
// Make newform 6030.2.d.j in Magma, downloaded from the LMFDB on 03 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6030_d();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_6030_d_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_6030_2_d_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_6030_2_d_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 := [4, 0, 16036, 0, 41293, 0, 36772, 0, 16111, 0, 3876, 0, 519, 0, 36, 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, 10321564, 0, 27059854, 0, 21144180, 0, 7499857, 0, 1353680, 0, 123508, 0, 5016, 0, 57], [0, -12228614, 0, -31840219, 0, -27049648, 0, -11058568, 0, -2461588, 0, -305161, 0, -19730, 0, -516], [329028, 0, 677236, 0, -5874285, 0, -7255081, 0, -3175738, 0, -636150, 0, -58425, 0, -1977, 0], [0, 30680424, 0, 57554006, 0, 25401519, 0, -65241, 0, -2456754, 0, -610472, 0, -58425, 0, -1977], [-230080, -9303280, -2775104, -25460810, -4390814, -24359801, -2787975, -11245706, -912120, -2795276, -159030, -380804, -13658, -26603, -447, -740], [332792, -9303280, 2775104, -25460810, 4390814, -24359801, 2787975, -11245706, 912120, -2795276, 159030, -380804, 13658, -26603, 447, -740], [0, -4830228, 0, -23101196, 0, -37106779, 0, -23349573, 0, -7104130, 0, -1114754, 0, -86251, 0, -2585], [0, 85883832, 0, 210318866, 0, 171560325, 0, 67408995, 0, 14314902, 0, 1674352, 0, 101193, 0, 2463], [-151268, 0, 11363520, 0, 26438303, 0, 18326919, 0, 5759508, 0, 912924, 0, 70745, 0, 2117, 0], [611668, 0, -15315920, 0, -37492323, 0, -28440475, 0, -9775258, 0, -1675058, 0, -138243, 0, -4343, 0], [881532, 0, 26403696, 0, 56465971, 0, 39719383, 0, 12952366, 0, 2139046, 0, 172071, 0, 5311, 0], [0, -9441406, 0, -31892425, 0, -39944865, 0, -22989322, 0, -6827302, 0, -1074603, 0, -84227, 0, -2562], [1155036, 0, -23205608, 0, -62897213, 0, -47211081, 0, -15835558, 0, -2653638, 0, -215245, 0, -6677, 0], [0, 33771266, 0, 92797759, 0, 89653347, 0, 42318483, 0, 10838358, 0, 1525895, 0, 110029, 0, 3147], [203436, 0, -57051452, 0, -128998247, 0, -92396805, 0, -30433338, 0, -5060170, 0, -409079, 0, -12673, 0]];
    Rf_basisdens := [1, 102712, 102712, 205424, 205424, 102712, 102712, 205424, 205424, 102712, 205424, 205424, 102712, 205424, 102712, 205424];
    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_6030_d();"
function MakeCharacter_6030_d()
    N := 6030;
    order := 2;
    char_gens := [4691, 1207, 3151];
