
// Make newform 7098.2.a.cu in Magma, downloaded from the LMFDB on 16 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_cu();".
// 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_cu();".
// 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 := [-29, -16, 32, 12, -11, -2, 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], [15, 7, -9, -2, 1, 0], [-6, 13, 9, -9, -2, 1], [29, 8, -19, -3, 2, 0], [31, 23, -12, -12, 0, 1]];
    Rf_basisdens := [1, 1, 2, 2, 2, 2];
    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], [2, 0, 0, 0, 0, -1], [-1, 0, 0, 0, 0, 0], [1, 2, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 2, -2, 0], [0, -1, 0, 2, 0, 0], [-1, 1, 1, 0, 2, 0], [0, 1, -2, -1, 0, 0], [-1, 0, 1, 2, 0, 3], [2, -1, 0, 0, -1, 0], [8, -3, -4, -2, 1, -2], [2, 0, 1, 1, 3, 0], [4, -2, 0, -1, 0, 1], [2, -3, -1, -3, 1, -1], [2, -2, 1, 2, -3, 3], [2, 0, -2, -3, -2, 1], [6, 1, -4, -5, -2, 2], [0, 1, -3, 4, 0, 3], [0, -1, -2, -4, 2, 1], [4, 2, 3, -2, 1, -1], [0, -1, 5, 2, 3, 0], [2, -2, -1, 1, 0, 1], [0, 0, -1, 6, 1, -3], [-2, -3, 3, 6, -3, -1], [-7, 2, 3, 5, 0, 2], [6, -2, -9, -5, -1, 1], [0, 1, 4, 1, 3, -3], [-4, 0, -1, -5, 3, -2], [-2, -3, 8, 8, 0, 3], [-6, -3, 0, 0, 0, -1], [-6, 4, 5, 5, 1, 4], [-11, 0, -1, -2, 2, 3], [2, 1, -3, 0, 3, 0], [-4, 5, 7, -1, 1, 1], [2, 0, 2, 8, -2, -2], [-2, 3, 9, -3, -3, -1], [6, 3, -12, -2, -2, -1], [-4, 2, -1, 2, -7, 2], [-10, 4, -2, -3, 4, 3], [-4, -6, -3, 6, -3, -1], [-6, -1, 7, -2, -1, -1], [3, -3, -1, 4, -4, 0], [6, 3, -2, -4, -4, 5], [8, -2, -2, 2, 3, -5], [8, -3, -16, -12, 0, 3], [13, -1, -13, -8, 2, -4], [-4, 1, 0, 5, 0, -2], [-6, 2, 9, 2, -1, -3], [-6, 7, 1, 9, -1, 3], [0, -4, 11, 4, -1, 4], [8, -4, -5, -7, 3, -4], [-8, -1, 10, -2, 4, 1], [0, -1, -5, -7, -1, 3], [-3, 2, -4, 10, -3, 2], [0, -2, -5, -9, 4, 3], [-8, 6, 5, 2, 1, 4], [8, -2, -8, -5, -2, 6], [8, -3, 5, -1, 1, -1], [-5, 5, 11, -3, -2, 1], [2, -3, 3, 13, 2, -4], [-2, 2, 8, -6, -3, 1], [4, 0, -12, 2, -8, 0], [-16, 7, 5, 4, 3, 4], [6, -1, 6, -5, -6, 4], [-4, 1, -9, 8, -5, 0], [-22, 2, 4, 4, 2, 3], [-16, 1, 6, 1, 0, 10], [6, 4, -13, -9, 3, -4], [3, -1, -2, -7, 7, -4], [1, 6, 7, -8, 4, 1], [12, 4, 7, -4, 3, -8], [8, 0, -9, -7, 0, 3], [-2, 6, 1, -5, 5, 4], [-2, -2, -9, -17, -1, 2], [0, 1, 2, -4, -2, 5], [20, 0, -22, -11, -4, 1], [-8, 5, 12, 8, 0, -3], [12, -5, -1, -1, 1, -3], [6, 2, 6, 3, 