
// Make newform 7098.2.a.cp in Magma, downloaded from the LMFDB on 19 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_cp();".
// 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_cp();".
// 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 := [-41, -9, 44, 11, -12, -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], [-25, 20, 20, -9, -3, 1], [-45, 16, 24, -9, -3, 1], [28, -7, -23, 5, 4, -1], [-41, 21, 37, -12, -7, 2]];
    Rf_basisdens := [1, 1, 4, 4, 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], [0, 1, 0, 0, 0, -1], [-1, 0, 0, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [3, -2, -1, 0, 1, 0], [1, 0, -3, 1, 3, 0], [-1, 0, -2, 1, 0, 0], [1, -2, 1, -1, 0, 2], [-2, 1, 1, -2, 1, 1], [-2, 0, 1, 0, -2, -3], [-4, 0, 5, 0, -6, 1], [0, 0, 1, -1, 3, 1], [-4, -3, 0, 0, -1, 1], [1, -3, -4, -2, 4, 0], [0, -1, 1, 1, 0, 0], [4, -1, 2, 2, 3, 3], [-3, -2, -3, -1, -2, 0], [4, -1, -8, -1, 4, 1], [-3, -3, -1, 3, -3, 3], [-4, 1, -1, 1, 0, -2], [-3, 0, 6, 0, 1, -1], [3, -3, -3, 0, -2, -1], [0, 3, -3, -5, 4, -2], [7, 1, -4, -2, 3, 2], [-4, 2, -1, -4, -4, -2], [2, -1, -1, 3, 3, 4], [-2, -5, 5, 4, -5, 2], [-2, -4, 5, 1, -7, 1], [-3, -1, 5, 1, 1, 1], [1, 1, 3, -1, -3, 1], [4, -2, 1, 1, -3, 3], [2, 1, -1, -2, 9, -1], [5, 0, -6, 0, 11, 1], [-11, -1, 4, -2, -8, 0], [-2, 2, 6, 2, 0, 0], [-3, -1, -2, 2, 4, 0], [-1, -3, 5, 3, -3, 9], [8, 0, 3, 1, -6, -3], [-2, -1, -8, -2, 1, -5], [4, -1, 5, 5, -6, 2], [-7, 5, 10, -2, 7, -2], [-3, -2, -6, -5, 4, -2], [-3, 3, -7, -1, 7, 1], [-1, 3, -4, -3, -5, -4], [-1, -3, -5, -1, 5, 1], [-7, -4, 0, 5, -10, 6], [9, 2, -3, 1, 6, 2], [-8, -1, 7, 1, -16, 2], [-3, 3, -2, -4, 0, 0], [4, 2, 9, 1, -4, 1], [-14, 6, 7, -5, 1, -3], [7, -1, 3, 1, -5, 3], [13, 3, -10, -2, 4, -2], [2, 2, 8, 3, -3, -3], [1, 3, 7, -4, 4, -1], [-18, 6, 3, -1, -4, -3], [2, 6, -10, 0, -1, -6], [-3, -3, 12, 4, -10, -2], [3, -3, 4, 7, 1, 1], [-2, 4, -12, -3, -1, -6], [-13, 5, -2, 1, 3, -2], [12, 0, -8, 4, -2, -4], [-5, 2, 0, -2, 1, -7], [-7, 6, 5, 1, 8, -4], [-11, -4, 2, 2, -17, 3], [8, -5, -14, 0, 2, 3], [-19, 8, 7, -3, -4, -10], [-6, -6, 11, 3, -3, 7], [-3, 4, -13, -6, 5, -7], [14, -5, 3, 4, -3, 1], [12, -6, -7, 5, -4, 5], [-1, -7, 13, 8, 0, 5], [0, -4, -11, -3, 3, -3], [-6, -2, -5, -1, 9, -1], [-3, 1, -7, 5, -3, 1], [-12, 9, 2, 0, -1, -1], [-13, 5, 15, -1, 3, 1], [1, -5, -8, -6, 2, 4], [-16, 