
// Make newform 930.2.z.b in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_z();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_930_z_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_930_2_z_b();".
// 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_930_2_z_b();".
// 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, 6, 18, 44, 63, 46, 110, 120, -79, -120, 110, -46, 63, -44, 18, -6, 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], [-42999, -359371, 4650650, -1359926, -873725, 6615911, 3298328, -16079401, 15420868, -10751771, 8759897, -5698130, 2542453, -838945, 185843, -18722], [-629332, -1841688, -4477900, -5886168, -3759245, -10400187, -8317566, 6305807, 9525654, -8953028, 3505826, -4895655, 3474934, -1425885, 480599, -81136], [513063, 626822, 12844655, 9434107, 54055, 36771263, 45291284, -54539308, 3639454, 1487407, 7541156, 3613495, -5438846, 2668400, -1066126, 197674], [-1446151, -1975344, -4485370, -9300519, -3624410, -10526601, -23488953, -3525559, 39789357, -31215764, 18325103, -18261090, 11063617, -4308870, 1318367, -202723], [-482471, -1411609, -10678290, -11608004, -5841015, -17159506, -32680678, 18505491, 24116182, -21315414, 9398523, -13443350, 9367137, -3845335, 1270047, -208618], [-38786, -187100, -436540, -931050, -428460, -1503207, -2077970, 351590, 3045030, -2478180, 1318156, -1436140, 910990, -361140, 114030, -18068], [-878996, -1544709, -3809630, -8525809, -5416770, -7564856, -16631718, 7965031, 14902967, -13289049, 6432533, -8121210, 5456387, -2204690, 715962, -116478], [45616, 261608, 775534, 2015058, 280949, 2188490, 5005910, -19064, -7132500, 5584616, -3220296, 3354508, -2067724, 812178, -250784, 38786], [1934304, 6850076, 21804440, 35888671, 18549085, 60908954, 81825647, -40191574, -84472868, 72732346, -33844927, 43122850, -29116493, 11808575, -3857128, 629332], [145107, 335418, 972686, 2484148, 678181, 2195322, 5763042, -769120, -7091813, 5693440, -3201630, 3468822, -2177219, 860612, -268474, 41958], [-683537, -2607623, -5085725, -13185518, -6961040, -14305332, -24278411, -1142168, 42098584, -34032578, 19185661, -19527595, 12019889, -4702060, 1457174, -227516], [-12088, -45554, 7954, -2592859, 90154, -11850, -5492984, -3528836, 11058536, -8238056, 5452844, -4941532, 2819282, -1071872, 312482, -45616], [-1113587, -4043868, -10607445, -20606473, -10020190, -29123452, -49999671, 15035337, 58529849, -48495373, 25100526, -28945995, 18750324, -7495250, 2389864, -381541], [555224, 1692418, 4948608, 12730418, 4760148, 12269836, 30385624, -2702376, -40300156, 32272344, -18267510, 19409306, -12092649, 4764706, -1481454, 230968]];
