5, 2, -5, -2, 12, 1], [9, 0, 9, 0, -2, -5, 2, 0, 0, 5], [-11, 0, 0, -3, -3, 18, 0, 11, 1, 9], [9, 0, 12, 0, -1, 2, 1, 0, 0, -2], [-9, -5, -3, -5, 10, 2, -5, 5, 0, -2], [6, 2, 0, 11, 11, -8, 2, -4, -2, -4], [-8, -16, 1, -5, 8, 0, -5, 10, 1, 0], [-3, -6, -4, -3, 3, 5, -3, 19, -4, 10], [11, 4, 7, 4, 0, -3, -4, -4, 0, 3], [0, -3, 0, -5, -5, 8, -3, -3, 1, 4], [-18, 0, 1, 0, 2, 0, -2, 0, 0, 0], [-4, -4, 0, 5, 5, -4, -4, 0, 4, -2], [0, 0, -2, -1, 0, 0, -1, -14, -2, 0], [-3, 3, 0, -3, -3, 4, 3, 6, -12, 2], [-4, -3, 0, -3, -3, -6, -3, 1, 2, -3], [2, -5, 2, -5, -5, 2, 10, 5, 0, -2], [5, 10, -6, 8, -5, 1, 8, 5, -6, 2], [0, 0, 3, 1, 0, 2, 1, 5, 3, 4], [0, 6, 0, 3, 3, -8, 6, 6, 4, -4], [5, 10, 10, 4, -5, 6, 4, 3, 10, 12], [-2, -4, 6, -3, 2, 2, -3, 1, 6, 4], [-7, -6, 6, -6, 14, -3, -8, 6, 0, 3], [8, 4, 0, 1, 1, -14, 4, -4, -6, -7], [1, 2, 12, -1, -1, 5, -1, 15, 12, 10], [14, 11, 10, 11, -10, -5, -1, -11, 0, 5], [-16, -3, 0, 2, 2, -8, -3, 13, -1, -4], [4, 8, 6, 10, -4, -2, 10, -24, 6, -4], [6, 4, -1, 4, -8, 5, 4, -4, 0, -5], [2, 4, 2, -2, -2, 8, -2, -8, 2, 16], [13, 2, -1, 2, 4, -4, -6, -2, 0, 4], [1, 2, -10, 2, -1, 3, 2, -6, -10, 6], [-5, 5, 0, 5, -11, -2, 6, -5, 0, 2], [1, 2, -11, 3, -1, 3, 3, -6, -11, 6], [-10, -4, 0, -6, -6, 6, -4, 6, 0, 3], [-2, 2, 0, 2, 3, -2, -5, -2, 0, 2], [-5, -10, 6, 4, 5, -7, 4, 7, 6, -14], [-9, -5, -3, -5, 15, 1, -10, 5, 0, -1], [31, 2, 0, 9, 9, -10, 2, -29, 5, -5], [-2, -4, 7, -2, 2, -4, -2, 2, 7, -8], [-10, 3, 0, -4, -4, 4, 3, 13, 4, 2], [-25, -2, 8, -2, -1, 2, 3, 2, 0, -2], [4, -4, 0, -3, -3, -6, -4, -8, 4, -3], [-7, -1, 0, 3, 3, 14, -1, 6, 2, 7], [3, -1, 1, -1, 6, -8, -5, 1, 0, 8], [7, -6, 0, -1, -1, 12, -6, -13, 8, 6], [-1, -2, -14, -3, 1, -5, -3, -3, -14, -10], [1, 5, 1, 5, -6, -2, 1, -5, 0, 2], [-11, -11, 0, 5, 5, -2, -11, 0, 6, -1], [-4, -1, 4, -1, 2, 1, -1, 1, 0, -1], [-6, 0, 0, 5, 5, 8, 0, 6, 14, 4], [-3, -6, 1, -6, 2, -1, 4, 6, 0, 1], [-4, -8, 3, 7, 4, -3, 7, 7, 3, -6], [8, 16, -4, 16, -8, -3, 16, -10, -4, -6], [16, 2, 20, 2, -3, -4, 1, -2, 0, 4], [-2, -4, 7, -6, 2, 3, -6, 27, 7, 6], [-10, -7, -8, -7, 2, 9, 5, 7, 0, -9], [-17, -5, 0, 3, 3, -8, -5, 12, 5, -4], [-1, -2, -7, -2, 1, 4, -2, -8, -7, 8], [10, -10, 8, -10, -2, 3, 12, 10, 0, -3], [2, 4, 3, 0, -2, 8, 0, 19, 3, 16], [-16, 7, 4, 7, -14, 