7, -4, -4, 1, -7], [-1, 10, -7, -7, 5, -4], [0, -9, -8, 2, -2, 1], [-1, 0, 0, -2, 9, 3], [-4, -1, 6, 0, -6, -1], [-14, 7, -3, -2, -5, -4], [0, -2, -4, 0, 4, -6], [-8, 8, 10, 2, -9, 2], [4, 7, -8, 1, 6, -4], [-7, -6, 20, 4, -1, 3], [-1, -3, 0, 2, -4, 10], [9, 1, 7, -1, -9, -3], [-5, 0, -2, 2, -5, 1], [-10, -1, 12, 3, -4, 4], [-7, 3, -21, -5, 7, -5], [-7, 6, 14, -2, -15, 5], [-3, -4, 1, 12, -5, 5], [20, -5, -3, 2, 7, 1], [-10, -4, 7, 1, -4, 7], [-6, 2, -4, -2, 7, -8], [-20, 1, -4, 2, 1, -1], [0, 0, -15, 1, 11, 5], [0, 6, 10, 2, -14, 2], [-6, -1, -7, 5, 8, 4], [-19, 1, 20, 0, -22, 0], [-8, -3, 3, 9, 0, 0], [-8, 1, 13, 1, -4, 4], [-15, -4, 4, -2, 3, 3], [-7, 7, -13, 3, -1, -5], [-13, 13, -11, -1, -3, -5], [2, -4, 0, -1, 13, 10], [-12, 4, 3, -4, 4, 6], [-22, 6, 13, -3, -17, -7], [-2, 0, -7, -7, 3, -11], [9, -2, -3, -1, 10, 0], [3, 4, -6, -4, 3, 1], [-2, 5, -10, -3, -4, -8], [18, -2, 3, -1, 7, -1], [-17, 6, 10, 4, -9, -1], [-25, -6, 11, 6, -9, 3], [-4, 0, 17, 11, -19, 3], [-3, 1, 8, -4, -19, 0], [0, 7, 1, -5, -2, -6], [-4, -5, 5, 8, -9, 14], [-4, -4, -2, 7, -7, 3], [9, 9, -18, -2, 8, -16], [-6, -3, -16, 0, 0, 5], [-1, -4, -5, -3, 6, -8], [-23, 3, 13, 1, 4, 1], [-11, 12, 6, -4, 7, -7], [10, -1, -1, 3, 8, 6], [7, -7, 4, 3, -3, 3], [-24, 2, 16, 6, -20, -2], [-1, 3, -3, 4, 2, -5], [0, -10, -4, -4, -11, -2], [1, -11, -1, -3, -5, 1], [13, 8, -12, 2, 23, -5], [-4, -7, 5, 4, 1, -5], [-11, 1, -8, -1, 9, 4], [4, -2, 15, 7, 11, 7], [-8, 0, -7, -8, -6, 1], [7, -4, -8, 0, -11, 5], [-5, 2, -16, -14, 19, -1], [18, 0, -6, -1, -1, 10], [11, -2, -8, -6, -5, 1], [7, -1, -28, -2, 8, -8], [17, -5, -7, -5, 13, 9], [6, -1, -21, -7, 1, 0], [-18, -11, 18, 6, -12, 7], [-1, -5, -8, -1, 13, 8], [-29, 5, 15, -2, -14, -9], [-12, -7, -1, 5, -9, 0], [2, 3, -11, 7, 6, 4], [-15, -8, -10, -4, -5, 3], [-27, 0, -1, -7, 14, 4], [-9, 3, -12, -8, 3, -12], [8, -7, -11, -3, 12, -6], [17, -1, -13, -5, 29, -3], [-24, -2, 22, 2, -12, 2], [20, -7, 5, 5, 5, 6], [-6, 13, 26, -2, -2, -9], [-10, 7, 5, 1, 6, 4], [-2, 10, -7, -3, 7, -1], [17, -8, -19, 7, 12, -4], [13, -9, 8, 6, 14, 4], [13, 3, -10, 6, -2, -10], [5, -15, -18, -2, 2, -4], [35, 0, 6, 6, 15, 5], [11, -5, 24, 4, -1, 4], [-19, 3, 6, 1, -3, 0], [-7, 6, 18, -6, 2, -3], [12, -2, -4, -2, 10, 6], [-31, 4, 17, 4, -19, 3], [14, 4, -19, 0, 12, 7], [20, -3, -2, 1, -6, 4], [0, -8, -2, 2, -19, 2], [-17, 2, 