    Rf_basisdens := [1, 1, 782325, 782325, 782325, 782325, 782325, 52155, 260775, 52155, 782325, 52155, 260775, 52155, 260775, 156465];
    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_930_z();"
function MakeCharacter_930_z()
    N := 930;
    order := 10;
    char_gens := [311, 187, 871];
    v := [10, 5, 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_930_z_Hecke();"
function MakeCharacter_930_z_Hecke(Kf)
    N := 930;
    order := 10;
    char_gens := [311, 187, 871];
    char_values := [[1, 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], [-1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1]];
    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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [1, -1, 1, 0, 0, 0, 1, 0, 1, -1, 0, 1, 1, 0, 1, 0], [-1, 0, 1, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, -1, -1, -1], [1, 0, 1, 0, 1, -1, 0, 0, 0, 1, -1, 0, -1, -1, -1, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0], [0, -2, 2, 0, -2, 0, 2, 0, 0, -2, 0, 0, 2, -2, 0, -2], [2, 0, 1, 0, 1, -1, 0, 1, -1, 0, -1, -4, -1, -1, -1, 2], [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0], [2, 1, 1, -1, 1, 0, 0, 1, 0, -1, -1, 4, -1, -1, -1, 1], [2, 0, 3, -1, 2, -2, 1, 1, 0, -3, -2, 0, -2, -2, -2, -2], [0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, -2, -3, 0, -3, 0], [3, 0, 1, 0, 1, -1, 0, 1, -1, 0, -1, -1, -1, -1, -1, 3], [-1, 0, 1, 0, -1, -1, 0, -1, -1, 0, -6, -1, -2, -1, -8, -1], [0, -2, 5, -5, -2, 0, -3, -3, 2, -4, 2, 2, -4, -2, -8, -2], [2, -3, 2, -2, -1, 2, 1, -2, 0, -1, 3, 0, 1, -1, -1, -1], [0, 1, 4, -4, 1, 0, 3, 3, 1, -6, -1, 3, -1, -1, -1, -3], [1, 4, -4, 0, 0, 4, -4, -1, 1, 4, 0, -4, 0, 0, 0, 0], [-1, 1, -4, 0, 0, -1, -1, 2, 2, -2, 3, 2, 6, 0, 6, 0], [-5, 0, 0, -1, -1, 1, 1, 1, 0, -7, 1, 6, 1, 1, 1, -7], [4, 0, -5, 1, 4, 4, 1, 0, -1, 5, -5, -1, -5, 4, 4, 4], [0, -3, 0, 1, -2, -1, 2, -1, 0, 2, 2, -1, 2, 2, 2, 2], [-1, 2, -1, 2, 1, -1, 0, 1, -1, 2, -3, -1, -5, 1, -1, 1], [1, 