
// Make newform 2100.2.q.l in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2100_q();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2100_q_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_2100_2_q_l();".
// 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_2100_2_q_l();".
// 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, 4, 16, -4, 38, 8, 10, -2, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [712, -786, 2992, 820, 1009, -137, 78, 7], [-44, -18, -54, -390, -108, -81, 14, -9], [-124, 122, -434, 310, 7, 124, -31, 11], [-682, 696, 788, -1270, -424, -493, 117, -52], [-478, -1716, 1502, -1780, 29, -697, 168, -58], [-20, 72, -50, 154, 19, 43, -9, 4]];
    Rf_basisdens := [1, 1, 450, 150, 150, 450, 450, 18];
    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_2100_q();"
function MakeCharacter_2100_q()
    N := 2100;
    order := 3;
    char_gens := [1051, 701, 1177, 1501];
    v := [3, 3, 3, 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_2100_q_Hecke();"
function MakeCharacter_2100_q_Hecke(Kf)
    N := 2100;
    order := 3;
    char_gens := [1051, 701, 1177, 1501];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -1, 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+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, -1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1, -1, 0], [0, 0, 0, -1, 0, 0, -1, -1], [0, -1, -1, 0, -1, -1, 1, 1], [0, 2, 1, -2, 0, 1, 0, 0], [-1, 1, -1, -1, -1, -1, 0, 0], [-2, 0, 0, 1, 0, 0, 2, 2], [0, 2, -2, 0, 1, -2, 2, 2], [-2, -2, -1, 2, -2, 0, 1, -1], [3, 0, -1, 0, 0, 1, 0, -1], [4, 0, 3, 0, 0, -3, 0, 3], [1, 3, 3, -3, 1, 0, -3, 3], [0, -2, 0, 0, 4, 0, 0, 0], [0, 3, -2, 0, -2, 2, -2, 2], [-5, -2, 3, 2, -5, 1, -2, 2], [0, 3, 1, 0, 6, 1, -1, -1], [-2, 0, -2, -3, 0, 2, 2, 0], [0, 0, 0, 0, -2, 3, -3, 0], [4, 4, 5, -4, 4, 1, -4, 4], [-3, 0, 0, 1, 0, 0, 3, 3], [5, 6, -1, -6, 5, 0, 1, -1], [-4, 0, -1, 3, 0, 1, -1, -2], [0, 3, 2, 0, 2, 0, 0, -2], [-8, -4, -1, 4, -8, 0, 1, -1], [-4, 4, 0, -4, -4, -1, -1, 1], [0, 4, -1, 0, 2, 1, -1, 1], [8, 0, 2, -4, 0, -2, 0, 2], [4, 0, -6, 1, 0, 6, 1, -5], [-5, 1, 3, -1, -5, 0, -3, 3], [0, -2, -3, 0, 4, 0, 0, 3], [2, 0, -2, -2, 0, 2, 3, 1], [-5, -1, 1, 1, -5, 2, 1, -1], [0, 0, -1, 0, 5, 