22, 0, -13, -1], [0, 4, 15, 9, -21, -11], [-21, 18, 8, 3, -10, -11], [-14, 9, 23, 1, -28, 2], [11, 6, -1, -9, 14, -4], [-9, 5, 7, -1, 5, -9], [-7, -7, 11, -3, 12, 9], [-16, 0, 13, -7, -6, 7], [13, 2, 4, 2, -24, 7], [6, 10, 2, -8, 5, -6], [18, -3, -4, 5, -14, -4], [13, -8, -21, 10, 7, -4], [-43, 8, 13, -5, -11, -4], [20, -2, 6, -8, -2, 0], [31, -7, -10, -2, 18, -4], [-1, -3, -4, 2, -15, -2], [2, 4, 21, 7, -29, 5], [-4, 7, 12, -1, -4, 9], [-8, -11, 0, 4, -4, -5], [9, 2, -26, -5, -8, -10], [7, -5, -17, 3, 7, 3], [-2, 9, 3, 4, -11, 2], [19, -6, -11, 6, -5, -10], [9, -1, 14, 10, 20, 10], [36, -3, -8, -6, -1, 5], [21, 2, -28, 6, 31, -1], [-10, 13, 3, -7, 4, 2], [-5, -6, 23, -5, -20, -2], [9, -9, -1, -5, -3, -3], [-13, 6, 12, 11, -10, -10], [-7, -2, 14, 7, -22, -2], [-15, 23, -6, -7, 3, -6], [2, -2, 6, 6, 14, 0], [9, 0, -30, 8, 23, -1], [-12, 15, 9, -6, -7, -10], [38, -19, -13, 10, 11, 6], [-15, 2, -8, 0, 19, 5], [-31, -8, 19, 1, -8, 10], [25, 8, 14, 2, -5, -7], [1, 5, -2, 8, 18, 10], [-16, -3, 16, 2, -29, 1], [5, 7, -4, 3, -5, -5], [42, -10, -13, 10, 24, 6], [-2, 4, 0, -12, 24, -8], [2, 13, 0, -7, 2, -3], [14, -6, -25, 2, 18, -11], [12, -4, -17, -5, -17, -5], [-13, -2, -8, -10, 9, 7], [-16, 9, 8, -8, 21, -1], [22, -1, -20, -7, 36, 2], [-10, 5, 11, 6, -1, 1], [-5, 6, 10, 11, -16, -8], [3, 11, -9, -4, 22, 9], [28, -6, -24, -6, 29, 10], [17, 0, -2, 1, -20, 4], [9, 5, 7, 6, 6, 0], [24, 0, -5, -1, -1, 13], [17, 9, 1, -7, -13, 1], [-41, 17, 12, 0, 0, -6], [7, -8, 17, -5, -14, 0], [30, -11, -18, 6, 11, 3], [-10, 0, 14, -4, -2, 6], [-38, 5, 6, 3, 2, 1], [18, -1, -7, 5, -10, -2], [-38, 3, 4, -8, 4, -5], [15, -7, -1, 6, -20, 2], [17, -13, -32, 0, -1, 6], [-1, -2, 2, -7, -4, -1], [-13, -1, 24, 7, -17, 22], [-13, -5, -1, 3, -29, -3], [17, 5, 9, 6, 8, -1], [45, -2, -18, 0, -11, 3], [7, 8, -14, 8, 11, -9], [3, 2, 4, -6, 12, 1], [-22, -19, -5, -1, -31, 10], [-7, -7, 15, -8, -18, 0], [7, -20, -15, 8, -9, 9], [2, -11, 25, 9, -14, 12], [2, 0, 8, 11, 25, 6], [-2, -11, -1, -1, -23, -2], [36, -1, -19, -4, 33, -7], [-3, -3, -5, -8, 32, -10], [41, 2, -22, -3, 38, 2], [5, -9, -23, -7, 33, -5], [-7, -13, -2, 0, -20, 2], [-2, 6, -3, 6, -12, -8], [-10, 7, 8, -20, -5, -1], [6, -22, -17, 1, 9, 5], [33, -4, -16, 7, -8, -5], [-24, -3, -8, 3, 0, -8], [-5, 9, -1, -5, -5, 5], [30, 17, -23, -8, 25, -17], [26, -19, 2, 2, -9, -1], [4, -4, 4, 