0, -2, 1, -1, 1, -1, 0, -1, 2, 1, -1, 1, 1, 1, -1], [-1, 0, -12, 0, -1, -1, 0, 0, 0, -1, 4, 0, 4, -1, -1, -1], [2, 3, 0, 0, 3, 0, -3, 0, 0, -1, -3, -2, -3, -3, -3, -1], [1, 3, -4, 3, 4, 1, 0, 4, 1, 3, -7, 1, 3, 4, 1, 4], [-4, 2, 2, 4, -2, -4, 2, 4, 0, -2, 4, 0, 2, -2, 0, -2], [0, -1, -5, 5, -1, 0, -4, -4, -1, 11, 1, -12, 1, 1, 1, 12], [5, 0, -2, -1, 5, 5, -1, 0, 1, 4, 3, 1, 3, 5, 5, 5], [0, -1, -5, -2, -1, 0, -1, -1, 1, -2, 1, 1, 6, -1, 5, -1], [-4, 0, 2, 2, 4, -4, -2, 0, -2, -2, -4, -2, -4, -4, -4, -4], [0, -3, 6, -6, -3, 0, -3, -3, 3, -6, 3, 3, -3, -3, -1, -3], [0, -4, -5, 5, -4, 0, -1, -1, -4, 9, 4, -7, 4, 4, 4, 7], [-7, -3, 3, 0, 0, -3, 3, 2, -2, -10, 0, 10, 0, 0, 0, 0], [-8, 0, -6, 3, -3, 3, -3, 0, -3, -5, 3, -3, 3, 3, 3, -4], [4, -4, 0, -4, 0, 4, 0, 0, 4, -4, 7, 4, 8, 0, 7, 0], [-1, 8, -5, 1, 7, -1, -7, 1, 0, 7, -13, 0, -7, 7, -2, 7], [-4, 1, 3, 1, -3, -4, 0, -3, -4, 1, -3, -4, -1, -3, -9, -3], [0, -1, 1, 5, -1, 0, 6, 6, 1, -2, 1, 1, 7, -1, 17, -1], [1, 0, 4, 1, 5, -5, -1, 0, -1, 2, -5, -1, -5, -5, -5, 11], [-15, 5, -5, 0, 0, 5, -5, -8, 8, -9, 0, 9, 0, 0, 0, 0], [-12, 4, -4, 0, 0, 4, -4, -4, 4, -8, 0, 8, 0, 0, 0, 0], [7, 0, -6, 0, 7, 7, 0, 0, 0, 7, 2, 0, 2, 7, 7, 7], [5, 0, -3, 0, 5, 5, 0, 0, 0, 5, -3, 0, -3, 5, 5, 5], [0, 1, -4, 4, 1, 0, -5, -5, 1, -3, -1, 6, -1, -1, -1, -6], [4, 8, -8, 0, 0, 8, -8, 1, -1, -6, 0, 6, 0, 0, 0, 0], [1, -1, 4, 0, 0, 1, 1, -11, -11, 11, -3, -11, -14, 0, -14, 0], [-1, 2, -1, 2, 1, -1, 0, 1, -1, 2, 7, -1, 11, 1, 9, 1], [-10, -1, 2, 1, 2, -3, 0, 2, -3, 1, -2, 6, -2, -2, -2, -9], [0, -4, 11, -1, -4, 0, 3, 3, 4, -8, 4, 4, 0, -4, 2, -4], [-4, -4, 0, 2, -2, -2, 2, -2, 0, -8, 2, 2, 2, 2, 2, -8], [-10, 0, -2, 2, 0, 0, -2, 0, -2, -8, 0, -2, 0, 0, 0, -6], [0, -1, 3, -3, -1, 0, 4, 4, -1, -8, 1, 5, 1, 1, 1, -5], [6, -3, -4, -6, 3, 6, -3, -6, 0, 3, 11, 0, -3, 3, 1, 3], [0, -5, 4, -6, -5, 0, -1, -1, 5, -10, 5, 5, 5, -5, 5, -5], [-7, 15, 6, -15, 6, 9, 0, 6, 9, -15, -6, 11, -6, -6, -6, -22], [-11, 0, 0, 1, 1, -1, -1, -1, 0, -10, -1, 10, -1, -1, -1, -10], [-6, 6, 0, 6, 0, -6, 0, 0, -6, 6, 2, -6, -10, 0, 2, 0], [-1, -5, -2, 5, -2, -3, 0, -2, -3, 5, 2, -11, 2, 2, 2, 4], [3, 0, 8, 3, 3, 3, 3, 0, -3, 6, 4, -3, 4, 3, 3, 3], [-4, -2, 12, 4, -6, -4, 6, 4, 0, -6, 2, 0, 6, -6, -6, -6], [0, -7, 8, -7, -7, 0, 0, 0, 7, -14, 7, 7, 6, -7, 5, -7], [2, -6, 