
// Make newform 7600.2.a.ck in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_7600_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_7600_2_a_ck();".
// 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_7600_2_a_ck();".
// 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 := [-1, 0, 13, 0, -9, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [-1, 0, -6, 0, 1, 0], [0, 5, 0, -8, 0, 1], [-11, 0, 10, 0, -1, 0], [0, 9, 0, -8, 0, 1], [0, -12, 0, 9, 0, -1]];
    Rf_basisdens := [1, 2, 2, 2, 2, 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_7600_a();"
function MakeCharacter_7600_a()
    N := 7600;
    order := 1;
    char_gens := [4751, 5701, 5777, 401];
    v := [1, 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_7600_a_Hecke(Kf)
    return MakeCharacter_7600_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 := [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 1, -1], [0, 0, -2, 0, 1, -1], [1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 1, 0], [6, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, -1, 0, -1, -1], [2, 1, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 3, 0, 0, -1], [0, 0, -3, 0, -1, -1], [-4, -1, 0, 1, 0, 0], [-2, 2, 0, 1, 0, 0], [0, 0, 2, 0, 0, 5], [-8, 1, 0, -1, 0, 0], [0, 0, 0, 0, 1, -3], [4, 1, 0, 1, 0, 0], [0, 0, -1, 0, -3, 0], [2, -2, 0, 4, 0, 0], [0, 0, -1, 0, 1, -1], [4, 1, 0, -1, 0, 0], [0, 0, 2, 0, -2, -1], [0, 0, -4, 0, 0, 1], [6, -1, 0, 1, 0, 0], [0, 0, 3, 0, -1, -1], [0, 0, 0, 0, -4, 3], [-2, -3, 0, 2, 0, 0], [0, 0, 2, 0, -1, -3], [4, 1, 0, -2, 0, 0], [10, 0, 0, -1, 0, 0], [-4, 0, 0, 2, 0, 0], [0, 0, -2, 0, 2, -2], [0, 0, -9, 0, 5, -6], [0, 0, -2, 0, 2, -3], [0, 0, 5, 0, 1, -5], [-12, -3, 0, 3, 0, 0], [-2, -4, 0, 4, 0, 0], [-2, -1, 0, 2, 0, 0], [0, 0, -1, 0, 1, -1], [0, 0, -4, 0, 4, 0], [10, 1, 0, -2, 0, 0], [-4, -4, 0, 2, 0, 0], [0, 0, 4, 0, 4, 1], [0, 0, -4, 0, -2, -5], [14, 4, 0, -1, 0, 0], [0, 0, -4, 0, 3, 1], [2, -3, 0, -2, 0, 0], [-6, -1, 0, -1, 0, 0], [-2, 1, 0, 2, 0, 0], [0, 0, -3, 0, -5, 1], [0, 0, 1, 0, -2, 5], [6, -5, 0, -3, 0, 0], [2, -2, 0, -4, 0, 0], [0, 0, 4, 0, -1, 7], [-2, -1, 0, -1, 0, 0], [0, 0, 1, 0, 2, 1], [0, 0, 1, 0, -5, 3], [0, 0, -4, 0, -2, -1], [0, -1, 0, 0, 0, 0], [0, 0, 2, 0, -2, 8], [0, 0, 7, 0, 3, 5], [-8, 0, 0, 0, 0, 0], [0, 0, -5, 0, -3, 1], [0, 0, -7, 0, 8, -5], [-4, 3, 0, 2, 0, 0], [0, 0, -8, 0, 8, -6], [0, 3, 0, 0, 0, 0], [0, 0, -5, 0, 1, -2], [0, 0, 1, 0, -1, -5], [0, 2, 0, -4, 0, 0], [0, 0, 0, 0, -2, -5], [12, -1, 0, 0, 0, 0], [0, 