
// Make newform 2352.2.bl.q in Magma, downloaded from the LMFDB on 17 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2352_bl();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2352_bl_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_2352_2_bl_q();".
// 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_2352_2_bl_q();".
// 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, -8, 0, 14, 0, -4, 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, 1, 0, 0, 0, 0, 0, 0], [20, 0, 0, 0, 0, 0, 1, 0], [0, 34, 0, 0, 0, 0, 0, 1], [2, 0, -28, 0, 7, 0, -2, 0], [0, 16, 0, -28, 0, 7, 0, -2], [2, 0, -21, 0, 7, 0, -2, 0], [0, 6, 0, -70, 0, 21, 0, -6]];
    Rf_basisdens := [1, 1, 14, 14, 14, 14, 7, 14];
    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_2352_bl();"
function MakeCharacter_2352_bl()
    N := 2352;
    order := 6;
    char_gens := [1471, 1765, 785, 2257];
    v := [3, 6, 6, 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_2352_bl_Hecke();"
function MakeCharacter_2352_bl_Hecke(Kf)
    N := 2352;
    order := 6;
    char_gens := [1471, 1765, 785, 2257];
    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, -1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, -1, 0, -1, 1, -1], [0, -2, 0, 0, 0, 2, 0, 1], [0, 0, 2, -1, 0, 2, 1, -1], [0, 1, -2, 1, 0, -2, -2, 2], [2, -1, 1, 1, -2, 0, -1, 0], [2, 1, -1, -2, 0, 1, 0, -1], [0, -2, 0, -1, -4, 1, 2, 1], [0, -2, -1, -2, 0, 4, -1, -4], [2, -1, 1, 0, 4, 1, 2, 0], [2, -2, 0, 0, 4, 2, 0, -6], [2, -1, -2, 1, 2, 2, -2, 2], [0, -4, 0, -2, 2, 2, 2, 2], [0, 6, 0, -1, 6, -3, 2, 1], [4, 0, -2, -1, -4, 0, 2, 0], [-8, 0, 0, -2, -4, 2, 0, -2], [-4, -3, 1, 0, -8, 3, 2, 3], [8, 0, 4, 1, 4, -2, 2, 1], [-2, 4, 0, 4, 2, 0, 0, 0], [0, 2, -2, -8, 0, 2, 0, -4], [4, -2, -3, -7, -4, 0, 3, 0], [4, 6, 2, 0, 8, -6, 4, 1], [4, 0, 6, 0, 2, -3, 3, 0], [0, -1, -6, -3, 0, 2, -6, -6], [-2, -5, 1, 5, 2, 0, -1, 0], [0, -8, 0, 0, 2, 4, 3, 0], [0, 4, 0, -4, 0, 4, 0, -2], [0, -2, 0, 0, 0, 2, 0, 2], [8, -4, 2, 2, 8, 8, 2, 4], [0, -6, 0, -1, 6, 3, 1, 1], [0, -2, -4, 0, 0, -2, 0, 0], [2, 0, 0, -4, 2, 0, 0, -8], [-4, 0, -8, 2, -2, -6, -4, 2], [0, 0, 4, -2, 0, -3, 2, -2], [0, -6, -4, -2, 0, 0, 4, 0], [-10, 1, 4, -10, 0, 1, 0, -5], [0, -10, -1, 1, 0, 0, 1, 0], [8, 0, 2, -5, 4, 7, 1, -5], [0, -1, 