    v := [1, 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_6030_d_Hecke();"
function MakeCharacter_6030_d_Hecke(Kf)
    N := 6030;
    order := 2;
    char_gens := [4691, 1207, 3151];
    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, 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]];
    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 := [[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], [-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, 1, 0, 0, 0], [-1, 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, -1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0], [-1, 0, 0, 0, 0, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, 0, 1, -1, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0], [0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 1], [0, 0, 0, -2, 0, 1, -1, 0, 0, 1, 1, 0, 0, 1, 0, -1], [-1, 0, 0, 0, 0, 1, 1, 1, -1, 0, 0, 0, 0, 0, 3, 0], [-2, 1, 1, 0, -1, 2, 2, 0, -1, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0], [-2, 1, 1, 0, -1, 2, 2, -2, 1, 0, 0, 0, 1, 0, 0, 0], [-2, 2, 2, 0, -1, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, -1, 1, -1, 0, 1, 0, 0, -1, 0, -1, 0, 1, 1], [0, 0, -3, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, -2, 0], [1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, -1], [2, 0, -1, 0, 0, -2, -2, 1, -2, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, -1, 0, 0, 3, -1, 0, 0, 0, -2, 0, 2, 0], [-1, -2, -1, 0, -1, 1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0], [1, -1, -2, 0, -2, -1, -1, 0, 2, 0, 0, 0, 0, 0, -2, 0], [-2, 0, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1], [-1, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, -3, 0, -1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0], [-1, 2, 1, 0, 0, 1, 1, -1, 0, 0, 0, 0, 2, 0, -2, 0], [3, 0, 0, -1, 0, 1, -1, 0, 0, 1, -1, 2, 0, 3, 0, 1], [-1, 0, 0, 3, 0, -3, 3, 0, 0, 0, -3, -3, 0, -4, 0, 2], [0, -3, -3, 0, -3, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0], [3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, -3], [-2, -2, -2, 0, -3, 2, 2, -1, 2, 0, 0, 0, 0, 0, -1, 0], [-1, -1, 3, 0, -1, 1, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0], [2, 0, 0, 0, 0, 1, -1, 0, 0, 2, 0, 2, 0, 3, 0, 1], [3, 0, 0, -4, 0, 0, 0, 0, 0, -1, -1, 4, 0, 1, 0, 1], [-5, 0, 0, 2, 0, -1, 1, 0, 0, -3, 0, -2, 0, -2, 0, -2], [-1, 2, 2, 0, 2, 1, 1, 1, -1, 0, 0, 0, -2, 0, 2, 0], [3, 0, 0, 0, 2, -3, -3, 5, -3, 0, 