
// Make newform 927.2.o.a in Magma, downloaded from the LMFDB on 27 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_927_o();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_927_o_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_927_2_o_a();".
// 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_927_2_o_a();".
// 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, -60, 0, 3553, 0, -2796, 0, 1488, 0, -444, 0, 97, 0, -12, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1498291, 0, 23727, 0, -1405008, 0, -99276, 0, -496980, 0, 126720, 0, -31123, 0, 1551, 0], [0, -32461655, 0, -57520, 0, 3406080, 0, -3772620, 0, 1204800, 0, -307200, 0, 39433, 0, -3760], [-24311591, 0, -57520, 0, 3406080, 0, -3772620, 0, 1204800, 0, -307200, 0, 39433, 0, -3760, 0], [-135698, 0, -2157, 0, 127728, 0, -112086, 0, 45180, 0, -11520, 0, 1642, 0, -141, 0], [0, -121145912, 0, -373161, 0, 22096944, 0, -23074080, 0, 7816140, 0, -1992960, 0, 257944, 0, -24393], [20633, 0, -89922237, 0, 72993408, 0, -38999004, 0, 11400444, 0, -2549712, 0, 315641, 0, -29085, 0], [0, -232092825, 0, -913130, 0, 54071520, 0, -54032484, 0, 19126200, 0, -4876800, 0, 647223, 0, -59690], [0, -108476, 0, 489043273, 0, -383755776, 0, 205033488, 0, -61231644, 0, 13404864, 0, -1659452, 0, 138601], [-8258540, 0, 489043273, 0, -383755776, 0, 205033488, 0, -61231644, 0, 13404864, 0, -1659452, 0, 138601, 0], [132869, 0, -611652765, 0, 470050944, 0, -251139372, 0, 74454348, 0, -16419216, 0, 2032613, 0, -173373, 0], [192559, 0, -847326990, 0, 681216384, 0, -363961092, 0, 109240584, 0, -23795376, 0, 2945743, 0, -242430, 0], [0, -108476, 0, 487005757, 0, -383755776, 0, 205033488, 0, -61231644, 0, 13404864, 0, -1659452, 0, 138601], [0, -405845, 0, 1817590396, 0, -1435758720, 0, 767098860, 0, -229163100, 0, 50152080, 0, -6208565, 0, 518332], [0, -1924415, 0, 8606731847, 0, -6808007040, 0, 3637390020, 0, -1087124628, 0, 237808560, 0, -29439455, 0, 2454359]];
    Rf_basisdens := [1, 1, 8150064, 8150064, 8150064, 78366, 8150064, 8150064, 8150064, 8150064, 8150064, 8150064, 8150064, 2037516, 2037516, 8150064];
    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_927_o();"
function MakeCharacter_927_o()
    N := 927;
    order := 6;
    char_gens := [722, 829];
    v := [3, 5];
    // 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_927_o_Hecke();"
function MakeCharacter_927_o_Hecke(Kf)
    N := 927;
    order := 6;
    char_gens := [722, 829];
    char_values := [[-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, -1, 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, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, -2, 0, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1], [3, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -1, 0, 0, 1, 0, 1, -2, 0, 0, 0, -2, 2, 1], [0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 3, 0], [0, -2, 0, -2, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0], [2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0], [0, -2, 