0, 0, 0, 1, 0, 6], [0, 7, 5, 3, 0, 0, -5, 0], [0, 0, 0, -4, -2, 0, -8, 4], [4, -2, -10, 0, 0, -2, 0, 0], [0, -4, 0, 4, 0, 2, -4, -4], [4, -4, -4, 0, 8, 4, -8, 0], [4, -4, 8, 0, 0, -4, 0, 0], [0, 6, 0, 1, 2, -3, 8, -1], [0, 1, -4, 10, 0, 0, 4, 0], [-2, -3, 3, 5, -2, 6, 3, 10], [2, 7, 7, 0, 4, -7, 14, 3], [0, 0, 4, 4, 0, 1, 2, 4], [10, -1, -12, -6, 0, -1, 0, -3], [-2, -1, -1, 0, 2, 0, 1, 0], [0, 0, 10, 7, 0, -1, 5, 7], [4, 0, -2, -2, 2, 5, -1, -2], [4, 7, 2, -1, 4, -14, 2, -2], [0, 8, 0, 4, -4, -4, 2, -4], [14, -1, -5, 2, 0, -1, 0, 1], [0, -10, 0, -5, 12, 5, -6, 5], [-6, -1, 1, 0, -12, 1, 2, -6], [16, -1, -2, 6, 0, -1, 0, 3], [0, 14, 0, 1, -2, -7, 0, -1], [-8, 0, 4, 3, 8, 0, -4, 0], [0, 2, 10, 0, 0, -4, 10, 0], [-4, -12, 4, -8, 4, 0, -4, 0], [-4, -6, 9, -4, 0, -6, 0, -2], [12, 0, 2, 5, 6, 3, 1, 5], [0, -1, -6, 0, 0, 1, -12, 6], [4, 0, -6, -10, 2, -3, -3, -10], [2, 9, -1, 15, -2, 0, 1, 0], [0, 12, 0, 0, -4, -6, -8, 0], [12, 0, -2, 4, 12, 0, -2, 8], [-4, 4, -4, 0, -8, -4, -8, 0], [8, 0, 4, 0, 8, 0, 4, 0], [0, 6, 0, 5, 14, -3, -5, -5], [4, 2, 6, -9, -4, 0, -6, 0], [14, 1, 11, 1, 14, -2, 11, 2], [-8, 0, -12, -3, -4, -10, -6, -3], [-6, 9, 2, 2, 0, 9, 0, 1], [0, 0, 16, 0, 0, 0, 0, 0], [0, 0, 6, 1, 0, 13, 3, 1], [0, 7, 0, 0, 0, -7, 0, 2], [-12, 4, -4, 2, -12, -8, -4, 4], [0, -7, 3, -11, 0, 0, -3, 0], [0, -6, 10, 8, 0, -6, 0, 4], [8, 4, 10, 0, 8, -8, 10, 0], [-8, 10, -1, 0, -16, -10, -2, -7], [12, 2, 2, 0, 24, -2, 4, 6], [-10, -7, 10, 7, -10, 14, 10, 14], [0, 14, 0, -5, -10, -7, -2, 5], [-12, 0, 0, 14, -6, 2, 0, 14], [-2, 13, 1, 0, -4, -13, 2, -11], [6, 2, -6, -10, -6, 0, 6, 0], [16, 4, -2, -12, 0, 4, 0, -6], [-10, -9, 3, -8, 10, 0, -3, 0], [-4, 0, -2, -10, -2, 7, -1, -10], [0, 0, 8, -2, 0, 0, 8, -4], [-6, 0, 6, 8, -6, 0, 6, 16], [-10, -8, 0, 0, -20, 8, 0, -4], [0, 8, 0, 2, 4, -4, -20, -2], [0, -6, 0, 3, 14, 3, 12, -3], [14, 5, 5, 1, 14, -10, 5, 2], [4, 0, -4, 12, 2, 12, -2, 12], [16, 0, 0, 0, 8, -7, 0, 0], [10, -5, -6, -10, 0, -5, 0, -5], [4, 0, 5, 9, -4, 0, -5, 0], [0, 0, -2, 13, 0, -15, -1, 13], [-16, 2, 0, 0, -32, -2, 0, -1], [-4, 0, -8, -2, -4, 0, -8, -4], [0, 12, 0, -2, -6, -6, -9, 2], [18, -1, 5, -6, 0, -1, 0, -3], [0, 0, 0, 6, -12, 0, -8, -6], [4, 6, 2, 0, 8, -6, 4, -10], [0, 10, 0, -1, -6, -5, 7, 1], [8, 9, -2, -10, 0, 