0, 0, -1, 0, 3, 0], [6, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 2, 0, 2, 0, 0], [1, 0, 0, -1, 0, 1, -1, 0, 0, 2, 2, 1, 0, 0, 0, 0], [6, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2], [-2, 0, 0, 2, 0, -3, 3, 0, 0, 1, -2, -2, 0, -3, 0, 1], [-3, 0, 0, 3, 0, -1, 1, 0, 0, 0, -3, 1, 0, -1, 0, 2], [3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, -1], [6, 0, 0, 1, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0], [9, 0, 0, -2, 0, 2, -2, 0, 0, 3, 3, 2, 0, 3, 0, 1], [-2, -1, 2, 0, -2, 2, 2, 2, 3, 0, 0, 0, 0, 0, 1, 0], [3, 1, -2, 0, -1, -3, -3, 4, -2, 0, 0, 0, -1, 0, -1, 0], [2, 0, 0, -1, 0, 2, -2, 0, 0, 1, -1, 2, 0, -1, 0, 1], [-5, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, -1, 0, 3, 0, -1], [-11, 0, 0, 1, 0, -1, 1, 0, 0, 1, -3, -2, 0, -1, 0, 3], [-8, 0, 0, 3, 0, -1, 1, 0, 0, -2, 1, -5, 0, -3, 0, 1], [-2, 2, 5, 0, 0, 2, 2, 2, -1, 0, 0, 0, -1, 0, 5, 0], [-1, -4, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, -2, 0, 4, 0], [-3, 3, 3, 0, -3, 3, 3, 0, -1, 0, 0, 0, 1, 0, 1, 0], [2, 1, 0, 0, 3, -2, -2, 2, -4, 0, 0, 0, 2, 0, 2, 0], [-6, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 6, 0, 1, 0, -1], [3, 0, 0, -3, 0, 0, 0, 0, 0, 5, -3, 5, 0, 1, 0, 3], [-1, 0, 0, -4, 0, 2, -2, 0, 0, 2, 1, 5, 0, 2, 0, 2], [-2, 3, 3, 0, -1, 2, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0], [-3, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -3, 0, -1, 0, 1], [-9, 0, 0, 3, 0, -2, 2, 0, 0, -5, -2, -5, 0, -3, 0, -3], [-4, -1, -2, 0, -4, 4, 4, -3, 3, 0, 0, 0, 0, 0, -1, 0], [-1, -2, 0, 0, 3, 1, 1, 0, 3, 0, 0, 0, -2, 0, 1, 0], [1, -1, 0, 0, 2, -1, -1, 2, -2, 0, 0, 0, -4, 0, 2, 0], [-1, -3, 3, 0, 0, 1, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0], [2, 0, 0, -3, 0, 2, -2, 0, 0, -2, 4, -1, 0, 0, 0, 0], [3, 0, 0, -2, 0, 1, -1, 0, 0, 2, 0, -2, 0, 0, 0, 0], [-8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0], [1, 1, -1, 0, -2, -1, -1, -2, 0, 0, 0, 0, 1, 0, -5, 0], [-1, 2, 4, 0, 0, 1, 1, 0, 0, 0, 0, 0, 4, 0, -1, 0], [-4, 2, 2, 0, 1, 4, 4, -1, 4, 0, 0, 0, 2, 0, 3, 0], [1, 0, 0, -3, 0, 1, -1, 0, 0, 3, 2, 6, 0, 2, 0, 1], [-2, -1, 1, 0, -3, 2, 2, 2, -3, 0, 0, 0, 1, 0, 5, 0], [-8, 0, 0, -4, 0, 1, -1, 0, 0, 0, -2, 1, 0, -2, 0, 0], [7, 0, 0, 0, 0, 1, -1, 0, 0, 2, -1, 6, 0, -2, 0, 4], [-4, -2, 2, 0, -4, 4, 4, -6, 4, 0, 0, 0, 2, 0, -4, 0], [1, -1, 1, 0, -3, -1, -1, 2, -1, 0, 0, 0, -1, 0, -2, 0], [-4, 0, 0, 4, 0, -4, 4, 0, 0, -2, 0, -6, 0, -6, 0, 