2, -4, -12], [37, 3, 2, -2, 16, -2], [2, -8, 21, 11, -19, 7], [4, 12, -31, -5, -5, -5], [-21, -4, 22, -8, -17, 13], [33, -7, -21, 3, -9, -1], [-9, -10, -13, 5, 5, 2], [1, 16, 25, 11, -30, 0], [-15, 1, 29, 6, -8, -5], [-6, -7, -10, 3, -14, 1], [26, -21, -8, -4, 3, 11], [-37, 17, 29, -11, -23, 1], [6, -12, -34, -4, 36, -18], [-14, -11, 14, 0, -31, -5], [23, -21, -19, 3, 7, 3], [-37, -2, -2, -7, -22, 0], [-28, -5, 20, 5, -18, 1], [37, 3, 4, -9, 13, -8], [-1, 3, -19, -9, 33, 3], [35, -11, 20, 12, 4, 14], [1, 4, -3, 0, 3, -9], [-9, -21, 40, 10, -12, 18], [26, 4, 0, 4, -20, 2], [-34, 3, 43, -3, -8, 4], [1, -5, -11, 7, -15, -5], [-10, -22, 18, 9, -27, 2], [-37, 12, 0, -3, -10, -5], [31, -5, -5, -13, 13, 5], [-24, 10, 6, 7, -23, 4], [0, -1, 11, 1, -18, 16], [-17, 7, 11, 8, -12, -17], [32, -5, -22, 0, -3, -19], [15, 6, -4, -4, 21, -3], [28, 9, -6, -10, 19, -19], [-1, -11, 28, 7, 9, 8], [-29, 10, 6, -8, -5, -13], [3, -11, -6, 10, 13, -4], [-11, -8, -13, -1, -1, -2], [-6, 0, 5, -7, -23, -5], [9, -13, 24, 4, 0, 2], [28, 7, -29, -6, 39, -17], [19, 18, -27, -19, 28, 2], [-6, -11, -7, 7, -6, 18], [14, -3, -28, 2, 23, 19], [-11, 3, 26, 16, -30, 4], [-42, 2, 19, 3, 15, -7], [25, 12, -18, -4, -9, -5], [-14, 5, 4, 10, 15, -7], [-28, 19, 13, 2, -7, -3], [-19, 4, -1, -13, 4, -10], [-16, -3, -5, -1, 24, -10], [6, 6, -11, -20, 22, -3], [7, 5, -9, -1, 40, -1], [-17, -2, 11, 8, -5, 18], [8, 1, 15, 3, -26, 20], [-30, -4, 5, -13, -7, 7], [23, -4, 29, 5, -6, 0], [7, 7, 10, 10, 42, 4], [-2, 5, -19, -5, -4, -16], [20, -4, -19, 1, 37, -1], [-9, 10, -16, -8, 17, -3], [-25, -5, 22, 3, 17, -5], [25, 2, -14, -12, 25, 1], [-32, -9, -30, -5, 2, 0], [-13, 19, 18, -4, -10, -14], [-21, 21, -11, -9, 3, -15], [-10, 18, -14, -12, 0, -12], [11, -15, -10, 10, -24, 10], [-3, -9, 19, 6, -22, 12], [-1, -6, 13, 1, -12, -10], [7, 2, -11, 3, 9, 8], [-4, 5, -19, -4, -1, -14], [-8, 9, 14, 14, -5, 3], [28, -7, -5, 18, 13, 5], [-2, 0, -5, 9, -13, 13], [-22, -7, -38, -12, 21, -5], [-27, -1, 6, 3, -35, -7], [15, 18, 13, 1, -6, -6], [-5, 3, -33, -11, 1, -5], [10, 1, 11, 7, 30, 6], [9, -8, 21, 5, 1, 20], [-10, 2, 15, -5, 19, -11], [2, 17, 5, -5, 2, -10], [-4, 1, 23, 3, -20, -4], [-32, -2, 7, 7, -11, -9], [7, -12, 5, 21, -9, 18], [5, -6, -16, 6, 10, -1], [3, 13, 13, 1, 27, -1], [43, 1, -9, -15, -3, 5], [-5, -2, 7, 9, 2, -8], [-21, -13, -29, -10, 2, -2], [-11, -24, 