3, 7, -7, 0, -3], [-14, 2, 0, 2, -12, 2, 10, -2, 0, -2], [-6, -12, 0, -15, 6, 4, -15, -8, 0, 8], [-32, -6, 0, -12, -12, 4, -6, 26, -9, 2], [-7, -2, 0, -5, -5, 0, -2, 5, 7, 0], [-1, -3, 0, 0, 0, 12, -3, -2, -3, 6], [9, -1, 20, -1, -1, -3, 2, 1, 0, 3], [12, 0, 7, 0, 8, 2, -8, 0, 0, -2], [-13, -5, 0, -9, -9, 2, -5, 8, -7, 1], [-2, -4, 9, 0, 2, -7, 0, 1, 9, -14], [10, -1, 10, -1, -6, 1, 7, 1, 0, -1], [-5, -12, 0, 0, 0, 6, -12, -7, 3, 3], [-5, -7, 0, 3, 3, 0, -7, -2, 3, 0], [4, 4, -14, 4, -7, 7, 3, -4, 0, -7], [-11, -22, 15, 1, 11, 0, 1, 31, 15, 0], [19, 5, 0, -5, -5, -6, 5, -14, -8, -3], [7, -7, -1, -7, 8, 1, -1, 7, 0, -1], [-4, -7, 0, -7, 17, 1, -10, 7, 0, -1], [0, 9, 0, -1, -1, 0, 9, 9, 2, 0], [-4, -8, -12, -15, 4, 2, -15, 20, -12, 4], [-3, -6, 0, -19, 3, 1, -19, 21, 0, 2], [3, 6, -4, -6, -3, 2, -6, -1, -4, 4], [9, 18, 9, 7, -9, 6, 7, 16, 9, 12], [-3, -7, 5, -7, 0, 2, 7, 7, 0, -2], [-2, -6, 0, 9, 9, -28, -6, -4, -8, -14], [9, 18, -9, 7, -9, 0, 7, -18, -9, 0], [-21, 5, 9, 5, -8, 5, 3, -5, 0, -5], [5, 10, 0, -5, -5, 14, 10, 5, 2, 7], [14, 28, 3, 15, -14, 1, 15, -29, 3, 2], [-3, -6, -5, -2, 3, 9, -2, 8, -5, 18], [-2, -7, 3, -7, 21, -10, -14, 7, 0, 10], [-29, 3, -5, 3, 0, 7, -3, -3, 0, -7], [1, 2, -8, 15, -1, -5, 15, -19, -8, -10], [19, -7, 9, -7, -5, 8, 12, 7, 0, -8], [7, -10, 0, -6, -6, 14, -10, -17, 7, 7], [21, 1, 0, 8, 8, 0, 1, -20, 4, 0], [-20, -1, -8, -1, -6, 3, 7, 1, 0, -3], [-23, 3, -17, 3, -9, -2, 6, -3, 0, 2], [7, 9, 0, -9, -9, 10, 9, 2, -8, 5], [7, 14, -20, -3, -7, -4, -3, 5, -20, -8], [-3, -6, -5, -11, 3, 5, -11, 6, -5, 10], [-5, -10, 11, 2, 5, -2, 2, -3, 11, -4], [4, 8, -5, 14, -4, -8, 14, -10, -5, -16], [-6, -10, 0, -7, -7, 10, -10, -4, -2, 5], [1, 2, 11, 10, -1, 1, 10, 7, 11, 2], [10, 14, 0, 8, 8, -4, 14, 4, -6, -2], [1, 4, 3, 4, -6, 0, 2, -4, 0, 0], [-13, 5, 0, 5, 5, 10, 5, 18, -3, 5], [2, 5, 0, 0, 0, -2, 5, 3, -19, -1], [-1, -2, -3, 5, 1, -8, 5, 8, -3, -16], [14, 28, -15, 6, -14, -3, 6, -18, -15, -6], [7, 14, -1, 12, -7, 2, 12, 8, -1, 4], [34, 9, 0, -7, -7, 2, 9, -25, -11, 1], [-16, -8, 0, -8, 11, 7, -3, 8, 0, -7], [12, -6, 0, -9, -9, 4, -6, -18, 3, 2], [-9, -18, -7, -23, 9, -4, -23, -7, -7, -8], [13, 1, -8, 1, 2, -10, -3, -1, 0, 10], [11, 5, 0, 7, 7, -16, 5, -6, -12, -8], [3, 6, 2, -7, -3, -4, -7, 1, 