0], [-1, 1, -1, 0, 1, 1, 1, -10, 3, 0, 0, 0, 4, 0, -8, 0], [-2, 3, 3, 0, 4, 2, 2, -7, 1, 0, 0, 0, 3, 0, -5, 0], [-11, 0, 0, 3, 0, -1, 1, 0, 0, -1, -3, 0, 0, -1, 0, 3], [-5, 0, 0, 2, 0, -3, 3, 0, 0, 0, -4, -2, 0, -4, 0, -2], [0, -1, 3, 0, -5, 0, 0, 6, -1, 0, 0, 0, -2, 0, 3, 0], [6, 0, 0, 0, 0, -1, 1, 0, 0, -5, 2, -6, 0, -5, 0, -3], [1, 1, -3, 0, 1, -1, -1, -1, 2, 0, 0, 0, 1, 0, 0, 0], [3, -1, 1, 0, 2, -3, -3, 2, -2, 0, 0, 0, -3, 0, 5, 0], [-4, 3, 3, 0, -2, 4, 4, -2, -1, 0, 0, 0, 1, 0, -1, 0], [-1, 1, -3, 0, 1, 1, 1, 1, 2, 0, 0, 0, -2, 0, -3, 0], [0, 1, 0, 0, 2, 0, 0, -8, 0, 0, 0, 0, 0, 0, -5, 0], [0, 5, 5, 0, 3, 0, 0, 4, -7, 0, 0, 0, 3, 0, 6, 0], [-2, 4, 0, 0, -4, 2, 2, -2, -2, 0, 0, 0, 1, 0, -1, 0], [1, 0, 0, 2, 0, -2, 2, 0, 0, 2, 1, -2, 0, -4, 0, 5], [-3, -3, -3, 0, 1, 3, 3, 0, 3, 0, 0, 0, -1, 0, 3, 0], [-8, 0, 0, 3, 0, -4, 4, 0, 0, -4, -1, -5, 0, -4, 0, -2], [2, 0, 0, -7, 0, 2, -2, 0, 0, -1, 1, 6, 0, 3, 0, -3], [0, -2, 3, 0, 3, 0, 0, 8, 0, 0, 0, 0, -7, 0, 6, 0], [-1, 2, 4, 0, -4, 1, 1, -4, 0, 0, 0, 0, 2, 0, -2, 0], [-2, -1, 1, 0, 6, 2, 2, -1, 1, 0, 0, 0, -1, 0, 2, 0], [5, 0, 0, 4, 0, -3, 3, 0, 0, -6, 0, -8, 0, -4, 0, -4], [2, 1, -5, 0, 5, -2, -2, 0, -3, 0, 0, 0, -4, 0, 1, 0], [1, 0, 0, 4, 0, -1, 1, 0, 0, 4, -1, 2, 0, -5, 0, 4], [4, 1, -3, 0, 2, -4, -4, 3, 1, 0, 0, 0, 1, 0, 3, 0], [2, 0, 0, 3, 0, 0, 0, 0, 0, 2, 4, 1, 0, 2, 0, -2], [0, 0, 0, 9, 0, -3, 3, 0, 0, -4, -2, -1, 0, -5, 0, 1], [14, 0, 0, -1, 0, 4, -4, 0, 0, 2, 2, 7, 0, 2, 0, -2], [3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -1, -1, 0, -2, 0, -1], [-7, 0, 0, -3, 0, 4, -4, 0, 0, -1, 1, 1, 0, -1, 0, -1], [-6, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2], [-2, 0, 3, 0, -2, 2, 2, 2, 3, 0, 0, 0, -1, 0, 1, 0], [-3, 0, 0, 9, 0, -3, 3, 0, 0, -2, -1, -1, 0, -7, 0, 4], [0, -2, 1, 0, -4, 0, 0, 3, 4, 0, 0, 0, 1, 0, -1, 0], [-5, 0, 0, 4, 0, -1, 1, 0, 0, 0, 1, -4, 0, -6, 0, -4], [-2, 0, 0, -3, 0, -1, 1, 0, 0, -1, 0, 1, 0, 1, 0, -7], [-7, 0, 0, 5, 0, -3, 3, 0, 0, 1, -3, -4, 0, 1, 0, 3], [9, 0, 0, 1, 0, -3, 3, 0, 0, 2, -3, -1, 0, 1, 0, 4], [1, -5, -3, 0, -5, -1, -1, 0, 5, 0, 0, 0, -3, 0, 2, 0], [4, 3, -2, 0, 8, -4, -4, 3, -4, 0, 0, 0, -4, 0, 5, 0], [2, -1, -5, 0, 2, -2, -2, 0, 0, 0, 0, 0, -3, 0, 4, 0], [-5, 0, 0, 0, 0, 1, -1, 0, 0, 6, -1, 0, 0, 3, 0, 0], [-6, 0, 0, -6, 0, 4, -4, 0, 0, -4, 4, 0, 0, 2, 0, -8], [-4, 0, 0, -8, 0, 4, -4, 0, 0, 2, 6, 8, 0, 6, 0, 0], [16, 0, 0, -3, 0, 0, 0, 0, 0, 3, 1, 4, 0, 3, 0, -3], [-7, 