6, 0, 0, -6, 6, -5, 5, 13, 0, -13, 0, 0, 0, 0], [0, 11, -8, 7, 11, 0, -4, -4, -11, 22, -11, -11, -18, 11, 0, 11], [1, 0, -8, -1, 1, 1, -1, 0, 1, 0, -9, 1, -9, 1, 1, 1], [0, 14, 10, -14, 10, 4, 0, 10, 4, -14, -10, 12, -10, -10, -10, -14], [-1, 0, 16, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, -1, -1, -1], [6, -6, 4, 0, 0, 6, 6, -5, -5, 5, 2, -5, 0, 0, 0, 0], [9, 3, 0, -3, 0, 3, 0, 3, 0, 11, 0, -6, 0, 0, 0, 11], [-4, 1, 3, 1, -3, -4, 0, -3, -4, 1, 5, -4, 3, -3, -1, -3], [0, -10, -6, 6, -10, 0, 4, 4, -10, 14, 10, -6, 10, 10, 10, 6], [-4, 4, 2, 0, 0, -4, -4, -8, -8, 8, -6, -8, -4, 0, -4, 0], [-4, 4, -11, 0, 0, -4, -4, -2, -2, 2, 7, -2, -10, 0, -10, 0], [10, 0, -6, -3, -9, 9, 3, 0, 3, 7, 9, 3, 9, 9, 9, -13], [8, 0, -11, -7, 8, 8, -7, 0, 7, 1, 4, 7, 4, 8, 8, 8], [11, 5, 0, -13, -8, 13, 8, 13, 0, -8, 8, 2, 8, 8, 8, -8], [6, -6, 7, 0, 0, 6, 6, 0, 0, 0, -1, 0, -10, 0, -10, 0], [17, 1, 0, -1, 0, 1, 0, 0, 1, -1, 0, -21, 0, 0, 0, 16], [-4, 4, -4, 0, 0, 4, -4, -6, 6, -2, 0, 2, 0, 0, 0, 0], [0, -3, -5, 5, -3, 0, -2, -2, -3, 2, 3, -11, 3, 3, 3, 11], [0, -9, -3, 3, -9, 0, 6, 6, -9, -5, 9, -8, 9, 9, 9, 8], [0, -5, 3, -3, -5, 0, 8, 8, -5, 0, 5, 11, 5, 5, 5, -11], [1, -1, 11, 0, 0, 1, 1, 4, 4, -4, -10, 4, 5, 0, 5, 0], [5, -9, 9, 0, 0, -9, 9, -3, 3, 0, 0, 0, 0, 0, 0, 0], [4, 3, -4, -4, 7, 4, -7, -4, 0, 7, 7, 0, -7, 7, -3, 7], [0, 0, 5, -5, 0, 0, 5, 5, 0, 0, 0, 6, 0, 0, 0, -6], [-2, -2, -14, 2, -4, -2, 4, 2, 0, -4, 18, 0, 4, -4, 18, -4], [17, 0, -5, 2, -3, 3, -2, 0, -2, 19, 3, -2, 3, 3, 3, 25], [-9, 6, 3, 6, -3, -9, 0, -3, -9, 6, -22, -9, -11, -3, -28, -3], [2, -3, 1, -3, -1, 2, 0, -1, 2, -3, -11, 2, -13, -1, -13, -1], [-14, 6, 0, -2, 4, 2, -4, 2, 0, -8, -4, 16, -4, -4, -4, -8], [-6, 5, 19, 6, -1, -6, 1, 6, 0, -1, -23, 0, 1, -1, -18, -1], [-8, -4, 4, 0, 0, -4, 4, -1, 1, 9, 0, -9, 0, 0, 0, 0], [0, 5, 14, -14, 5, 0, 9, 9, 5, -38, -5, 20, -5, -5, -5, -20], [-2, 0, 7, -5, -2, -2, -5, 0, 5, -7, 8, 5, 8, -2, -2, -2], [0, 8, 0, 0, 8, 0, -8, -8, 8, 4, -8, 6, -8, -8, -8, -6], [18, 2, -2, 0, 0, 2, -2, -1, 1, 11, 0, -11, 0, 0, 0, 0], [7, 0, -8, 5, 7, 7, 5, 0, -5, 12, -12, -5, -12, 7, 7, 7], [15, -5, 0, 4, -1, -4, 1, -4, 0, 35, 1, -19, 1, 1, 1, 35], [-2, 0, -10, 5, -2, -2, 5, 0, -5, 3, 11, -5, 11, -2, -2, -2], [-12, 12, -2, 0, 0, -12, -12, -2, -2, 2, -10, -2, -10, 0, -10, 0], [-4, 