
// Make newform 7098.2.a.ct in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_7098_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_7098_2_a_ct();".
// 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_7098_2_a_ct();".
// 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 := [-281, -131, 111, 39, -17, -3, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [-7, -1, 1, 0, 0, 0], [0, -7, -1, 1, 0, 0], [41, 13, -12, -2, 1, 0], [-47, 33, 27, -11, -3, 1]];
    Rf_basisdens := [1, 1, 1, 1, 1, 1];
    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_7098_a();"
function MakeCharacter_7098_a()
    N := 7098;
    order := 1;
    char_gens := [4733, 5071, 6931];
    v := [1, 1, 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;

function MakeCharacter_7098_a_Hecke(Kf)
    return MakeCharacter_7098_a();
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 := [[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 1, 0, 1], [1, 0, -1, 1, -1, -1], [1, 0, 2, -1, -1, 1], [1, -1, -2, 0, 1, 0], [4, -2, 3, -1, -2, -2], [2, -2, -1, -1, 2, -2], [-3, 2, -1, 0, 2, 1], [3, -1, 3, -2, -3, 0], [-3, 1, -4, 1, 0, 2], [2, 1, -4, 2, 3, 1], [5, 1, 3, -2, -3, 0], [-5, 0, -6, -1, 3, 1], [2, -1, -5, 1, 1, 1], [0, 1, 3, -1, -2, -1], [-2, -1, -2, -2, -1, -3], [2, 0, -3, 1, -1, 2], [7, -1, 7, 0, -4, 0], [4, -3, 4, -2, -3, -3], [4, -3, 3, -3, -3, -2], [6, 0, 3, 2, 0, 0], [-1, -3, -1, 0, -2, -1], [-5, 1, -4, 1, 9, 2], [1, -2, 1, 0, 4, -1], [0, 1, -1, 1, -2, -1], [-4, -1, -5, 1, -4, 1], [7, 0, 1, -4, -4, -1], [7, -1, 0, 0, -5, -2], [2, 2, -7, 3, -1, 2], [5, -3, 6, 1, -4, 0], [-6, -2, -8, 0, 6, 2], [3, 1, -4, 3, 2, 2], [12, -3, 5, 3, 0, 1], [-8, 2, -2, 2, 7, 1], [-1, -1, 1, -2, -3, 0], [2, 3, 2, -2, 9, 1], [-8, 1, 1, 3, 5, 2], [3, 4, 7, 3, -9, 3], [2, -1, 3, -1, 4, -1], [-4, -3, -4, 2, 12, -1], [0, 1, 7, 3, -8, 1], [-3, -2, -5, -1, 3, 1], [9, -2, -6, -1, 7, -1], [-8, 3, -6, 2, -1, 1], [-9, -5, -4, -1, 8, -2], [-2, 0, 2, 0, -9, -5], [5, -2, 1, -4, 4, -1], [-12, -3, -1, -1, 0, 3], [7, -1, 0, 1, -8, -4], [3, 0, 6, -2, -12, -1], [1, -1, 5, 2, 8, 0], [8, 0, 18, -2, -11, -3], [-5, 0, 7, 0, 13, 2], [1, 1, 4, -1, 6, 2], [-2, -3, 0, 1, -6, 3], [5, -2, 4, -1, 0, 1], [6, -1, 0, 2, 4, -3], [-10, -4, -6, 4, 2, 0], [-6, 0, -9, -1, 3, 0], [9, 0, 12, -1, -3, -1], [2, 4, -1, -1, -9, 2], [2, -5, -8, -2, 6, -4], [-3, 0, 12, 1, 9, 1], [-7, 4, 1, 2, -10, 5], [4, 0, 6, 3, -5, 