0, 0, 0, 0, -3, 3, 0, 0, -4, 0, -8, 0, 0, 0, -2], [0, 2, -2, 0, 1, 0, 0, 2, -1, 0, 0, 0, 2, 0, 1, 0], [-1, -1, 1, 0, -4, 1, 1, -6, 6, 0, 0, 0, -1, 0, -5, 0], [3, -2, -2, 0, 6, -3, -3, 2, -2, 0, 0, 0, 0, 0, -1, 0], [-1, -3, -3, 0, -4, 1, 1, 2, -4, 0, 0, 0, 3, 0, 2, 0], [-2, 1, 1, 0, 5, 2, 2, -2, 3, 0, 0, 0, 3, 0, -1, 0], [-4, 0, 0, 3, 0, -2, 2, 0, 0, -4, 2, -1, 0, -2, 0, -4], [1, -2, -4, 0, 2, -1, -1, -8, 0, 0, 0, 0, -2, 0, -9, 0], [-4, 3, 5, 0, 3, 4, 4, 0, 1, 0, 0, 0, 0, 0, 5, 0], [3, -5, -3, 0, -1, -3, -3, -1, 6, 0, 0, 0, -5, 0, -3, 0], [4, -3, -7, 0, 1, -4, -4, -2, -5, 0, 0, 0, -2, 0, -6, 0], [5, 0, 0, 0, 6, -5, -5, 1, 5, 0, 0, 0, 0, 0, -5, 0], [6, -3, -6, 0, 0, -6, -6, -1, 3, 0, 0, 0, 0, 0, -6, 0], [-13, 0, 0, -2, 0, 1, -1, 0, 0, 0, -3, 4, 0, 0, 0, 4], [-1, 1, 1, 0, 3, 1, 1, 3, -6, 0, 0, 0, 2, 0, 8, 0], [-2, -3, 7, 0, 3, 2, 2, 0, 1, 0, 0, 0, -1, 0, 7, 0], [-9, 0, 0, 6, 0, 1, -1, 0, 0, -2, 1, -6, 0, 0, 0, 4], [2, 2, 2, 0, 1, -2, -2, -3, 1, 0, 0, 0, -2, 0, -2, 0], [6, 0, 0, -2, 0, -2, 2, 0, 0, 0, -4, -2, 0, 4, 0, 2], [2, 6, -2, 0, -1, -2, -2, -1, -2, 0, 0, 0, 2, 0, -2, 0], [2, 0, 0, 7, 0, -3, 3, 0, 0, 7, -5, 1, 0, -3, 0, 7], [6, 0, 0, 5, 0, 2, -2, 0, 0, -1, 5, 4, 0, 3, 0, -5], [3, 0, 0, -1, 0, 1, -1, 0, 0, 2, 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0], [2, 0, -10, 0, -2, -2, -2, 4, -8, 0, 0, 0, -4, 0, 9, 0], [1, -7, 1, 0, -9, -1, -1, 2, -1, 0, 0, 0, -3, 0, 5, 0], [-2, -1, 0, 0, -3, 2, 2, 2, -2, 0, 0, 0, -4, 0, 8, 0], [22, 0, 0, -11, 0, 4, -4, 0, 0, -4, 2, -3, 0, 4, 0, -4], [-4, 5, 5, 0, -3, 4, 4, 8, -9, 0, 0, 0, -3, 0, 0, 0], [9, -4, -4, 0, 0, -9, -9, 12, -4, 0, 0, 0, 0, 0, -4, 0], [-3, 2, 6, 0, -10, 3, 3, 4, 0, 0, 0, 0, 7, 0, -1, 0], [6, -7, -3, 0, 5, -6, -6, -2, 1, 0, 0, 0, -2, 0, 0, 0], [16, 0, 0, -10, 0, 3, -3, 0, 0, 6, -10, 16, 0, 3, 0, 5], [-2, 1, -1, 0, 0, 2, 2, 2, 7, 0, 0, 0, -3, 0, 7, 0], [-15, 0, 0, 10, 0, -1, 1, 0, 0, 8, -2, 4, 0, 0, 0, 4], [6, 7, 5, 0, 6, -6, -6, -9, -7, 0, 0, 0, 3, 0, -13, 0], [0, -2, 15, 0, -3, 0, 0, 15, -1, 0, 0, 0, 1, 0, 14, 0], [-13, 0, 0, -5, 0, 1, -1, 0, 0, 4, 2, 9, 0, 8, 0, -6], [0, 4, -14, 0, 1, 0, 0, -1, -4, 0, 0, 0, 0, 0, 2, 0], [-9, 0, 0, 0, -2, 9, 9, -6, 0, 0, 0, 0, 0, 0, -1, 0], [3, 0, 0, -7, 0, -3, 3, 0, 0, 3, -5, 8, 0, 5, 0, 9], [-2, 1, 7, 0, -3, 2, 2, 4, -1, 0, 0, 0, 1, 0, 11, 0], [1, -7, -7, 0, 3, -1, -1, 2, -1, 0, 0, 0, -8, 0, 11, 0], [14, 0, 0, -3, 0, -1, 1, 0, 0, 2, 2, -1, 0, -1, 0, -1], [10, -9, -1, 0, 5, -10, -10, 