4, -10, 0, 0, -4, -4, 6, 6, -6, 6, 6, -4, 0, -4, 0], [-4, 0, 9, -15, -6, 6, 15, 0, 15, -19, 6, 15, 6, 6, 6, -4], [0, 6, 2, -2, 6, 0, -4, -4, 6, -8, -6, 8, -6, -6, -6, -8], [14, -9, -5, -9, 5, 14, 0, 5, 14, -9, 18, 14, 4, 5, 28, 5], [-16, 16, 0, 16, 0, -16, 0, 0, -16, 16, -20, -16, -20, 0, -20, 0], [-4, 0, -8, 12, -4, -4, 12, 0, -12, 8, 6, -12, 6, -4, -4, -4], [14, -4, 0, 4, 0, -4, 0, 0, -4, 4, 0, -24, 0, 0, 0, 18], [5, 6, 6, -6, 6, 0, 0, 6, 0, -6, -6, -8, -6, -6, -6, -1], [0, -5, 3, -14, -5, 0, -9, -9, 5, -10, 5, 5, -2, -5, 5, -5], [4, 0, 7, 6, 4, 4, 6, 0, -6, 10, -11, -6, -11, 4, 4, 4], [0, -2, -15, -5, -2, 0, -3, -3, 2, -4, 2, 2, 16, -2, 14, -2], [6, -1, 1, 0, 0, -1, 1, -1, 1, -4, 0, 4, 0, 0, 0, 0], [-5, 0, 13, -7, 6, -6, 7, 0, 7, -12, -6, 7, -6, -6, -6, -20], [-11, -9, -4, 9, -4, -5, 0, -4, -5, 9, 4, 11, 4, 4, 4, -2], [11, -19, 15, -11, -8, 11, 8, -11, 0, -8, 15, 0, 8, -8, -7, -8], [4, 0, 10, -2, 4, 4, -2, 0, 2, 2, -18, 2, -18, 4, 4, 4], [10, -8, -2, -8, 2, 10, 0, 2, 10, -8, 26, 10, 16, 2, 30, 2], [1, 20, 0, -11, 9, 11, -9, 11, 0, -11, -9, 10, -9, -9, -9, -11], [-9, -17, -1, 17, -1, -16, 0, -1, -16, 17, 1, -2, 1, 1, 1, 8], [-3, 7, -9, 3, 4, -3, -4, 3, 0, 4, -14, 0, -4, 4, 5, 4], [3, -3, -29, 0, 0, 3, 3, -1, -1, 1, 32, -1, 14, 0, 14, 0], [13, -13, -15, 0, 0, 13, 13, 8, 8, -8, 28, 8, 34, 0, 34, 0], [12, 10, 0, -1, 9, 1, -9, 1, 0, -17, -9, -11, -9, -9, -9, -17], [2, -3, 3, 3, 3, -6, 0, 3, -6, 3, -3, 18, -3, -3, -3, 5], [-20, 0, -14, 10, -4, 4, -10, 0, -10, -10, 4, -10, 4, 4, 4, -4], [-8, 14, -14, 0, 0, 14, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -2, 0, -4, 2, 4, -2, -4, 0, 2, -8, 0, -2, 2, -2, 2], [-4, 0, 14, 8, -4, -4, 8, 0, -8, 4, -26, -8, -26, -4, -4, -4], [16, -11, 11, 0, 0, -11, 11, 1, -1, 0, 0, 0, 0, 0, 0, 0], [-11, 11, -1, 0, 0, -11, -11, 4, 4, -4, -10, 4, -4, 0, -4, 0], [-12, 0, -8, 4, -4, 4, -4, 0, -4, -8, 4, -4, 4, 4, 4, 4], [0, -14, 13, -16, -14, 0, -2, -2, 14, -28, 14, 14, 13, -14, 2, -14], [16, -5, 0, -2, -7, 2, 7, 2, 0, 23, 7, -14, 7, 7, 7, 23], [6, 14, -14, 0, 0, 14, -14, -8, 8, 9, 0, -9, 0, 0, 0, 0], [-3, 9, -6, 9, 6, -3, 0, 6, -3, 9, 10, -3, 34, 6, 22, 6], [14, -14, 0, -14, 0, 14, 0, 0, 14, -14, 22, 14, 20, 0, 22, 0], [5, -2, -2, -5, 3, 5, -3, -5, 0, 3, -11, 0, -3, 3, -1, 3], [0, 1, -15, 15, 1, 0, -16, -16, 1, 18, -1, -13, -1, -1, -1, 