3, -3, 1], [0, 0, 2, 0, -2, -4, 4, -2], [-2, 2, 0, -2, -2, 2, 2, -2], [2, 0, 1, -6, 0, -1, 3, 4], [-15, -1, -3, 1, -15, 0, 3, -3], [0, 6, 0, 0, 10, 0, 0, 0], [10, 0, -4, 0, 0, 4, 1, -3], [6, 4, 0, -4, 6, -2, -2, 2], [0, 2, 0, 0, 16, -1, 1, 0], [-2, 0, 3, -2, 0, -3, 3, 6], [0, -4, -1, 0, -7, -5, 5, 1], [5, 0, 2, -8, 0, -2, -1, 1], [-8, 0, -2, 0, 0, 2, -2, -4], [0, 0, -5, 0, -4, -2, 2, 5], [-9, -2, -8, 2, -9, -2, 6, -6], [1, 5, 3, -5, 1, -4, -7, 7], [-9, 0, 5, -5, 0, -5, -2, 3], [0, 2, 5, 0, 9, 7, -7, -5], [9, 0, 5, 0, 0, -5, 2, 7], [-8, 6, 2, -6, -8, -3, -5, 5], [0, 1, 0, 0, 17, -3, 3, 0], [0, -3, 6, 0, -1, 7, -7, -6], [1, 6, 1, -6, 1, -3, -4, 4], [0, -2, 4, 0, -2, 3, -3, -4], [-9, 0, -3, 5, 0, 3, -4, -7], [0, -6, 2, 0, -10, 1, -1, -2], [-7, 0, 7, -5, 0, -7, -2, 5], [2, 0, 4, 3, 0, -4, -3, 1], [0, -5, -4, 0, -6, -4, 4, 4], [-22, -4, -1, 4, -22, 0, 1, -1], [13, 9, -3, -9, 13, -5, -2, 2], [-3, 0, -2, 0, -3, -2, 0, 0], [10, 0, -2, -3, 0, 2, -5, -7], [0, 4, -4, 0, 10, -2, 2, 4], [6, 0, 4, 6, 0, -4, -6, -2], [0, -4, -5, 0, -8, -10, 10, 5], [0, 1, -8, -1, 0, -6, 2, -2], [0, 5, 1, 0, 0, -1, 1, -1], [6, -3, -5, 3, 6, -1, 4, -4], [5, 0, -6, 6, 0, 6, 0, -6], [-12, 6, 4, -6, -12, 0, -4, 4], [0, -9, -2, 0, 0, -2, 2, 2], [-10, 6, -1, -6, -10, 4, 5, -5], [-6, -6, -2, 6, -6, 4, 6, -6], [0, -6, 0, 0, 7, -8, 8, 0], [-4, 0, -6, 2, 0, 6, -4, -10], [0, 0, 8, 2, 0, -8, 3, 11], [0, -7, -2, 0, 7, -1, 1, 2], [-10, 0, -2, 1, 0, 2, 9, 7], [-9, -6, 3, 6, -9, -3, -6, 6], [-19, -5, 5, 5, -19, 6, 1, -1], [-12, 0, -2, 0, 0, 2, -8, -10], [4, -5, 1, 5, 4, 1, 0, 0], [-5, 0, -5, -2, 0, 5, -6, -11], [10, 0, 8, 7, 0, -8, -5, 3], [-12, -2, -2, 2, -12, 0, 2, -2], [0, -7, -2, 0, -15, -9, 9, 2], [0, 1, -3, 0, 20, -7, 7, 3], [-5, 0, 1, 7, 0, -1, 0, 1], [15, -2, -4, 2, 15, 2, 6, -6], [-12, 0, -8, 6, 0, 8, -2, -10], [20, -4, 2, 4, 20, -2, -4, 4], [0, -10, -2, 0, -14, -2, 2, 2], [-10, 13, 7, -13, -10, -1, -8, 8], [1, -14, -4, 14, 1, 0, 4, -4], [12, 0, -2, -4, 0, 2, 2, 0], [0, -5, 0, 0, -1, -7, 7, 0], [0, 2, 2, 0, -8, -2, 2, -2], [-21, -12, -1, 12, -21, 2, 3, -3], [0, 4, -5, 0, -6, 1, -1, 5], [0, 11, -1, 0, 16, 3, -3, 1], [14, 0, 3, 0, 0, -3, -1, 2], [-8, 6, 2, -6, -8, -3, -5, 5], [0, -5, 4, 0, 13, -1, 1, -4], [6, 0, 0, 6, 0, 