0, -4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -1, 0, -2, 1, 0, -1, 0, 0, 2, -2, -1, 0, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, -2, 2, 1], [0, 0, 0, -3, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -4, 0, 0, -4, 0, 2, 0, 0, -3, 0, 2, 0, 0, 0], [0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, -2, 0], [1, 0, -2, 0, 2, -1, 0, 4, 0, 0, 2, -4, -2, 0, 0, 0], [6, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, -4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 2, -4, 0], [0, 0, -2, 0, 2, -4, 0, 2, 0, 0, 3, -2, 2, 0, 0, 0], [0, 0, 0, -2, 0, 0, -1, 0, 2, 0, 0, 0, 0, -8, 2, 4], [11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, -7, 0, 0, 4, 0, -6, 0, 0, 0, 0, -1, -2, -6], [2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, -4, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, -1, 3, 2], [-1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0], [0, -2, 0, -1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, -4, 0], [-11, 0, 0, 0, 0, 0, 0, 3, 0, 0, -11, 6, 0, 0, 0, 0], [0, 4, 0, -8, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 2, 0, 2, -3, 0, 2, 0, 0, -2, 2, -1, 0, 0, 0], [2, 0, -1, 0, 0, 4, 0, -1, 0, 0, 1, 0, 4, 0, 0, 0], [0, 0, -1, 0, 0, -8, 0, 1, 0, 0, -1, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -2, -1, 3], [0, 0, 0, -3, 0, 0, -1, 0, 3, 0, 0, 0, 0, 6, -2, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 5, 5, -2], [4, 0, -1, 0, -2, 5, 0, -1, 0, 0, 2, -2, 3, 0, 0, 0], [0, -2, 0, -2, 0, 0, -1, 0, 2, -2, 0, 0, 0, 4, -1, -2], [2, 0, 2, 0, -4, 4, 0, -4, 0, 0, 4, 8, 0, 0, 0, 0], [0, 16, 0, -2, 0, 0, -4, 0, -2, -8, 0, 0, 0, 0, -3, -1], [-1, 0, 4, 0, 0, 4, 0, -2, 0, 0, 1, 0, -2, 0, 0, 0], [3, 0, -4, 0, 4, -16, 0, 2, 0, 0, -3, -2, 6, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, -2, 0, 0, 0], [0, -2, 0, -4, 0, 0, -3, 0, -2, -2, 0, 0, 0, 2, 5, 2], [-15, 0, 2, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, -22, 0, 0, 10, 0, -8, -2, 0, 0, 0, -7, 1, -4], [0, 6, 0, -3, 0, 0, -4, 0, 2, -6, 0, 0, 0, -5, -2, 2], [2, 0, -2, 0, 6, -6, 0, -2, 0, 0, 1, 6, 0, 0, 0, 0], [0, 2, 0, 6, 0, 0, 2, 0, -1, 2, 0, 0, 0, -7, -1, 1], [0, 2, 0, 0, 0, 0, -4, 0, 3, 2, 0, 0, 0, 3, 1, -3], [0, -2, 0, 4, 0, 0, -5, 0, -2, 4, 0, 0, 0, 12, -14, -4], [0, 8, 0, 4, 0, 0, -11, 0, 0, -8, 0, 0, 0, 4, -11, 0], [6, 0, 2, 0, 8, 2, 0, -1, 0, 0, -6, -4, -5, 0, 0, 0], [1, 0, -4, 0, -8, 0, 0, 2, 0, 0, -1, 4, 4, 0, 0, 0], [0, 0, 0, 6, 0, 0, -4, 0, -1, 0, 0, 0, 0, 14, -10, -2], [8, 0, 4, 0, -2, 3, 0, 4, 0, 0, 4, -2, 1, 0, 0, 0], [0, 2, 0, -8, 0, 0, 5, 0, -2, -4, 0, 0, 0, -12, 6, -4], [2, 0, -4, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0], [0, -2, 0, 13, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 4, 0, 0, -3, -6, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -1, 2, -5], [-3, 0, -1, 0, 0, 1, 0, 2, 0, 0, -6, 0, -2, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 18, 0, -1, 0, 0, 0], [0, 8, 0, 2, 0, 0, -7, 0, 0, -8, 0, 0, 0, 2, -7, 0], [8, 0, -4, 0, 