2], [7, -3, -10, -2, 9, 0], [10, -4, 6, 0, -17, -1], [-11, 3, -3, 2, 2, 8], [-3, 2, 1, -2, -4, -5], [9, 0, -9, 0, 8, 1], [0, 1, -5, -5, 4, -3], [1, 3, -3, 2, -1, -2], [-10, 3, -7, -5, -4, -1], [-9, 3, 2, -1, 6, -2], [1, 1, 11, 2, -7, 4], [-22, 8, -1, 3, 6, 3], [4, -3, -4, 4, 18, 0], [10, 2, 7, 7, -13, 0], [16, 3, 6, 2, -12, 0], [3, -3, 14, -3, 1, 0], [-4, 2, 16, 0, -4, -4], [1, 8, 1, 4, -3, 2], [20, -7, 5, 0, -17, -3], [-16, 2, -3, -1, 17, 2], [-5, 3, 6, 1, 0, 4], [4, -3, -3, 3, 2, 1], [-2, -4, -11, 1, -1, 4], [-16, 7, -15, 4, 11, 1], [0, -5, 9, -1, 6, -7], [4, -6, 9, -5, -7, -10], [-2, 4, 0, -3, 3, -4], [11, 3, 6, 0, -5, -4], [-20, 2, -4, -4, 3, -1], [3, 0, -13, -4, 7, -4], [5, 3, -13, 6, -7, 2], [-3, 4, -1, 0, 12, 5], [-14, -2, -18, -2, 8, 2], [-6, -1, 0, 4, -1, 1], [1, -5, 2, -1, 6, 0], [-24, 7, -16, 0, 19, 3], [-2, -5, 0, -4, 7, 5], [16, 4, -3, 1, -7, 0], [6, 5, -5, 3, -8, 5], [-6, 5, 5, -5, 14, -1], [9, 0, 6, 1, 4, -1], [2, -4, -9, -2, -4, -2], [-9, 4, -9, -2, -6, 7], [-15, 0, -7, 4, -4, -1], [-23, 6, 8, 3, 5, 1], [-2, 6, 7, 7, -5, 0], [6, -1, 21, -2, -7, -1], [-1, 8, -11, 4, 2, 5], [-24, 0, -7, -1, 15, 2], [-8, 2, 0, -7, 3, -2], [-17, 6, 7, 4, -10, 5], [0, -3, 15, -3, -7, -4], [-12, 9, -2, 0, 1, 3], [13, -3, 0, -3, -13, -6], [-7, -2, -4, -6, 16, -1], [-7, 1, -14, 5, 16, -2], [-10, 7, 6, -4, 12, 2], [-3, 6, 6, 3, -3, -5], [11, 7, 0, 3, -1, 5], [8, 6, 3, 3, 3, 4], [20, -5, 10, 4, -27, -3], [-14, 9, 0, 7, -2, 11], [-24, 2, -18, -2, -2, -2], [-5, -3, 11, -6, 4, 4], [11, 4, 7, 0, 7, -6], [18, 1, 3, 7, -18, 1], [-10, -4, -9, -3, 17, 2], [-15, 3, -16, 2, 9, 0], [-2, 3, 12, 0, -12, -5], [5, 0, 3, -6, -12, -3], [-20, 8, -9, 1, 20, 10], [30, -2, 13, -1, -3, -2], [10, -14, 3, -3, -1, 0], [7, 0, 18, -3, -14, -5], [10, 0, 23, -1, -23, -6], [-19, -7, -18, -1, 18, -6], [10, 5, -11, -3, -14, -1], [-1, 5, 5, -6, -8, 1], [-4, -5, -16, -4, 8, -8], [12, 5, 2, 4, -8, -1], [19, 3, 31, 2, -26, -2], [-21, 7, -29, 0, 10, 1], [-18, 3, -2, 2, -5, 9], [6, 4, 1, -3, -7, 4], [7, -2, 10, 3, -3, 7], [6, -1, 25, -7, -13, -4], [-22, 3, -16, 2, 11, -3], [4, 3, 5, 1, 8, -1], [-16, 6, 12, 2, 2, 2], [5, -5, -3, 4, -18, -7], [-26, 5, -28, 2, 30, 2], [20, 3, 26, -4, -15, 1], [-5, -10, 5, -2, -6, -7], [-13, 0, -14, -3, 7, 1], [1, 7, 2, 1, 4, -4], [-11, -3, -6, 1, -20, -2], [-1, -9, 10, -1, -6, 4], [6, -2, -3, 5, -3, -2], [-12, -1, -7, -9, 15, -4], [6, 1, 16, -8, 2, -3], [-7, 8, -14, 