0, -5, -5], [-6, -13, -3, 13, -6, 3, 6, -6], [0, 15, 3, 0, 22, 12, -12, -3], [14, 0, 6, -4, 0, -6, 6, 12], [0, 4, 6, 0, 11, 4, -4, -6], [6, 0, 8, -6, 0, -8, 0, 8], [0, 4, 6, 0, -1, 1, -1, -6], [0, 0, -2, 1, 0, 2, -7, -9], [0, 8, 1, 0, -6, 4, -4, -1], [3, -5, -7, 5, 3, 1, 8, -8], [-8, 0, 2, -2, 0, -2, 6, 8], [0, 6, -7, 0, 10, -1, 1, 7], [20, 0, 0, 5, 0, 0, 1, 1], [-7, -11, 1, 11, -7, -3, -4, 4], [0, 12, -1, 0, 32, 0, 0, 1], [1, -2, -2, 2, 1, 4, 6, -6], [-11, 0, 3, 10, 0, -3, 0, 3], [-1, 12, 1, -12, -1, 3, 2, -2], [23, -3, -5, 3, 23, -8, -3, 3], [6, 0, 5, -8, 0, -5, 0, 5], [-18, -9, 11, 9, -18, 5, -6, 6], [0, 8, -1, 0, -12, 1, -1, 1], [20, 0, -5, 6, 0, 5, 3, -2], [-11, -8, -2, 8, -11, 0, 2, -2], [-4, 0, 2, -2, 0, -2, 4, 6], [28, 5, 4, -5, 28, 0, -4, 4], [10, 0, -4, 4, 0, 4, 7, 3], [0, -3, 7, 0, -1, 9, -9, -7], [0, -4, 4, 0, -12, 2, -2, -4], [-10, 0, -7, 2, 0, 7, -7, -14], [0, -1, 2, 0, 7, 11, -11, -2], [-21, 0, -2, 4, 0, 2, 7, 5], [-11, 14, 5, -14, -11, -2, -7, 7], [0, -15, -5, 0, 16, -8, 8, 5], [7, 0, 3, 1, 0, -3, -2, 1], [0, -2, -1, 0, 22, 7, -7, 1], [-2, 0, 2, -13, 0, -2, 4, 6], [-6, 0, 5, -2, 0, -5, -2, 3], [0, 4, -1, 0, 6, 2, -2, 1], [-13, 10, 11, -10, -13, 1, -10, 10], [-7, -11, 3, 11, -7, 2, -1, 1], [16, 2, 2, -2, 16, 0, -2, 2], [-13, 0, 3, 5, 0, -3, 10, 13], [8, 0, -3, 0, 0, 3, 8, 5], [-2, 2, -16, -2, -2, -1, 15, -15], [0, -6, 4, 0, 20, 3, -3, -4], [-15, 0, 3, -6, 0, -3, 0, 3], [3, 4, -6, -4, 3, -8, -2, 2], [37, 8, 9, -8, 37, 4, -5, 5], [-4, 0, -3, -6, 0, 3, 0, -3], [0, 3, 6, 0, -12, -4, 4, -6], [-6, 0, 0, 0, -6, 9, 9, -9], [24, 0, 6, -6, 0, -6, -2, 4], [12, 0, 3, -6, 0, -3, -8, -5], [7, 11, -3, -11, 7, -2, 1, -1], [0, 5, 3, 0, -5, -11, 11, -3], [0, -6, 3, 0, -24, 8, -8, -3], [0, -2, 7, 0, -4, 11, -11, -7], [0, -2, -6, 0, -2, -9, 9, 6], [21, 0, 4, -6, 0, -4, 8, 12], [-24, -6, -12, 6, -24, -9, 3, -3], [0, 20, -2, 0, 20, 8, -8, 2], [-1, 0, 6, -16, 0, -6, 1, 7], [-21, -6, -11, 6, -21, -6, 5, -5], [0, 9, 3, 0, 16, -5, 5, -3], [0, 6, -8, 0, 1, 2, -2, 8], [-23, 0, -9, 5, 0, 9, 0, -9], [9, 0, -12, 6, 0, 12, 4, -8], [0, 4, -8, 0, -12, 6, -6, 8], [-16, 0, -6, -6, 0, 6, 10, 4], [-19, 6, -8, -6, -19, -2, 6, -6], [-28, 6, -1, -6, -28, -8, -7, 7], [-6, 0, -10, 17, 0, 10, 0, -10], [2, 0, -8, -9, 0, 