9, 0, -5], [0, -2, 0, 3, 2, 1, -18, -3], [-10, -5, 11, -1, -10, 10, 11, -2], [8, 1, -3, 0, 16, -1, -6, 11], [16, 0, -4, -6, 8, 1, -2, -6], [6, -4, -13, 0, 0, -4, 0, 0], [-4, -12, -3, 17, 4, 0, 3, 0], [8, 0, 14, -7, 4, 9, 7, -7], [8, 2, -4, 14, 8, -4, -4, 28], [18, -3, -7, -10, 0, -3, 0, -5], [-18, 4, 17, -8, -18, -8, 17, -16], [-4, -2, -4, 2, -4, 4, -4, 4], [-16, -7, -6, 10, 0, -7, 0, 5], [0, -7, 4, 6, 0, 0, -4, 0], [-16, 0, -12, 2, -8, 10, -6, 2], [4, 19, 3, 0, 8, -19, 6, -7], [0, 12, -6, -8, 0, 0, 6, 0], [2, 0, 7, 8, 0, 0, 0, 4], [-4, 10, -3, 1, 4, 0, 3, 0], [8, -1, -12, 0, 16, 1, -24, 0], [16, 0, 14, 9, 8, -14, 7, 9], [0, -12, 0, -4, -12, 6, 20, 4], [-14, 15, 1, 0, -28, -15, 2, -2], [0, -20, 0, 2, -10, 10, 6, -2], [-8, -4, -8, -8, 0, -4, 0, -4], [-16, -2, -14, 4, -16, 4, -14, 8], [28, 0, 12, 4, 14, 0, 6, 4], [6, -3, 1, 0, 12, 3, 2, -7], [0, 0, 0, -11, 0, 4, 0, -11], [-10, -1, 0, 18, 0, -1, 0, 9], [-8, -7, 10, 0, -16, 7, 20, 8], [24, 0, 6, -5, 12, 6, 3, -5], [-4, -3, -14, -7, -4, 6, -14, -14], [6, -3, -9, 11, -6, 0, 9, 0], [34, 2, -9, -2, 34, -4, -9, -4], [4, -4, 3, 0, 8, 4, 6, 15], [10, -14, 2, 0, 20, 14, 4, -6], [6, 5, -2, -9, 6, -10, -2, -18], [-20, 0, -8, 6, -10, -2, -4, 6], [-8, -13, -5, 0, -16, 13, -10, 9], [-6, -6, 12, 10, 6, 0, -12, 0], [-4, 22, -7, -3, 4, 0, 7, 0], [0, 6, 4, 0, 0, -6, 8, -5], [20, 0, 2, 24, 10, -7, 1, 24], [-2, 7, -7, 1, 2, 0, 7, 0], [2, 2, 18, -20, 0, 2, 0, -10], [-4, 2, 6, 0, -8, -2, 12, -6], [-16, 10, -6, 0, -16, -20, -6, 0], [0, 6, 0, -7, 2, -3, 3, 7], [0, -16, 0, -4, 20, 8, -4, 4], [-12, 0, -12, -14, -6, -6, -6, -14], [0, 0, 4, 10, 0, 1, 2, 10], [12, 0, 14, -8, 0, 0, 0, -4], [22, -1, 3, 6, -22, 0, -3, 0], [-28, 0, -6, 13, -14, -13, -3, 13], [20, -10, 6, 0, 40, 10, 12, -7], [-12, -9, 5, -5, 12, 0, -5, 0], [0, 12, 0, -2, 18, -6, 11, 2], [0, -12, 0, -8, -8, 6, 8, 8], [14, 1, -3, 0, 28, -1, -6, 20], [-14, 4, -2, 0, -28, -4, -4, -8], [0, -14, 0, 3, 22, 7, 3, -3], [-4, 1, -26, 2, 0, 1, 0, 1], [-8, 7, -6, -16, 8, 0, 6, 0], [2, -12, 12, 8, -2, 0, -12, 0], [-8, 4, 2, 20, 0, 4, 0, 10], [-12, 8, -13, -16, 0, 8, 0, -8], [2, 5, -1, -20, -2, 0, 1, 0], [-12, 0, 10, -15, -6, 11, 5, -15], [-40, 0, 2, 1, -20, -8, 1, 1], [0, -8, 0, -8, -4, 4, 10, 8], [0, 28, 0, 2, 4, -14, 12, -2], [6, 6, -13, -14, 