7, -2, 8], [-18, 2, 8, -6, 24, 2], [-16, 0, -2, -3, -13, 0], [-2, 0, 7, -1, 20, -4], [12, -7, 15, -4, -21, -1], [-9, 10, -17, 4, 5, 8], [-12, -2, -19, 7, -7, 4], [25, 4, 13, 8, -20, 1], [-17, 4, -1, 6, -5, -1], [-2, 1, -22, 8, 15, 9], [-9, 6, 6, 3, 5, 9], [-2, -1, 3, 3, -20, -7], [1, -9, 4, -3, 7, -1], [-8, 6, -16, 4, 7, 5], [1, 6, 12, -7, 14, 4], [33, -2, -11, 0, 9, 4], [8, 1, -7, 8, 7, 1], [4, -2, -6, -2, -7, -2], [-18, 2, -13, -1, -8, 3], [-10, -2, -12, -10, 22, -4], [-7, 1, 8, -11, -14, -6], [-22, -9, -7, 1, 19, -6], [-29, 2, 11, 0, -18, -3], [-2, 1, 13, -1, 3, 3], [-2, -3, -6, 8, 14, -4], [7, 6, 11, 3, 13, 9], [-2, -3, -5, -3, -6, -13], [-3, -9, -12, 3, -9, -2], [30, -4, 18, -4, -15, -2], [-17, 5, -12, 5, 18, 2], [21, -1, 15, -12, -5, -4], [0, -4, -35, 7, 19, 10], [-10, 1, -14, 4, -1, 9], [-17, 0, -20, 3, 19, 1], [-24, 17, -17, 3, 20, 5], [19, 8, -17, 7, -3, 3], [9, -4, 19, 3, -7, 7], [-6, 1, 6, 0, -16, -1], [-4, -6, 18, -4, -24, 6], [-2, -2, -17, 3, 17, 6], [-37, -1, -4, -5, 7, -2], [15, -7, 32, -7, -31, -6], [12, -10, 25, -11, -15, -14], [-13, 0, -26, -3, 1, 3], [-2, 0, -13, 1, 35, -2], [-9, -7, 6, -3, -12, -8], [19, -9, -9, -6, -3, -2], [0, 3, -20, -5, 18, -3], [30, 0, 27, 0, -10, 0], [10, -4, 8, 4, -8, -4], [-10, -9, 21, -1, 15, -3], [-6, -4, -7, 7, -6, 2], [-11, -2, -5, 0, 12, 5], [24, -10, 33, -7, -39, -4], [-27, -1, -25, 10, 9, 0], [10, 3, 3, 4, -27, 5], [17, 1, -16, -2, -5, 0], [13, -14, -3, 5, 13, 5], [19, -5, 1, 4, 16, -6], [7, -10, -13, 4, -5, -4], [7, 8, 13, -11, -5, -1], [-15, 5, -9, -3, -6, -4], [-11, -4, 1, 8, -8, -1], [-8, -5, -11, -15, 22, -7], [-23, -1, -2, -13, 18, 0], [21, -2, 26, 1, -41, -3], [-1, -1, -11, -6, -9, 4], [-12, -4, -28, 6, 2, 4], [2, 1, -13, 7, 15, 1], [2, -1, 8, -2, 21, 11], [-20, 11, 2, -2, -10, -4], [21, -3, 5, -5, 12, -4], [-14, -3, -23, 13, 3, 4], [15, -8, 5, -4, -9, 7], [-8, 5, -8, 0, 6, 1], [18, 7, 1, 5, -18, 5], [15, -7, 19, -6, -16, -16], [30, 6, 21, 3, -13, -6], [-8, 0, -3, -3, 21, -4], [-9, -2, 4, -5, -2, -4], [-13, 7, -29, 8, 26, 3], [-5, 1, 9, -1, 8, 4], [-8, 4, 16, -5, 9, 4], [40, -1, 52, -4, -23, -5], [43, -14, 12, 1, -8, -5], [-3, 3, -3, -4, 16, 3], [21, 15, 2, 2, -5, 2], [-13, -7, -1, 5, 6, -6], [33, -12, 7, -3, -9, -3], [8, -17, 3, -1, -8, -7], [21, -3, 34, -3, -18, 2], [8, 8, -13, 6, -10, 6], [-17, 5, -5, 0, 7, -2], [-27, 8, -41, 6, 48, 3], [13, 2, 13, 4, -11, 5], [0, 3, 17, -4, 19, 