8, -5, -13], [-14, -4, 10, 4, -14, 12, 2, -2], [0, 4, 6, 0, 10, 8, -8, -6], [0, 0, -6, 0, -28, 4, -4, 6], [0, 8, -4, 0, -12, 10, -10, 4], [0, 4, -6, 0, 4, -13, 13, 6], [-20, -6, 7, 6, -20, 5, -2, 2], [0, 6, 8, 0, -9, 11, -11, -8], [-18, 9, 3, -9, -18, 3, 0, 0], [1, 0, 0, 5, 0, 0, -13, -13], [28, 14, 4, -14, 28, 2, -2, 2], [16, -4, 12, 4, 16, 4, -8, 8], [0, 5, 3, 0, 27, 11, -11, -3], [0, 1, 1, 0, 11, -5, 5, -1], [0, 2, -2, 0, -5, -6, 6, 2], [18, -7, 4, 7, 18, 1, -3, 3], [-27, 0, 7, 5, 0, -7, 0, 7], [-11, -3, 1, 3, -11, 11, 10, -10], [0, 1, -4, 0, -7, -15, 15, 4], [3, 0, 0, -4, 0, 0, -4, -4], [6, 4, 10, -4, 6, 0, -10, 10], [0, 6, -1, 0, 17, 3, -3, 1], [-18, 0, 0, 7, 0, 0, 8, 8], [0, -14, 10, 0, 14, -8, 8, -10], [4, 12, -6, -12, 4, -4, 2, -2], [5, 17, -5, -17, 5, 4, 9, -9], [-37, 0, 5, -7, 0, -5, -4, 1], [0, -2, 11, 0, -7, 1, -1, -11], [36, 5, -3, -5, 36, -3, 0, 0], [-22, 0, -8, -5, 0, 8, -2, -10], [-4, 0, 2, -8, 0, -2, 0, 2], [15, -7, 3, 7, 15, 8, 5, -5], [0, -12, 6, 0, -15, 7, -7, -6], [-8, 10, -1, -10, -8, -9, -8, 8], [0, 16, -2, 0, 12, -10, 10, 2], [0, 6, -10, 0, -4, 0, 0, 10], [-17, -9, -9, 9, -17, 0, 9, -9], [-22, 0, 4, 8, 0, -4, 4, 8], [0, 4, 15, -4, 0, 1, -14, 14], [-16, 0, 2, 6, 0, -2, -9, -7], [-18, 11, 16, -11, -18, -8, -24, 24], [10, 16, 20, -16, 10, 8, -12, 12], [17, 0, -15, 3, 0, 15, 2, -13], [15, 0, 12, -2, 0, -12, 1, 13], [14, -8, -6, 8, 14, -2, 4, -4], [0, -7, -10, 0, 31, -9, 9, 10], [-12, 8, 3, -8, -12, -12, -15, 15], [13, -10, 5, 10, 13, 12, 7, -7], [0, -10, 0, 0, -12, -17, 17, 0], [0, 6, -4, 0, -2, 4, -4, 4], [6, 0, 0, -2, 0, 0, 5, 5], [0, 1, 2, 0, -10, 12, -12, -2], [28, 0, 3, -12, 0, -3, 0, 3], [0, 14, 7, 0, -14, -8, 8, -7], [-5, 8, 4, -8, -5, -6, -10, 10], [-3, -9, -17, 9, -3, -9, 8, -8], [-17, 0, -11, 21, 0, 11, -4, -15], [14, 0, 8, -7, 0, -8, -12, -4], [0, 12, 7, 0, -6, 8, -8, -7], [-24, -20, -9, 20, -24, -1, 8, -8], [0, -9, 11, 0, 10, 1, -1, -11], [29, -16, -9, 16, 29, -1, 8, -8], [-27, 0, -5, 17, 0, 5, 2, -3], [37, 9, -9, -9, 37, -10, -1, 1], [20, 0, -11, -2, 0, 11, 4, -7], [0, 9, -8, 0, -10, -12, 12, 8], [0, 4, 13, 0, -11, 7, -7, -13], [-13, 0, -3, 7, 0, 3, 14, 11], [-36, 0, 8, -5, 0, -8, -3, 5], [7, 3, -7, -3, 7, -2, 5, -5], [0, 4, 4, 0, 16, -2, 2, -4], [4, 0, -10, -10, 0, 