6, -12, -13, -28], [0, -12, 0, 2, 8, 6, 28, -2], [16, -1, -2, 2, -16, 0, 2, 0], [4, 7, -13, 0, 8, -7, -26, -11], [16, -8, 12, 0, -16, 0, -12, 0], [14, 7, -9, 2, -14, 0, 9, 0], [-28, 0, -14, -15, -14, 3, -7, -15], [8, 0, 22, -13, 4, 8, 11, -13], [0, -8, 0, 0, 18, 4, 5, 0], [0, 0, -13, 8, 0, 0, -13, 16], [8, -20, 5, 0, 16, 20, 10, 11], [-22, 9, -4, -3, -22, -18, -4, -6], [0, -36, 0, 2, -6, 18, -10, -2], [32, -4, 4, 4, 0, -4, 0, 2], [-8, 16, -8, 11, 8, 0, 8, 0], [0, 0, 12, 14, 0, 27, 6, 14], [-28, 4, 12, 16, 0, 4, 0, 8], [0, 0, 10, 23, 0, -10, 5, 23], [36, -4, -16, 4, 36, 8, -16, 8], [-4, 17, -9, 5, 4, 0, 9, 0], [4, -8, 12, 36, 0, -8, 0, 18], [0, -22, 0, -3, 16, 11, -10, 3], [-28, 0, 17, 0, -28, 0, 17, 0], [-6, -13, -1, 0, -12, 13, -2, 10], [-18, -2, 2, 0, -36, 2, 4, -18], [-8, 0, -18, -2, -8, 0, -18, -4], [0, -6, 0, -9, -10, 3, -12, 9], [-8, -1, -16, 6, 8, 0, 16, 0], [12, 0, 16, -2, 6, 6, 8, -2], [36, 0, -10, 0, 18, 5, -5, 0], [-10, -15, -5, -5, 10, 0, 5, 0], [10, 7, -15, 2, 0, 7, 0, 1], [18, 0, -1, -4, 18, 0, -1, -8], [4, 3, -2, -38, 0, 3, 0, -19], [10, 14, -14, -10, 10, -28, -14, -20], [4, -16, 2, -24, -4, 0, -2, 0], [12, -20, 14, 4, 0, -20, 0, 2], [36, -2, 3, 20, 0, -2, 0, 10], [12, 22, 9, -11, -12, 0, -9, 0], [-48, 0, 14, -23, -24, -3, 7, -23], [12, 7, 2, 15, 12, -14, 2, 30], [12, -11, -1, 5, -12, 0, 1, 0], [0, 8, 0, -8, 18, -4, 21, 8], [0, -10, 0, -1, -16, 5, -10, 1], [6, -26, 4, 0, 12, 26, 8, 6], [0, 4, 0, 0, -40, -2, -6, 0], [16, -11, -10, -14, 0, -11, 0, -7], [0, -16, 0, 18, -4, 8, 10, -18], [-16, -9, -14, 10, 16, 0, 14, 0], [10, -12, -16, 4, 10, 24, -16, 8], [-6, 15, -9, 0, -12, -15, -18, 19], [0, -6, -12, 12, 0, -6, 0, 6], [12, 0, 6, -17, 6, 5, 3, -17], [-20, -14, -4, 4, -20, 28, -4, 8], [0, -20, 0, -14, 36, 10, -16, 14], [10, 16, -2, 0, 10, -32, -2, 0], [10, -1, 13, 0, 20, 1, 26, 8], [-10, 13, -8, -7, -10, -26, -8, -14], [0, 7, 6, -22, 0, 7, 0, -11], [0, -6, 0, 1, -14, 3, -6, -1], [20, 0, 16, 20, 10, -24, 8, 20], [8, -7, -3, 0, 16, 7, -6, -9], [-20, -8, 6, -8, 0, -8, 0, -4], [10, 5, 7, 0, -10, 0, -7, 0], [8, 0, -14, -5, 4, 11, -7, -5], [16, 13, -10, 0, 32, -13, -20, -10], [-12, 0, 2, 30, -6, -3, 1, 30], [-2, 29, 3, -1, 2, 0, -3, 0], [0, 16, 0, 0, -4, -8, 17, 0], [0, 26, 0, 11, -4, -13, -2, -11], [-14, 23, -1, 0, -28, -23, -2, -16], [-8, 