4, -6, 0, 2, 0, 0, -8, -2, 1, 0, 0, 0], [0, -4, 0, 8, 0, 0, -2, 0, 3, 8, 0, 0, 0, 10, 2, 6], [0, 0, 0, -4, 0, 0, -14, 0, 3, 0, 0, 0, 0, -7, -11, 3], [6, 0, 0, 0, 0, 0, 0, -5, 0, 0, 6, 6, -3, 0, 0, 0], [-15, 0, 5, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 0, -4, -6, 0, -3, 0, 0, -6, 2, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 0, -10, 6, 10], [0, -4, 0, 0, 0, 0, 16, 0, -8, 2, 0, 0, 0, 4, 4, -4], [4, 0, 0, 0, 4, 14, 0, 0, 0, 0, -4, -2, -9, 0, 0, 0], [0, 4, 0, 1, 0, 0, -15, 0, 3, -4, 0, 0, 0, -2, -12, 3], [-20, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -5, 0, 0, -8, 0, 0, -2, 0, 0, 0, -5, -8, 0], [-7, 0, 3, 0, -12, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 11, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 2, 0, 0, -2, 0, -1, 0, 0, 8, 0, 1, 0, 0, 0], [3, 0, -3, 0, -4, -3, 0, 6, 0, 0, 6, 8, 14, 0, 0, 0], [0, 8, 0, -2, 0, 0, -12, 0, 6, -4, 0, 0, 0, -4, -3, 3], [0, 8, 0, -10, 0, 0, 10, 0, 4, -4, 0, 0, 0, -7, 7, 2], [0, 0, 2, 0, 8, 2, 0, -1, 0, 0, 0, -4, -5, 0, 0, 0], [0, 0, 0, 7, 0, 0, -10, 0, -6, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, 8, -6, 0, 2, 0, 0, 0, -4, -1, 0, 0, 0], [0, 4, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 8, 0, 0, -5, 0, 4, -2, 0, 0, 0, -4, 1, -4], [2, 0, 1, 0, 0, -6, 0, 1, 0, 0, 1, 0, -6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -1, 7, -10], [6, 0, 3, 0, 0, 6, 0, 3, 0, 0, 3, 0, 6, 0, 0, 0], [0, 6, 0, -4, 0, 0, 4, 0, -9, -6, 0, 0, 0, 5, -5, -9], [0, -2, 0, 12, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 6, 0, 0, -2, 0, 1, 4, 0, 0, 0, 10, -2, 2], [-2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 6, -18, 0, 2, 0, 0, 9, -6, 12, 0, 0, 0], [-6, 0, 0, 0, 0, 0, 0, -5, 0, 0, -6, -10, -17, 0, 0, 0], [0, 0, 0, 16, 0, 0, 8, 0, 4, 0, 0, 0, 0, 6, 6, 2], [0, 0, 0, 5, 0, 0, -11, 0, 3, 0, 0, 0, 0, 4, -16, 6], [0, 0, 0, -5, 0, 0, -8, 0, 2, 0, 0, 0, 0, -14, -12, 4], [2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, -8, -5, 0, 0, 0], [-10, 0, -4, 0, -2, 0, 0, -4, 0, 0, -5, -2, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 1, 11, 6], [0, -4, 0, 8, 0, 0, -3, 0, 0, 8, 0, 0, 0, 16, -6, 0], [0, 2, 0, -4, 0, 0, -9, 0, 0, -4, 0, 0, 0, -8, -18, 0], [-1, 0, -4, 0, 4, -4, 0, 2, 0, 0, 1, -2, 0, 0, 0, 0], [-7, 0, 0, 0, 0, 0, 0, -3, 0, 0, -7, 4, 10, 0, 0, 0], [9, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9, 8, 22, 0, 0, 0], [0, 16, 0, -6, 0, 0, -10, 0, 0, -8, 0, 0, 0, -3, -5, 0], [-14, 0, 9, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 15, -18, -3], [0, 0, -8, 0, 0, -11, 0, 8, 0, 0, 6, 0, 11, 0, 0, 0], [0, -8, 0, 7, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, -4, 0, 0, 12, 0, -1, 12, 0, 0, 0, -6, 22, -2], [0, -2, 0, 22, 0, 0, -14, 0, 3, 0, 0, 0, 0, 0, 0, 0], [-26, 0, -4, 0, 4, 2, 0, -4, 0, 0, -13, 4, 6, 0, 0, 0], [0, 0, -2, 0, 12, -18, 0, 2, 0, 0, 3, -12, 6, 0, 0, 0], [0, -8, 0, 4, 0, 0, 1, 0, 12, 0, 0, 0, 0, 0, 0, 0], [0, 10, 0, 1, 0, 0, -7, 0, -1, 10, 0, 0, 0, -2, 8, 1], [-7, 0, 6, 0, 0, 3, 0, -12, 0, 0, -14, 0, -6, 