21, 20, -17, 16], [-3, -14, -17, -15, -20, 2], [44, 10, -25, -9, 13, -9], [28, -18, -23, 5, -9, -11], [15, 5, 8, -1, 5, -8], [26, 15, -12, -3, 22, -15], [-3, 10, -20, -12, 14, -9], [-32, -2, 24, 2, 8, 8], [45, -19, 5, 6, 6, 9], [-27, 8, 13, -3, 15, 12], [10, 0, 23, 22, -18, 6], [47, -7, -6, 2, 21, -4], [-29, 19, 11, -11, -9, -1], [17, 8, 27, 2, -27, 10], [-32, 7, 54, 1, -38, -5], [0, 2, 3, 7, -27, -7], [32, -8, -22, 7, -3, 9], [-27, 2, -12, 4, 21, 7], [9, 17, -2, -23, 25, -16], [-49, 11, 16, -12, -18, -6], [16, -1, 13, -6, 35, -5], [3, -2, 19, 5, -32, 22], [-12, 0, 8, -4, -10, 0], [-25, -6, 13, 3, 12, -8], [-26, -7, -1, 14, 5, 4], [18, -17, 11, 13, 10, 12], [5, 5, -12, 6, 2, -16], [2, -3, -5, -13, 18, -10], [71, -13, -24, 6, 28, 4], [39, -15, -7, -1, -17, -7], [-4, -3, 12, -11, 40, 0], [-43, 5, -6, -5, -15, -1], [-19, -7, -38, -10, 8, -14], [13, 8, -3, -16, 29, -23], [-33, 14, 26, -11, 6, -6], [-8, 15, 31, 1, -1, 6], [-27, 20, 1, -2, 5, -12], [-29, -10, 29, -2, -7, 13], [37, -22, -17, -1, 8, 22], [-3, -8, 18, -6, 3, 1], [25, 2, -8, -2, 39, 11], [-29, 8, 2, 10, 3, -7], [-13, 22, 3, 13, 10, -6], [-44, -1, 10, 7, 12, -16], [10, 3, -30, -15, 24, -10], [13, 6, -4, 9, -16, 4], [25, -8, -31, -4, 15, 1], [-19, 9, -5, -15, -21, -21], [-20, 31, -4, 4, 4, -11], [8, 18, 29, 13, -11, 3], [29, -3, -9, 11, -5, 3], [40, 5, -30, -12, 19, 7], [-27, 8, 1, -16, -11, -22], [2, -3, 20, -10, -15, 5], [29, 9, -16, -19, 25, -26], [21, -10, -22, -5, 40, 0], [20, -24, -9, -17, 3, 13], [5, -4, -21, -14, 3, 5], [-19, 5, 8, 20, -1, 4], [-20, 6, 10, 6, -8, -12], [-2, 7, -35, 9, 26, 0], [-10, -10, 31, 13, 1, 13], [20, 5, 2, -5, -12, 2], [-5, 10, 33, 7, -40, 0], [36, 13, 9, -1, 24, -8], [35, 12, 4, -16, 16, -13], [-47, 9, 22, 2, -32, 2], [16, -14, -1, 11, -15, 19], [-22, -4, 53, 7, -12, 5], [14, 9, -6, -18, 27, -13]];
    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_cp();".
// 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_cp(: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_cp();".
// 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_cp( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_7098_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-41, -55, 39, 31, -13, -3, 1]>,<11,R![-2857, -1328, 476, 180, -35, -6, 1]>,<17,R![379, -2162, -52, 290, -13, -10, 1]>],Snew);
    return Vf;
end function;