13], [8, -12, 12, 0, 0, -12, 12, -10, 10, -12, 0, 12, 0, 0, 0, 0], [0, -4, 2, -2, -4, 0, 6, 6, -4, 10, 4, -14, 4, 4, 4, 14], [8, 7, -15, -8, 15, 8, -15, -8, 0, 15, -17, 0, -15, 15, 0, 15], [7, 1, -8, 1, 8, 7, 0, 8, 7, 1, -10, 7, 4, 8, 6, 8], [3, -7, 0, 10, 3, -10, -3, -10, 0, 23, -3, -13, -3, -3, -3, 23], [-21, -17, -12, 17, -12, -5, 0, -12, -5, 17, 12, -19, 12, 12, 12, -4], [0, 12, -4, 12, 12, 0, 0, 0, -12, 24, -12, -12, -20, 12, -28, 12], [6, 0, -3, 13, 6, 6, 13, 0, -13, 19, 10, -13, 10, 6, 6, 6], [-14, 15, 0, 0, 15, 0, -15, 0, 0, -10, -15, 14, -15, -15, -15, -10], [5, -5, 17, 0, 0, 5, 5, -2, -2, 2, -12, -2, -36, 0, -36, 0], [-2, 4, 16, 2, 2, -2, -2, 2, 0, 2, -2, 0, -2, 2, -18, 2], [0, -7, 3, -3, -7, 0, 10, 10, -7, 4, 7, 5, 7, 7, 7, -5], [0, 7, 15, 4, 7, 0, -3, -3, -7, 14, -7, -7, -32, 7, -16, 7], [-1, 9, -8, 9, 8, -1, 0, 8, -1, 9, -12, -1, -10, 8, 4, 8], [-11, 1, -1, 11, -10, -11, 10, 11, 0, -10, 31, 0, 10, -10, 11, -10], [-2, -10, 0, 10, 0, -10, 0, 0, -10, 10, 0, 22, 0, 0, 0, 8], [3, 0, -13, -3, -16, 16, 3, 0, 3, 0, 16, 3, 16, 16, 16, 14], [-2, 0, 0, 0, 0, 0, 0, -13, 13, -15, 0, 15, 0, 0, 0, 0], [4, 0, -13, -7, 4, 4, -7, 0, 7, -3, -5, 7, -5, 4, 4, 4], [18, 0, 9, -5, 4, -4, 5, 0, 5, 13, -4, 5, -4, -4, -4, -16], [-15, 6, -8, 15, -9, -15, 9, 15, 0, -9, 15, 0, 9, -9, 17, -9], [-13, 16, 10, 13, 3, -13, -3, 13, 0, 3, -21, 0, -3, 3, -13, 3], [-4, 4, 12, 0, 0, -4, -4, 5, 5, -5, -16, 5, 11, 0, 11, 0], [5, -19, -8, 19, -8, -11, 0, -8, -11, 19, 8, -1, 8, 8, 8, 24], [0, -13, 4, -4, -13, 0, 9, 9, 13, -26, 13, 13, 31, -13, 15, -13], [13, 0, -10, -13, 13, 13, -13, -13, 0, 13, -11, 0, -13, 13, -3, 13], [32, -3, 3, 0, 0, -3, 3, 0, 0, 3, 0, -3, 0, 0, 0, 0], [-8, 8, -4, 0, 0, -8, -8, -8, -8, 8, -4, -8, -11, 0, -11, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_930_z_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_930_2_z_b();".
// 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_930_2_z_b(:prec:=16)
    chi := MakeCharacter_930_z();
    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_930_2_z_b();".
// 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_930_2_z_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_z();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![121, 0, -11, 0, 16, 0, -6, 0, 1]>],Snew);
    return Vf;
end function;