1, 12, -14, 8, 0, -12, 0], [-4, 0, -24, -16, -2, 20, -12, -16], [-14, -19, 9, 0, -28, 19, 18, 25], [-16, 0, -32, 13, -8, -16, -16, 13], [0, 1, 6, 0, 0, -1, 12, -20], [-48, 0, 10, 3, -24, -2, 5, 3], [16, -6, 4, 2, 16, 12, 4, 4], [-30, 0, 16, 16, 0, 0, 0, 8], [-4, 28, 7, 0, -8, -28, 14, 7], [-2, 4, 12, 0, -4, -4, 24, -12], [0, 6, 0, -3, -2, -3, -15, 3], [8, -15, 18, 6, -8, 0, -18, 0], [24, 0, -20, -4, 12, 4, -10, -4], [48, 0, -12, 16, 24, 3, -6, 16], [12, 8, -16, 0, -12, 0, 16, 0], [-16, -11, -2, 0, -32, 11, -4, -22], [0, 9, 10, -1, 0, -18, 10, -2], [-2, -5, -15, 13, 2, 0, 15, 0], [0, -24, 0, 8, -36, 12, -8, -8], [10, 0, -24, 4, 10, 0, -24, 8], [-18, 5, 0, -3, -18, -10, 0, -6], [0, 16, 0, -4, 36, -8, 8, 4], [-16, 0, 24, 18, -8, 30, 12, 18], [-8, -12, -14, -20, 0, -12, 0, -10], [-4, 24, 6, 0, -8, -24, 12, -1], [0, -10, -24, -4, 0, 20, -24, -8], [0, 15, -7, -41, 0, 0, 7, 0], [0, 16, 0, -8, -22, -8, -18, 8], [-48, -6, -2, 8, 0, -6, 0, 4], [0, 26, 0, -1, -28, -13, -10, 1], [0, -24, -11, 0, 0, 24, -22, 7], [0, 36, 0, 10, 10, -18, -14, -10], [0, -16, 0, 8, -28, 8, 4, -8], [-6, 7, -1, 27, -6, -14, -1, 54], [18, 1, -24, 14, 0, 1, 0, 7], [-6, -8, 12, -16, 0, -8, 0, -8], [20, 0, -26, -8, 10, 13, -13, -8], [12, 4, -12, 20, 12, -8, -12, 40], [-16, -4, 11, 0, -32, 4, 22, -11], [-34, 1, 8, -7, -34, -2, 8, -14], [-24, 2, 20, 40, 0, 2, 0, 20], [0, 0, 12, 29, 0, 0, -12, 0], [-38, 5, -9, 5, -38, -10, -9, 10], [32, 0, -8, 18, 16, 30, -4, 18]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2352_bl_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2352_2_bl_q();".
// 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_2352_2_bl_q(:prec:=8)
    chi := MakeCharacter_2352_bl();
    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_2352_2_bl_q();".
// 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_2352_2_bl_q( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2352_bl();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![196, 336, -32, -384, 242, 0, -16, 0, 1]>,<11,R![16, 192, 848, 960, 404, 0, -20, 0, 1]>,<17,R![6724, -13776, 12032, -5376, 1106, 0, -32, 0, 1]>,<19,R![3136, 5376, 6976, 3840, 1656, 192, 40, 0, 1]>,<31,R![678976, -131840, 71744, -17408, 6520, -1216, 200, -16, 1]>],Snew);
    return Vf;
end function;