8, -5, 0, 0, 0, -3, 0, 1, 0], [-5, -9, -1, 0, -7, 5, 5, 7, 0, 0, 0, 0, 3, 0, 5, 0], [-6, -7, -1, 0, -7, 6, 6, -2, 7, 0, 0, 0, -1, 0, 2, 0], [-3, 0, 0, 14, 0, -6, 6, 0, 0, -7, -8, -14, 0, -9, 0, 3], [4, 0, 0, -2, 0, -1, 1, 0, 0, -3, -12, 2, 0, -3, 0, 5], [4, 0, 0, 5, 0, -4, 4, 0, 0, 0, 1, -5, 0, -14, 0, 4], [0, 0, 0, 1, 0, -4, 4, 0, 0, 2, 0, -9, 0, 4, 0, 0], [-19, 0, 0, -3, 0, 2, -2, 0, 0, -3, 8, -5, 0, 3, 0, -5], [1, 1, -11, 0, 3, -1, -1, 9, -2, 0, 0, 0, 3, 0, 6, 0], [-8, 5, 8, 0, -2, 8, 8, 10, 0, 0, 0, 0, -6, 0, 17, 0], [6, 5, 2, 0, 3, -6, -6, 3, 1, 0, 0, 0, -6, 0, 6, 0], [-4, 0, 0, -1, 0, 1, -1, 0, 0, -8, 10, -9, 0, -3, 0, -1], [19, 0, 0, -13, 0, 3, -3, 0, 0, 6, 4, 5, 0, 8, 0, 0], [15, 0, 0, 5, 0, -1, 1, 0, 0, 5, -1, -10, 0, -3, 0, 3], [1, 0, 0, -2, 0, 2, -2, 0, 0, 2, -8, 10, 0, 7, 0, 5], [-5, 0, 0, 3, 0, -5, 5, 0, 0, 6, -4, -5, 0, -4, 0, 2], [-6, 0, 0, -1, 0, 0, 0, 0, 0, -4, -4, 1, 0, 8, 0, -6], [9, -2, -6, 0, 8, -9, -9, 11, -11, 0, 0, 0, 5, 0, -1, 0], [-4, -1, 0, 0, -17, 4, 4, 2, 2, 0, 0, 0, 8, 0, -4, 0], [33, 0, 0, -3, 0, -1, 1, 0, 0, -2, -2, 13, 0, -2, 0, 8], [10, 0, 0, -12, 0, 6, -6, 0, 0, -2, 9, 2, 0, 7, 0, -10], [5, -8, -11, 0, -6, -5, -5, 2, 3, 0, 0, 0, 0, 0, 2, 0], [-10, 2, 3, 0, -3, 10, 10, -10, 2, 0, 0, 0, 7, 0, -2, 0], [-4, 0, -1, 0, -2, 4, 4, -4, 9, 0, 0, 0, -3, 0, 7, 0], [4, 2, -2, 0, 6, -4, -4, 4, 2, 0, 0, 0, -8, 0, 4, 0], [-5, 0, 0, 0, 0, 3, -3, 0, 0, 0, -1, 4, 0, -2, 0, 10], [12, 0, 0, -7, 0, 5, -5, 0, 0, 1, 3, 19, 0, 1, 0, 5], [-6, -1, 14, 0, 5, 6, 6, -5, -7, 0, 0, 0, 8, 0, 4, 0], [-3, 0, 0, -1, 0, -1, 1, 0, 0, -1, 6, 3, 0, 10, 0, -6], [11, 0, 0, 1, 0, 5, -5, 0, 0, -5, 3, 2, 0, 1, 0, 7], [-5, 10, 4, 0, 4, 5, 5, 1, -5, 0, 0, 0, 7, 0, -3, 0], [8, 0, 0, -1, 0, -1, 1, 0, 0, -9, -5, -3, 0, 1, 0, 1], [-2, 6, -9, 0, -1, 2, 2, -8, -8, 0, 0, 0, 1, 0, 0, 0], [1, -4, 4, 0, -2, -1, -1, -1, -1, 0, 0, 0, 10, 0, -1, 0], [5, 0, -10, 0, -5, -5, -5, 2, 1, 0, 0, 0, 2, 0, -3, 0], [-12, 0, 0, 8, 0, 0, 0, 0, 0, -12, 4, -8, 0, -6, 0, -2], [7, 0, 0, -3, 0, 7, -7, 0, 0, 4, 4, 11, 0, 4, 0, 12], [-1, -2, 6, 0, -2, 1, 1, -11, 11, 0, 0, 0, -3, 0, -6, 0], [-1, -3, -9, 0, -5, 1, 1, -5, 0, 0, 0, 0, 5, 0, -6, 0], [-1, -7, 5, 0, 0, 1, 1, 8, -2, 0, 0, 0, -5, 0, 3, 0], [8, -2, -1, 0, 3, -8, -8, 18, -8, 0, 0, 0, -5, 0, 6, 0], [-2, 0, 0, 15, 0, -11, 11, 0, 0, -2, -8, -9, 0, -17, 0, 11], [7, 3, -11, 0, -1, -7, -7, 13, -4, 0, 0, 0, 4, 0, -7, 0], [-4, 0, 0, 3, 0, -2, 2, 0, 0, 9, 2, 6, 0, -9, 0, 