5], [-16, -11, 5, -7, 4, -9], [-13, -3, 2, -2, -17, -10], [-19, 7, -1, -6, -21, 2], [-8, 8, -14, 2, 22, 2], [3, 19, 2, 7, -14, 8], [-19, 10, -11, 6, 12, 5], [5, -4, 21, 0, 14, 7], [-18, 0, 19, 3, -19, -2], [-14, 5, -31, 3, -8, 11], [-18, 6, 5, 1, 30, 7], [11, 0, 10, 1, -31, -1], [-37, 11, -21, -6, -8, 2], [-22, -9, 1, 5, 21, -5], [-3, 9, -3, 0, 11, 8], [-4, -11, -17, 1, 6, 7], [-6, 0, 10, -2, -12, 8], [-1, -9, 23, -4, 3, 0], [-10, 25, -13, 7, 4, 11], [-9, 10, 29, 3, -7, -1], [-16, 3, -13, -5, 17, 15], [-26, 5, -32, 10, 24, 3], [-38, 3, -11, 1, 26, 7], [7, -9, -18, 5, -12, -2], [26, 0, 20, -9, -13, 8], [39, -5, -12, 1, 8, 6], [6, 0, 8, -6, 12, -4], [46, -13, 2, -8, -21, -7], [-24, 13, -11, 5, 16, 1], [-1, -12, 26, -9, -20, -15], [23, -14, 1, 4, -9, -3], [20, 7, -3, -9, -22, 1], [-3, 4, 26, 1, 8, -5], [16, -3, -4, -2, 1, -11], [15, 5, 9, -18, 4, -10], [-17, 1, -3, 0, 7, -6], [10, -4, -19, -7, -3, -6], [15, 3, 9, 10, -23, -10], [6, 3, 8, 2, 4, -11], [-20, -2, 13, -5, -7, 0], [18, 1, 31, -5, -13, -2], [30, -8, -3, -3, -14, -3], [29, -2, 29, -6, -4, -9], [-25, -3, -18, 5, -2, 4], [-41, 15, -16, 10, 23, 8], [-17, 8, -2, -1, 35, 3], [-8, 3, -14, 8, 3, -7], [39, -5, 37, 4, -35, 0], [-7, -7, 8, -3, -2, 8], [1, -2, -11, -8, -2, -15], [-22, 6, -15, -7, -1, 10], [-31, 3, 11, 6, 9, 10], [9, 17, 14, 8, -29, 2], [25, 6, 16, 5, -5, 5], [20, 9, 24, 2, -27, 7], [22, 2, 35, -1, -32, 2], [-7, -5, 14, -5, 15, 7], [-12, 6, -22, 4, 3, -4], [-12, -5, -18, -6, 27, -1], [-3, -18, -1, -4, 2, 1], [5, 10, -2, -3, -1, 3], [-1, 5, 10, 3, 8, -6], [22, 13, 16, -6, 3, 3], [5, 0, -5, -6, -30, -5], [-34, 8, -47, 1, 29, -2], [0, -1, -8, 3, 8, -15], [28, 12, -9, 1, 5, -6], [16, -17, -19, -8, 17, -3], [9, 13, -16, 9, 0, 14], [2, 1, -13, -5, 2, -3], [6, 10, 14, 2, -8, -8], [9, 9, -8, 7, -12, -4], [23, 15, 35, 7, -42, 6], [-49, 0, -20, 1, 13, 3], [-18, 22, -19, 5, 0, 17], [57, -9, 8, -1, -3, -6], [1, -1, -17, 0, -11, -8], [7, -11, -6, -12, 3, -10], [-21, -8, -17, -14, 18, -3], [-39, 7, -11, 12, 11, 6], [-24, 9, -12, -11, 2, -3], [23, -2, 20, 1, -11, -5], [-24, 7, 1, -3, -26, -1], [-30, -7, -12, -6, 35, -3], [26, -6, 13, 1, 6, 9], [41, -14, 21, -8, -38, -7], [10, -5, 26, 2, -23, 3], [0, -1, -30, 2, 21, 5], [-27, 8, 3, 2, -6, -5], [-12, 2, -15, 7, -4, 11], [1, 12, 26, 3, -14, -10], [10, 5, -31, -1, 20, -1], [6, 11, 13, -5, 26, 3], [-9, 10, -30, 3, 41, -5], [-5, -9, 3, 1, 10, -4], [28, -18, 