6, -3], [0, 5, 10, 8, -2, -6], [10, 0, 2, -20, 0, -1], [-8, -9, -3, 8, -1, 2], [6, 4, -2, -16, 4, -3], [6, -1, -14, -19, 1, 1], [8, 4, -4, 4, 0, 2], [4, -8, -10, -1, 6, 0], [9, -6, -4, -3, -1, -7], [8, -3, -7, -6, -3, 0], [-2, 5, -11, 1, 3, -1], [-6, -1, 10, 10, -6, 3], [-4, 7, 1, -4, 5, -10], [-13, -8, -4, 5, -3, 1], [-26, 3, 16, 14, -4, 3], [12, 3, -3, -8, -3, -4], [-3, -7, -6, 1, -1, 4], [-7, -4, -11, 8, -2, 3], [-8, -4, -3, -2, -5, 2], [-16, -6, 6, 1, 8, -6], [6, 0, -4, 3, -10, -1], [-6, 2, 15, 7, 3, 6], [-2, 2, 4, 8, 0, -6], [20, -4, -3, 0, 9, -1], [-6, -7, -3, -3, -3, -5], [2, -2, -1, 20, 1, -1], [-4, 4, -1, 4, -1, 1], [-6, -1, -7, 4, -5, 4], [-6, -1, 12, 10, -12, -1], [4, -3, -12, -6, -2, 7], [-2, -11, -7, -1, 4, 0], [-13, -2, 21, 11, 2, -6], [22, -6, -13, -7, -1, -8], [0, -4, -11, -15, 1, -4], [6, -5, -14, -15, -8, 8], [-12, -1, 11, 18, 9, -10], [-5, -2, -10, -3, -1, 1], [-10, -2, 9, 3, 5, 2], [20, -5, -5, -8, 1, -10], [-11, 3, 22, 7, -1, -2], [4, -2, 15, 23, -7, -2], [-18, 5, 19, 14, 3, -7], [-8, 8, -9, 4, -3, 1], [10, -15, -14, -3, -3, -1], [5, -6, -20, -8, -5, -2], [20, -3, -19, -25, 5, -5], [-6, 2, -8, -22, 0, 3], [8, -11, -8, -1, -6, -2], [-22, 11, 6, 13, 2, 1], [-2, -7, 1, 16, -5, -8], [4, 2, -1, -2, 3, -17], [17, -9, 1, -3, 4, 3], [12, -6, -6, -8, 4, 6], [4, 0, -17, -9, -4, -7], [4, -4, -6, 9, 6, 2], [10, -1, 2, 0, 0, -11], [6, 11, 21, 2, 7, -2], [11, 10, 9, -12, 6, 5], [-4, 2, 4, 2, -9, 11], [8, 2, 3, 7, -1, -12], [-32, 11, 18, 8, 7, 4], [-6, 5, -13, -8, 7, 4], [6, 1, -15, -18, 3, -4], [44, -5, -17, -5, 4, -2], [-12, -9, -3, -16, 7, -2], [-14, 5, -5, 11, 1, -3], [2, 7, 2, -10, 4, 5], [-6, -8, 5, -13, 11, -3], [-22, -4, 16, 14, -4, 7], [8, 6, 6, -12, 9, -1], [12, 0, -5, 9, -2, 1], [6, -6, -13, 7, 1, -9], [-16, -4, 1, -8, 7, 1], [-24, 9, 31, 14, 1, -2], [10, 7, 2, -15, 0, -8], [-2, 1, -9, 0, 7, -3], [-2, 10, -7, 20, -7, 7], [-16, 1, 24, -4, 0, 7], [2, -14, 0, 6, -8, -10], [46, -6, -19, -11, 5, -7], [2, -4, -14, -28, 6, -3], [-4, 0, 9, -2, -3, 7], [0, 0, 15, -1, 3, 2], [-24, -3, 22, 9, 0, 8], [4, 3, -1, -9, 1, -11], [-12, 7, -1, 9, -9, 1], [4, -7, -3, 15, -7, -11], [-20, 9, 5, 12, -7, 8], [-34, 17, 11, 10, 3, 9], [20, -2, -2, -6, -3, -3], [4, -3, -11, 5, -19, 6], [-8, -10, 10, 14, 0, -10], [-1, -9, 20, 13, -3, 0], [-8, -15, 12, 18, -1, 4], [3, 14, 0, -23, 7, 1], [16, 0, -20, -1, 4, 8], [0, 