7], [-36, 0, 0, 13, 0, -6, 6, 0, 0, 1, -1, -4, 0, -11, 0, 5], [-32, 0, 0, -2, 0, 1, -1, 0, 0, 8, -7, 2, 0, -4, 0, 9], [-2, 0, 0, 7, 0, -4, 4, 0, 0, 7, -1, 1, 0, -6, 0, 10], [-1, -4, -5, 0, -1, 1, 1, 12, 3, 0, 0, 0, 1, 0, 0, 0], [-12, 1, 11, 0, -11, 12, 12, 0, 11, 0, 0, 0, 1, 0, 5, 0], [-1, 9, -3, 0, 5, 1, 1, 0, -1, 0, 0, 0, 3, 0, -2, 0], [-16, 0, 0, 3, 0, 2, -2, 0, 0, -3, 5, 4, 0, 7, 0, 3], [-2, 5, -6, 0, 2, 2, 2, -5, -5, 0, 0, 0, -2, 0, -3, 0], [12, -1, -10, 0, 10, -12, -12, 5, 3, 0, 0, 0, 2, 0, -2, 0], [17, 0, 0, 0, 0, -6, 6, 0, 0, -1, -11, 4, 0, -1, 0, 5], [1, 7, 9, 0, 11, -1, -1, -7, -2, 0, 0, 0, 3, 0, -7, 0], [0, 0, 0, 7, 0, -8, 8, 0, 0, 1, -6, -4, 0, -1, 0, -1], [28, 0, 0, 2, 0, -4, 4, 0, 0, -2, -6, 0, 0, 6, 0, 2], [-4, -1, -3, 0, 3, 4, 4, -16, 3, 0, 0, 0, 5, 0, -1, 0], [9, 0, 0, 5, 0, -11, 11, 0, 0, 0, -6, -5, 0, -6, 0, 6], [-6, -2, 9, 0, 2, 6, 6, 3, -6, 0, 0, 0, -7, 0, -1, 0], [-11, -2, 2, 0, -14, 11, 11, -2, 0, 0, 0, 0, 8, 0, -1, 0], [4, -5, -11, 0, -13, -4, -4, 4, -3, 0, 0, 0, -7, 0, 0, 0], [1, 0, 0, 3, 0, 2, -2, 0, 0, -7, 0, -5, 0, -7, 0, -1], [-13, 0, 0, 3, 0, 1, -1, 0, 0, -6, -2, 1, 0, -2, 0, -4], [5, 0, 0, 2, 0, -1, 1, 0, 0, -8, 5, 2, 0, 2, 0, -2], [8, 0, 0, -4, 0, 5, -5, 0, 0, -5, 2, -2, 0, -1, 0, -11], [-20, 0, 0, 13, 0, -2, 2, 0, 0, -9, -1, -14, 0, -7, 0, -3], [15, 0, 0, -1, 0, 4, -4, 0, 0, 0, 0, -5, 0, 1, 0, -7], [3, 3, -3, 0, 8, -3, -3, -2, -12, 0, 0, 0, -7, 0, -1, 0], [9, 0, 0, -7, 0, 2, -2, 0, 0, -8, 4, 3, 0, 13, 0, -3], [0, -2, 5, 0, -9, 0, 0, -5, 2, 0, 0, 0, 1, 0, 3, 0], [-6, 0, 0, 4, 0, -3, 3, 0, 0, 14, -3, 8, 0, -6, 0, 11], [12, -2, -7, 0, -2, -12, -12, 5, -10, 0, 0, 0, -9, 0, -11, 0], [28, 0, 0, 8, 0, -1, 1, 0, 0, -4, 2, -5, 0, -2, 0, -12], [-2, -8, 10, 0, -8, 2, 2, 0, 8, 0, 0, 0, 8, 0, -4, 0], [-11, 0, 0, 3, 0, 9, -9, 0, 0, -1, 9, -4, 0, 5, 0, -3], [3, 0, 0, 8, 0, -3, 3, 0, 0, -6, -1, -8, 0, -5, 0, 2], [12, 0, 0, 5, 0, -4, 4, 0, 0, -4, 5, -13, 0, -7, 0, 0], [-4, 1, -7, 0, 11, 4, 4, -6, -1, 0, 0, 0, 3, 0, -12, 0], [-2, 2, -2, 0, -8, 2, 2, 0, 8, 0, 0, 0, -4, 0, -4, 0], [-12, 0, 0, -16, 0, 4, -4, 0, 0, 14, 4, 20, 0, 12, 0, 4], [7, 0, 0, 1, 0, 0, 0, 0, 0, -7, 8, -11, 0, -7, 0, -11], [0, 0, 0, -4, 0, -3, 3, 0, 0, 2, -4, 10, 0, 1, 0, 7], [2, 4, -6, 0, 9, -2, -2, -4, -11, 0, 0, 0, 6, 0, 0, 0], [2, -6, 10, 0, -10, -2, -2, -2, 6, 0, 0, 0, -1, 0, 3, 0], [3, 0, 0, -15, 0, 9, -9, 0, 0, -6, 6, -1, 0, 4, 0, -8], [-2, 7, 10, 0, 4, 2, 2, -1, -4, 0, 0, 0, 12, 0, -5, 