0, 0, 0], [0, 6, 0, -14, 0, 0, 14, 0, -3, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, 0, 0, 0, -5, 0, 0, -9, 12, 8, 0, 0, 0], [0, 2, 0, 6, 0, 0, 0, 0, -1, -4, 0, 0, 0, 14, -2, -2], [-14, 0, -1, 0, -4, -2, 0, -1, 0, 0, -7, -4, -6, 0, 0, 0], [-3, 0, -10, 0, 4, 8, 0, 5, 0, 0, 3, -2, -6, 0, 0, 0], [0, 0, 0, 0, 4, 3, 0, 0, 0, 0, 4, -4, -7, 0, 0, 0], [0, -8, 0, -2, 0, 0, 10, 0, -8, 4, 0, 0, 0, 3, 1, -4], [12, 0, 8, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, -11, 0, 0, 6, -6, -13, 0, 0, 0], [0, -8, 0, -1, 0, 0, 6, 0, 4, -8, 0, 0, 0, 5, -10, -4], [-4, 0, -3, 0, 0, -5, 0, -3, 0, 0, -2, 0, -5, 0, 0, 0], [0, -6, 0, -7, 0, 0, 1, 0, 9, 6, 0, 0, 0, -16, 10, 9], [-15, 0, -13, 0, 6, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -16, 15, 15], [0, -2, 0, -4, 0, 0, 6, 0, -7, -2, 0, 0, 0, -3, 1, 7], [18, 0, 4, 0, -2, 4, 0, -8, 0, 0, 36, 4, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 8, 12], [6, 0, 3, 0, 2, 0, 0, -6, 0, 0, 12, -4, -4, 0, 0, 0], [0, -4, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, -1, -1], [9, 0, -14, 0, 8, -24, 0, 7, 0, 0, -9, -4, 8, 0, 0, 0], [0, -6, 0, 9, 0, 0, -1, 0, -1, 6, 0, 0, 0, 10, -2, -1], [0, 0, -9, 0, -12, 9, 0, 9, 0, 0, -4, 12, 3, 0, 0, 0], [0, 8, 0, 17, 0, 0, -28, 0, 6, -8, 0, 0, 0, 11, -22, 6], [-12, 0, 8, 0, -8, 9, 0, 8, 0, 0, -6, -8, 1, 0, 0, 0], [0, -8, 0, 30, 0, 0, -20, 0, 2, 4, 0, 0, 0, 14, -9, 1], [-9, 0, 2, 0, -8, -16, 0, -1, 0, 0, 9, 4, 12, 0, 0, 0], [0, 6, 0, 3, 0, 0, 2, 0, 4, -12, 0, 0, 0, -2, 12, 8], [0, 0, -2, 0, 6, 1, 0, 2, 0, 0, 24, -6, -7, 0, 0, 0], [0, -12, 0, -10, 0, 0, 25, 0, 0, 12, 0, 0, 0, -10, 25, 0], [0, 0, -2, 0, 18, -13, 0, 2, 0, 0, 0, -18, -5, 0, 0, 0], [0, 2, 0, -11, 0, 0, 2, 0, -2, -4, 0, 0, 0, -18, 0, -4], [0, 0, 4, 0, 2, 0, 0, -8, 0, 0, 0, -4, -4, 0, 0, 0], [0, 0, 0, -9, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 0, 0, -4, 10, 0, 0, 0, 0, -24, 8, -12, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 7, -1, -6], [0, 0, 0, 12, 0, 0, -1, 0, 4, 0, 0, 0, 0, 16, 6, 8], [0, 2, 0, -7, 0, 0, -21, 0, -3, 0, 0, 0, 0, 0, 0, 0], [4, 0, -6, 0, -8, 10, 0, 3, 0, 0, -4, 4, -1, 0, 0, 0], [0, -14, 0, -1, 0, 0, 11, 0, -3, 28, 0, 0, 0, 4, 16, -6], [0, -10, 0, 19, 0, 0, -11, 0, -3, 10, 0, 0, 0, 22, -14, -3], [0, -4, 0, -19, 0, 0, 7, 0, -5, 4, 0, 0, 0, -14, 2, -5], [-4, 0, 6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-13, 0, 8, 0, 12, 0, 0, -4, 0, 0, 13, -6, -6, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_927_o_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_927_2_o_a();".
// 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_927_2_o_a(:prec:=16)
    chi := MakeCharacter_927_o();
    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_927_2_o_a();".
// 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_927_2_o_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_927_o();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1, 0, -60, 0, 3553, 0, -2796, 0, 1488, 0, -444, 0, 97, 0, -12, 0, 1]>],Snew);
    return Vf;
end function;