4, -10, -5, -12], [53, -10, 18, -7, -17, -11], [29, -2, 19, -14, -16, -7], [31, 4, 13, 6, -38, -3], [-20, -5, -18, 2, 28, -5], [-46, -3, -23, 9, 3, 9], [-29, 10, -22, 1, -6, 20], [8, 2, 10, -4, 2, -10], [-29, -7, -1, -4, 8, -2], [30, 4, 49, 1, -28, 3], [-8, 6, -7, 10, -8, 8], [16, 1, -13, -11, 31, -6], [0, -5, -13, 3, 18, 1], [24, -4, 0, 2, 11, -6], [4, -15, 15, -9, -9, -19], [55, 6, 39, -10, -22, 3], [-23, -2, 0, 0, 4, -5], [-16, 0, -7, 3, 1, 10], [40, -1, 2, 2, -14, -9], [17, 15, 4, 3, -8, 12], [25, -1, 30, -8, -43, -2], [41, -10, 20, -3, -17, 3], [10, -4, 10, -4, 2, 4], [9, 2, -12, 9, 25, -3], [45, -15, 38, -1, -27, -6], [22, 7, -10, 4, 25, 11], [3, -9, -28, 3, 14, 4], [16, -15, -38, -2, 19, 7], [9, -11, -6, -1, 18, 6], [2, -11, 47, -9, -10, -3], [10, -5, -25, 14, 21, 13], [-6, -13, -6, -13, 4, -9], [-23, 19, -22, 7, 30, 4], [48, -4, 18, 3, -33, -8], [-9, 10, 5, -3, 21, 11], [47, 1, 53, -2, -32, 5], [36, -4, 10, 0, 19, -14], [-2, 2, 0, -7, -25, 6], [5, 0, 26, 9, -11, 5], [6, 2, 15, 5, 21, 20], [28, 8, 27, -7, -27, -2], [26, -6, 37, -3, -3, 6], [-45, 6, -56, 3, 39, 7], [-16, -5, -17, 16, 27, 3], [12, 5, 1, 10, -11, 1], [19, -4, 37, -5, -3, -3], [-6, 0, -36, 5, -9, 4], [0, -1, 27, 3, -30, -3], [10, 5, 20, 2, -10, -6], [-25, 10, -17, 6, -8, 1], [14, -19, 17, -5, -4, -17], [-19, 3, -17, 4, 53, -2], [-16, -8, 8, 4, -31, 0], [-49, -13, -17, 4, 1, 2], [-26, -5, -30, 4, 6, 5], [27, -8, -1, 1, -25, -5], [59, -4, 25, -2, -34, -3], [50, -8, 8, 9, 7, -2], [-16, -1, -31, -1, 19, 4], [4, -14, -16, 4, 30, -6], [-8, 9, -28, 14, 1, 7], [-15, -8, -13, -10, 16, -1], [12, 7, 39, 10, -17, 5], [-15, -2, 14, -5, -5, 5], [64, -1, 4, 6, -31, -3], [7, 4, -32, 7, -4, 0], [-15, -5, -30, -9, 14, -12], [35, -12, 13, -2, 18, -15], [-20, 18, 0, 8, 9, 5], [-35, -1, -49, 6, 43, 2]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_7098_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_7098_2_a_ct();".
// 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_7098_2_a_ct(:prec:=6)
    chi := MakeCharacter_7098_a();
    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_7098_2_a_ct();".
// 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_7098_2_a_ct( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_7098_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-281, -131, 111, 39, -17, -3, 1]>,<11,R![-1, 6, -5, 1]>,<17,R![1, -2, -1, 1]>],Snew);
    return Vf;
end function;