2, -8], [-11, 5, 2, 5, -5, 4, 0, -5, 0, -4], [6, 12, -3, 7, -6, 1, 7, -13, -3, 2], [-22, -7, 0, 16, 16, 4, -7, 15, 25, 2], [11, -10, 0, 6, 6, -8, -10, -21, -1, -4], [7, 6, -13, 6, -7, 2, 1, -6, 0, -2], [13, 26, 13, 10, -13, 7, 10, -9, 13, 14], [21, 9, 0, -1, -1, -24, 9, -12, 4, -12], [29, -1, -3, -1, -5, -2, 6, 1, 0, 2], [-3, -11, -5, -11, 5, 4, 6, 11, 0, -4], [-5, -1, 0, -1, -1, -14, -1, 4, 2, -7], [1, 2, -5, -4, -1, 3, -4, 23, -5, 6], [-54, -1, 0, -3, -3, -2, -1, 53, 2, -1], [-4, -8, 6, 5, 4, 3, 5, -21, 6, 6], [-5, -10, 9, -7, 5, -5, -7, -12, 9, -10], [4, 15, 0, 3, 3, 16, 15, 11, 3, 8], [-3, 6, 11, 6, -13, -3, 7, -6, 0, 3], [7, 3, 0, -4, -4, -16, 3, -4, -25, -8], [26, -6, -1, -6, 6, -8, 0, 6, 0, 8], [6, -8, 0, 11, 11, 2, -8, -14, 3, 1], [0, 14, 0, 7, 7, 10, 14, 14, 14, 5], [-39, 10, -11, 10, -8, -5, -2, -10, 0, 5], [-19, 4, -2, 4, 0, 12, -4, -4, 0, -12], [-37, -2, 0, -4, -4, 8, -2, 35, 10, 4], [9, 18, -10, 2, -9, 4, 2, -53, -10, 8], [1, -2, 0, 1, 1, 14, -2, -3, -2, 7], [18, 4, 0, -18, -18, 4, 4, -14, -16, 2], [-3, -6, 15, 12, 3, -4, 12, -2, 15, -8], [7, 14, 7, 9, -7, -6, 9, -16, 7, -12], [-5, -5, -8, -5, 7, -2, -2, 5, 0, 2], [4, 8, -15, 8, -4, -1, 8, 21, -15, -2], [11, -6, -2, -6, 1, -3, 5, 6, 0, 3], [-7, -14, 14, -13, 7, -6, -13, 14, 14, -12], [-3, 2, 0, 9, 9, -22, 2, 5, -5, -11], [-4, 6, 0, 7, 7, 6, 6, 10, -17, 3], [24, -9, 1, -9, 10, 7, -1, 9, 0, -7], [-57, 0, -1, 0, 3, 4, -3, 0, 0, -4], [11, 22, -7, 13, -11, 6, 13, -4, -7, 12], [-4, -6, 0, -7, -7, 0, -6, -2, 16, 0], [-12, -24, 8, -5, 12, 2, -5, 26, 8, 4], [14, -9, 0, -18, -18, 2, -9, -23, 1, 1], [7, 17, -5, 17, -11, -3, -6, -17, 0, 3], [36, -1, 0, 0, 0, 0, -1, -37, -11, 0], [-6, -1, 18, -1, 8, -4, -7, 1, 0, 4], [-8, -16, 10, -12, 8, -3, -12, 19, 10, -6], [2, 4, 4, 2, -2, 1, 2, -56, 4, 2], [-8, 7, -1, 7, -10, -5, 3, -7, 0, 5], [9, 1, 8, 1, 4, -1, -5, -1, 0, 1], [23, -2, 0, 13, 13, -2, -2, -25, -5, -1], [-2, -4, 13, -7, 2, 8, -7, 25, 13, 16], [24, -1, -4, -1, 2, -1, -1, 1, 0, 1], [0, 0, 11, 7, 0, -9, 7, -2, 11, -18], [18, -3, 0, 4, 4, -16, -3, -21, -1, -8], [-8, -16, -3, -5, 8, -3, -5, -25, -3, -6], [-2, -4, -7, 0, 2, -5, 0, -3, -7, -10], [-13, -2, 13, -2, 11, -6, -9, 2, 0, 6], [-38, -14, 0, 8, 8, -6, -14, 24, 8, -3], [-4, -8, -4, 12, 4, -8, 12, -24, -4, -16], [-12, 