10, -5, -15], [0, -8, -10, 0, 8, -4, 4, 10], [-16, -17, 8, 17, -16, 6, -2, 2], [0, -10, -11, 0, 4, -5, 5, 11], [0, -5, -3, 0, -4, 1, -1, 3], [-11, 0, 6, 19, 0, -6, -3, 3], [2, 0, 0, 0, 2, -4, -4, 4], [0, -2, 6, 0, -16, 17, -17, -6], [2, 0, 0, 6, 0, 0, -2, -2], [0, -4, 8, 0, 13, 12, -12, -8], [14, 0, 0, 7, 0, 0, 13, 13], [0, 12, 6, 0, 12, 18, -18, -6], [-13, -8, -4, 8, -13, 10, 14, -14], [-40, 0, 4, -1, 0, -4, 2, 6], [-37, 0, 5, -5, 0, -5, 6, 11], [10, 0, 11, -15, 0, -11, -13, -2], [0, -28, 1, 0, -36, -2, 2, -1], [-16, -10, -1, 10, -16, -1, 0, 0], [0, 7, -3, 0, 8, 4, -4, 3], [0, -10, 12, 0, 26, 5, -5, -12], [29, -6, 6, 6, 29, -6, -12, 12], [-18, 0, 6, -8, 0, -6, 0, 6], [14, 20, 0, -20, 14, -2, -2, 2], [-45, -15, 13, 15, -45, 3, -10, 10], [0, -2, 4, 0, 17, 12, -12, -4], [32, 2, -7, -2, 32, -7, 0, 0], [-17, -13, 9, 13, -17, 4, -5, 5], [0, 16, -2, 0, 18, 6, -6, 2], [0, 10, 3, 0, 8, 1, -1, -3], [-21, 0, -5, 21, 0, 5, 2, -3], [48, 0, 8, -12, 0, -8, 7, 15], [2, -16, 4, 16, 2, 6, 2, -2], [21, 12, 9, -12, 21, 4, -5, 5], [0, 6, -8, 0, -28, -9, 9, 8], [7, 0, 6, -21, 0, -6, -13, -7], [0, -10, 5, 0, 28, 1, -1, -5], [24, 0, 14, -27, 0, -14, 0, 14], [0, -24, 0, 0, -18, -10, 10, 0], [0, 5, 2, 0, -23, 5, -5, -2], [22, 20, -16, -20, 22, -7, 9, -9], [49, 0, -1, -12, 0, 1, 0, -1], [-22, 0, -9, -6, 0, 9, -8, -17], [0, -18, 6, 0, -42, 0, 0, -6], [-12, -28, -5, 28, -12, 1, 6, -6], [11, 0, -12, -5, 0, 12, 3, -9], [17, -16, -11, 16, 17, 0, 11, -11], [24, 0, -1, -2, 0, 1, 6, 5], [32, -12, 2, 12, 32, -6, -8, 8], [56, -4, -6, 4, 56, -6, 0, 0], [0, -20, 17, 0, 1, 3, -3, -17]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2100_q_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2100_2_q_l();".
// 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_2100_2_q_l(:prec:=8)
    chi := MakeCharacter_2100_q();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(1999) - 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_2100_2_q_l();".
// 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_2100_2_q_l( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2100_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<11,R![196, -308, 568, 20, 110, 20, 22, 4, 1]>,<13,R![75, 0, -24, 2, 1]>],Snew);
    return Vf;
end function;