9, -5, -10, 9, 6], [-8, 2, -19, 5, -1, -2], [-14, 2, 2, -15, 5, 14], [10, 0, -15, -20, 15, -7], [10, -5, 0, -1, -12, 16], [6, 7, -2, -6, -6, -1], [14, 1, 12, -1, 6, 1], [16, 0, -23, -18, -3, 10], [4, 1, -1, -7, 9, 0], [-4, -2, -18, 1, 0, 10], [-7, 6, 10, -21, -3, 1], [4, 2, 7, 8, -4, 2], [12, 5, -22, -32, 4, 2], [4, 6, -20, 6, -6, 6], [-14, -1, -7, 13, 1, 1], [6, 5, 13, 6, 7, -5], [4, 4, 9, -15, -5, 8], [-12, -1, 11, 8, 4, 13], [10, -6, -6, -24, 6, -13], [-13, 13, 9, 6, 2, -8], [-4, -5, -6, 0, -10, -5], [28, -3, 4, -27, 3, -7], [-40, 8, 25, 20, -4, 4], [0, 1, -15, -15, 5, 3], [8, -8, -12, -15, -6, -3], [-8, -1, 27, 0, -7, -6], [-2, 16, 7, -4, 5, -5], [-16, 3, 22, 23, -6, 6], [32, -15, -26, -22, -10, -1], [-21, -5, 9, -2, 8, 4], [-7, -17, -7, 8, 4, 2], [-6, -10, 16, 4, 9, 3], [10, 8, -2, -2, -2, 6], [-24, -13, -7, 22, -9, 6], [26, 7, 4, 13, -1, 3], [4, -3, -4, -1, -9, 15], [6, -7, -19, 16, 5, 0], [8, -17, -8, 11, -10, -16], [2, -17, -11, 8, -7, -2], [-30, -7, 3, 9, -3, -9], [12, 0, -26, 5, 4, 11], [-11, 3, 9, -11, 4, 17], [-5, -6, -13, 9, 14, -6], [18, 8, 4, -4, 4, -12], [40, -5, -29, -12, 2, -5], [26, -17, -22, -30, 3, -6], [-10, 4, 23, 3, -1, -18], [-10, 7, 11, 4, 9, -12], [38, -2, -2, -1, 6, -9], [9, 2, 6, -11, -3, -5], [-17, -6, -3, -4, -4, 5], [-15, 9, 37, 30, 8, -6], [-20, 2, -9, 7, -16, 3], [-8, 8, -2, -11, 4, 0], [1, -13, 1, -8, 6, 6], [-17, 5, 20, 10, -9, -3], [8, -10, -21, -7, 3, 8], [16, 5, 20, -22, 12, -1], [22, 7, -31, -49, 5, -5], [-10, 1, 8, -29, 2, 10], [-26, 0, -8, -13, 8, 9], [2, -2, -16, -34, 2, 4], [-2, 9, 7, -18, -2, 7], [22, -8, -5, 12, 11, -3], [-30, 0, 12, 30, -16, 15], [-1, -1, -22, -10, -11, -11], [2, 11, 11, 6, -13, 5], [-10, -4, 26, 31, -11, -2], [14, -2, -20, -2, 5, 1], [-14, 11, 16, -12, 4, 19], [-28, 8, 13, 29, -4, 15], [-22, 17, 27, 12, 5, -2], [-26, 3, 41, 8, 3, 8], [8, 5, -9, -11, 5, -4], [-10, 0, -1, -9, 19, -3], [-23, -3, -4, -4, 3, -5], [-39, 11, 22, 7, 1, 12], [-2, -10, 7, 0, 11, 5], [10, 1, -9, 17, -6, 0], [-14, 6, 21, -1, 1, -15], [-1, -6, -1, 12, -12, 9], [-9, 11, -12, 18, -5, -1], [3, -11, 9, 16, 4, 12], [-4, 3, 16, 12, 0, -13], [-8, -1, -17, 1, 9, -5], [-15, 20, 9, 9, 0, 0], [-2, 6, 2, -3, 14, -5], [-16, 12, 5, 7, 3, -12], [0, 0, -34, -25, 7, 4], [-19, 0, -6, 5, 5, -5], [0, -11, 14, 28, -10, 3], [-23, -6, -15, 18, -10, 7], [22, -12, 6, -11, 2, -7], [-28, 10, 