6, 6, 6, -17, -2, 11, -6, 0, 2], [-5, -10, -2, -11, 5, 7, -11, 41, -2, 14], [-4, 4, -17, 4, 8, 1, -12, -4, 0, -1], [3, 6, 19, -3, -3, 12, -3, -15, 19, 24], [25, 0, 0, 15, 15, -14, 0, -25, 8, -7], [-10, 0, -22, 0, 12, 0, -12, 0, 0, 0], [16, -2, -25, -2, 13, -1, -11, 2, 0, 1], [-14, -3, -6, -3, -18, 14, 21, 3, 0, -14], [0, 0, 15, 9, 0, 5, 9, 1, 15, 10], [-27, 8, 0, 8, 8, -22, 8, 35, -13, -11], [8, 16, -4, 17, -8, -8, 17, -18, -4, -16], [-10, -20, 0, 0, 10, 2, 0, 1, 0, 4], [22, -2, 0, 18, 18, 0, -2, -24, -8, 0], [-33, -7, 19, -7, 8, -3, -1, 7, 0, 3], [15, 13, 0, 8, 8, 8, 13, -2, -6, 4], [-2, 2, 0, 0, 0, 0, 2, 4, 1, 0], [-3, -6, 4, -5, 3, 7, -5, 38, 4, 14], [27, 0, 0, 10, 10, 4, 0, -27, 17, 2], [-7, -3, 0, 9, 9, 0, -3, 4, 8, 0], [6, 12, -9, 2, -6, 0, 2, 36, -9, 0], [-4, -8, -4, -9, 4, -6, -9, -12, -4, -12], [-30, 3, 11, 3, -17, 9, 14, -3, 0, -9], [7, -8, 12, -8, 16, 8, -8, 8, 0, -8], [9, 2, 0, 7, 7, 6, 2, -7, 3, 3], [41, 3, 0, -14, -14, 6, 3, -38, -8, 3], [-3, -6, -13, 10, 3, -14, 10, -25, -13, -28], [20, 14, 12, 14, -13, -6, -1, -14, 0, 6], [-2, -4, 9, 9, 2, 6, 9, -3, 9, 12], [6, 5, 14, 5, -7, 1, 2, -5, 0, -1], [-1, -2, -22, -8, 1, 11, -8, 11, -22, 22], [3, 6, -20, -2, -3, 2, -2, 16, -20, 4], [14, 11, 0, 12, 12, -6, 11, -3, -5, -3], [17, -5, -17, -5, 18, -2, -13, 5, 0, 2], [-5, 19, -2, 19, -6, -9, -13, -19, 0, 9], [-7, -14, 18, 6, 7, -1, 6, 24, 18, -2], [16, 6, 0, -1, -1, -26, 6, -10, -14, -13], [25, -5, 5, -5, -8, 14, 13, 5, 0, -14], [40, -3, 0, -9, -9, -8, -3, -43, -13, -4], [-8, -11, 0, -11, 8, -6, 3, 11, 0, 6], [-19, 6, 0, 2, 2, 20, 6, 25, 15, 10], [-16, -8, 0, 3, 3, -22, -8, 8, 1, -11], [-15, -30, 12, -13, 15, 4, -13, 4, 12, 8]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1232_q_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1232_2_q_o();".
// 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_1232_2_q_o(:prec:=10)
    chi := MakeCharacter_1232_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_1232_2_q_o();".
// 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_1232_2_q_o( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1232_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![9, 30, 112, 2, 83, 11, 43, 1, 8, 1, 1]>,<13,R![1, 12, 10, -39, -1, 1]>],Snew);
    return Vf;
end function;