0], [2, -1, 8, 0, -5, -2, -2, 15, -1, 0, 0, 0, -10, 0, 12, 0], [0, 7, -10, 0, -2, 0, 0, -2, -4, 0, 0, 0, -10, 0, -1, 0], [15, 0, 0, 1, 0, -5, 5, 0, 0, -5, -7, 2, 0, -11, 0, 11], [-6, 0, 0, -17, 0, 10, -10, 0, 0, 7, 7, 14, 0, 17, 0, -3], [-12, 1, 4, 0, -19, 12, 12, -12, 4, 0, 0, 0, 10, 0, -6, 0], [6, 4, 0, 0, 4, -6, -6, -8, 6, 0, 0, 0, 2, 0, -15, 0], [1, 0, 4, 0, 9, -1, -1, 10, -5, 0, 0, 0, 4, 0, 18, 0], [29, 0, 0, -10, 0, 10, -10, 0, 0, 2, 7, 9, 0, 12, 0, 2], [-2, 0, 0, 9, 0, -6, 6, 0, 0, -5, -4, -16, 0, -3, 0, -3], [-37, 0, 0, 9, 0, -10, 10, 0, 0, -3, 0, -7, 0, -13, 0, 7], [-5, 4, -1, 0, -5, 5, 5, -4, 7, 0, 0, 0, -7, 0, 11, 0], [-3, -9, 0, 0, -3, 3, 3, -3, 5, 0, 0, 0, -3, 0, 7, 0], [-1, 0, 0, -6, 0, 9, -9, 0, 0, 4, 2, 16, 0, 12, 0, 8], [-4, -5, -6, 0, -8, 4, 4, -8, 8, 0, 0, 0, 2, 0, -6, 0], [-9, -1, 13, 0, -5, 9, 9, 5, 6, 0, 0, 0, -5, 0, 14, 0], [-9, -2, 10, 0, -17, 9, 9, 8, -1, 0, 0, 0, 12, 0, 3, 0], [9, 0, 0, -3, 0, 11, -11, 0, 0, 2, 7, 1, 0, -2, 0, -4], [-4, 1, 10, 0, 9, 4, 4, -5, -3, 0, 0, 0, 6, 0, 4, 0], [3, -2, -8, 0, 14, -3, -3, 7, -5, 0, 0, 0, -10, 0, 8, 0], [32, 0, 0, 16, 0, -3, 3, 0, 0, 0, 2, -6, 0, -3, 0, 5], [-6, 0, 0, -1, 0, 0, 0, 0, 0, -1, -9, -3, 0, -2, 0, -2], [33, 0, 0, -7, 0, 3, -3, 0, 0, 0, 8, 5, 0, -2, 0, -4], [-8, 0, 0, -10, 0, 6, -6, 0, 0, 1, -1, 4, 0, 10, 0, 0], [3, -4, 0, 0, 12, -3, -3, 5, -3, 0, 0, 0, -5, 0, 6, 0], [1, 0, -12, 0, 5, -1, -1, -6, -1, 0, 0, 0, -4, 0, -3, 0], [7, 8, -3, 0, 6, -7, -7, 0, -1, 0, 0, 0, 2, 0, -6, 0], [6, -2, 10, 0, -5, -6, -6, 14, -3, 0, 0, 0, -8, 0, 2, 0], [-7, 0, 0, 8, 0, -13, 13, 0, 0, 0, -14, -8, 0, -12, 0, 2], [-22, 0, 0, 2, 0, 4, -4, 0, 0, 0, 12, -6, 0, 4, 0, -6]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6030_d_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6030_2_d_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_6030_2_d_j(:prec:=16)
    chi := MakeCharacter_6030_d();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 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_6030_2_d_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_6030_2_d_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6030_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![10653696, 0, 21456384, 0, 15513616, 0, 5215776, 0, 887880, 0, 80856, 0, 3985, 0, 100, 0, 1]>,<11,R![-1224, -2280, 1238, 1256, -230, -204, 1, 10, 1]>,<41,R![-760608, -1005888, -213392, 66784, 15702, -956, -240, 4, 1]>],Snew);
    return Vf;
end function;