38, 28, 4, 4], [-12, 13, 1, -29, 5, 17], [18, 6, -11, -37, 7, 0], [-12, 12, -7, -11, 15, 2], [-8, -5, 25, -4, -1, 18], [0, -15, 10, 2, -2, -5], [-8, -17, 2, 20, -4, -12], [24, -9, -20, 9, -10, -10], [0, 4, 1, 1, -10, -3], [-38, 11, -3, -6, -6, -7], [-22, 0, 8, -5, 4, 1], [22, -1, 26, -22, 2, -7], [-26, -6, -4, 12, -2, 0], [18, -12, -8, 19, 14, -5], [-2, -7, -16, -6, -14, 5], [-23, 13, 11, 6, 8, 2], [28, -3, -27, -10, 0, -11], [10, 10, -32, -2, -11, -7], [10, 1, -8, 0, -14, 9], [2, -5, -5, 13, -13, -5], [49, 1, 4, -3, -1, -12], [-4, 13, -9, 5, -7, 13], [12, -6, 6, 2, 2, -12], [22, 4, -11, 6, -13, 5], [-24, 19, 22, 22, 0, 7], [14, -1, -9, 9, -8, 16], [10, 12, -12, -21, 1, -6], [-14, -3, -6, 2, -6, 15], [10, 1, 21, 27, 6, 6], [8, -14, -23, -6, -13, -11], [-30, 2, 1, 3, 0, -17], [-20, -2, 14, -5, 0, 13], [24, -9, 9, 6, -19, -6], [2, 12, 16, -5, 4, -25], [-2, 0, 20, -8, -7, 1], [-12, 15, 13, 34, -5, 6], [-2, -11, -11, -4, -7, 7], [0, 5, 0, -38, 8, 0], [-34, 16, 15, 9, 3, 10], [22, -7, -55, -25, 5, 5], [27, -2, -3, 6, 2, -19], [-26, 17, 26, 19, 6, 4], [-40, 2, 35, 20, -7, -5], [64, -12, -26, -25, 8, -13], [-42, -1, 29, 21, 7, -15], [-4, 14, 5, 21, -11, 6], [8, -3, -27, 4, -5, -6], [10, 2, -6, 9, 12, -3], [1, 8, 3, -10, 12, 5], [-20, 7, 20, 27, -24, 8], [28, -2, -27, -14, 1, 9], [12, -5, -20, 18, -1, -2], [30, -3, -16, -29, 8, -19], [34, 2, -11, -18, 2, 2], [-10, 2, 25, 6, -11, -3], [-10, 0, -3, -21, 7, 2], [6, 5, -10, -9, -2, 4], [32, 3, 5, -17, 9, -17], [22, 6, -3, -2, -13, 3], [28, -12, -21, -1, -1, -4], [20, 13, 7, -14, 7, 6], [9, -5, -29, -29, 0, 3], [4, 1, 1, 12, -5, -10], [-7, -18, 8, 35, -3, 7], [2, -9, -27, -3, 7, -5], [-30, 15, 14, 8, -4, -7], [30, -18, -4, 4, -18, -6], [-8, 5, -25, -31, 7, -3], [7, 5, 12, 34, -23, 1], [-30, 15, -22, -13, 6, -10], [4, -11, 0, -16, -6, -8], [32, 11, -30, -33, 9, -21], [16, -8, -8, 9, 8, 7], [7, 0, 27, -6, 16, 1], [-6, 16, 15, 23, -11, 4], [-2, -4, 6, 31, -8, -11], [3, 1, -13, -21, 2, -1], [-26, 3, 32, 17, -4, 0], [-24, 1, 34, 20, 0, 15], [38, 8, -29, -28, 11, -11], [12, -15, 10, -14, 6, -4], [-36, 20, -5, -3, 11, -6], [-16, 6, 41, -4, 7, 13], [14, -16, -9, -18, 3, -17], [24, 8, -19, -49, 13, -18], [0, 11, 22, 42, -6, -8], [-4, 19, 7, -17, -11, 10], [-28, 7, 4, 30, -8, 23], [-12, 5, -2, 8, 0, 13], [-22, 15, 2, 31, -8, 10], [13, -5, -16, -14, 15, -3], [46, -8, -37, -8, 6, -14], [-6, 21, -14, -5, 4, -12], [-16, -12, 21, 19, 5, -2], [28, -10, 11, 19, 3, 6], [-14, -18, 10, -12, 17, -1], [6, -7, -47, -10, 0, 1], [-4, -3, -23, -29, -3, 0], [-6, 4, -16, -2, 14, 10], [26, 4, -1, -3, 10, -19], [-24, -31, 6, 34, -6, -12], [-39, -14, -17, 27, -6, 2], [42, -5, 15, -6, -13, 9], [20, -7, 16, 16, 6, -5], [-34, 8, 57, 32, 8, -8], [48, -9, -11, -22, 10, -15], [-18, 10, 11, -23, -17, -2], [-33, 8, 36, 14, -5, 0], [40, 5, -21, -18, -9, 24], [18, -20, 0, 10, 3, -7], [16, -7, -31, -25, -7, 11], [-35, 16, 5, 18, -4, 3], [28, -5, 16, 25, -18, 2], [-24, -4, 16, 14, 8, -12], [24, 3, -10, 13, 4, -14], [34, -11, 20, 17, 1, 7], [10, -6, 1, 20, -13, 3], [-46, 11, 9, -13, 3, 7], [10, 2, -29, -6, -1, 5], [10, -9, -5, 27, -15, -1], [42, -27, -20, -8, -6, -3], [9, -2, 8, -1, -15, 1], [-49, 7, 37, 43, 8, -3], [10, 3, -9, 11, -5, 1], [-53, 7, 26, 13, -15, 8], [-47, -5, 23, 26, -2, -10], [-46, 2, 25, 7, 7, -7], [-2, -18, -25, -40, 10, 0], [23, -13, 14, 11, -1, 6], [-10, 25, 12, -5, -8, 6], [18, -17, -13, 28, -1, -20], [28, -13, -11, -10, 11, -6], [-12, 1, 25, 22, 5, 10], [56, -1, -28, -15, -2, 0], [-5, 4, 22, 13, 17, -13], [19, -12, -24, -25, 13, -3], [-17, 21, 1, -18, 18, 10], [-13, 3, 6, 31, -15, 4], [-16, 1, 28, -2, 10, -7], [30, 18, -12, -4, -4, 11], [6, 18, 13, -3, 9, -6], [-24, 17, 6, -6, -6, 3], [52, -16, -10, -5, -12, -1], [-40, 4, 5, 46, -18, 16], [6, 22, 34, -3, 0, -9], [26, -4, 14, 30, -15, -9], [45, -3, -19, 0, 6, -24], [-8, 24, 27, 15, 3, 4], [-19, 21, 2, 1, -3, 8], [2, -17, 7, 4, 11, -5], [-28, 12, -2, -8, 10, -10], [20, 4, -13, -24, -1, -21], [56, 8, -13, -11, 5, -4], [25, 4, -8, -3, -3, -13], [-16, 19, 64, 31, -2, -14], [48, -24, -21, -18, 1, 3], [24, -5, -21, 15, 11, -2], [-26, -7, -3, 17, 9, -13], [8, -6, 21, 23, -3, 4], [16, 0, 13, 34, -1, -18], [-30, 10, 18, 9, 14, 15]];
    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_cu();".
// 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_cu(: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_cu();".
// 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_cu( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_7098_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![13, -15, -49, 9, 21, -9, 1]>,<11,R![937, -1630, -342, 296, -9, -10, 1]>,<17,R![337, -2486, 452, 256, -55, -4, 1]>],Snew);
    return Vf;
end function;