0, -6, 0, -5, 9], [10, -2, 0, -4, 0, 0], [-2, 3, 0, -3, 0, 0], [20, 6, 0, -2, 0, 0], [-6, 3, 0, -7, 0, 0], [4, -6, 0, 2, 0, 0], [0, 0, 3, 0, -9, 3], [4, -3, 0, 7, 0, 0], [0, 0, 7, 0, 0, 5], [6, -3, 0, 3, 0, 0], [0, 0, -2, 0, -9, 7], [16, -3, 0, 2, 0, 0], [0, 0, -7, 0, 6, -7], [0, 0, -7, 0, 0, 7], [10, 2, 0, -4, 0, 0], [0, 0, 8, 0, 8, -1], [12, 10, 0, -6, 0, 0], [-12, -1, 0, 2, 0, 0], [0, 0, -1, 0, 5, 0], [26, 0, 0, -2, 0, 0], [-10, 4, 0, -2, 0, 0], [0, 0, 6, 0, 6, -3], [10, 0, 0, -5, 0, 0], [0, 0, -2, 0, 0, 13], [0, 0, -8, 0, 3, -13], [0, 0, -2, 0, -2, 5], [26, 3, 0, 1, 0, 0], [14, 6, 0, -4, 0, 0], [0, 0, 8, 0, -7, -1], [0, 0, 3, 0, 2, 11], [0, 0, -8, 0, -4, -12], [-8, -11, 0, 5, 0, 0], [-14, 1, 0, 1, 0, 0], [0, 0, 0, 0, -6, -3], [0, 0, -2, 0, 3, 1], [0, 0, -8, 0, -7, 5], [6, -6, 0, 8, 0, 0], [-20, -3, 0, 0, 0, 0], [-2, 7, 0, 5, 0, 0], [0, 0, 3, 0, -4, 9], [0, 0, -11, 0, -4, 3], [0, 0, -6, 0, -5, -7], [-16, -1, 0, 1, 0, 0], [-6, -1, 0, 5, 0, 0], [0, 0, 9, 0, 5, -3], [0, 0, -7, 0, 5, -3], [0, 0, -6, 0, 0, -5], [-12, -13, 0, 4, 0, 0], [0, 1, 0, 3, 0, 0], [14, 4, 0, -4, 0, 0], [-12, -1, 0, 0, 0, 0], [0, 0, 5, 0, -14, 11], [0, 0, 12, 0, -4, 12], [14, -3, 0, 6, 0, 0], [0, 0, -2, 0, 4, 5], [-12, -8, 0, 4, 0, 0], [0, 0, 14, 0, -7, 5], [-10, -2, 0, -5, 0, 0], [18, 2, 0, -5, 0, 0], [0, 0, 11, 0, -5, 13], [0, 0, 2, 0, 4, -7], [0, 0, 13, 0, -5, 11], [-12, -11, 0, 6, 0, 0], [-12, 3, 0, -5, 0, 0], [0, 1, 0, 6, 0, 0], [0, 0, -5, 0, -6, 1], [0, 0, -4, 0, 2, -5], [-18, -7, 0, 7, 0, 0], [0, -5, 0, -3, 0, 0], [0, 0, -18, 0, 14, -12], [0, 0, 9, 0, 9, -5], [-10, -5, 0, 0, 0, 0], [0, 0, 6, 0, -2, -5], [0, 0, -3, 0, 13, -3], [2, -2, 0, -5, 0, 0], [0, 0, 7, 0, -2, -11], [0, 0, 10, 0, 6, -3], [0, 0, 4, 0, 14, -5], [-8, 10, 0, -4, 0, 0], [40, 2, 0, -2, 0, 0], [-14, 6, 0, -10, 0, 0], [0, 0, 8, 0, 9, 5], [22, -4, 0, -4, 0, 0], [0, 0, 11, 0, -3, 4], [0, 0, 9, 0, -9, 17], [0, 0, -9, 0, 5, 0], [40, -1, 0, -1, 0, 0], [0, 0, -11, 0, -5, -13], [0, 0, -12, 0, 2, -5], [4, 12, 0, -6, 0, 0], [0, 0, 0, 0, 9, -3], [-30, 4, 0, -2, 0, 0], [0, 0, 10, 0, 1, 3], [-20, -10, 0, 8, 0, 0], [10, 0, 0, -2, 0, 0], [30, -4, 0, 6, 0, 0], [0, 0, -8, 0, -8, 4], [-40, 0, 0, 0, 0, 0], [-38, 2, 0, -1, 0, 0], [-4, 4, 0, -4, 0, 0], [26, 8, 0, 1, 0, 0], [0, 0, -10, 0, -12, 5], [-14, 2, 0, 3, 0, 0], [0, 0, 9, 0, 0, 3], [0, -3, 0, -3, 0, 0], [0, 0, 11, 0, 3, 5], [0, 0, 17, 0, 1, 21], [0, 0, 5, 0, 10, -3], [8, 11, 0, -2, 0, 0], [0, 0, 1, 0, -7, 7], [0, 0, 10, 0, -6, 1], [30, 5, 0, 1, 0, 0], [0, -2, 0, -6, 0, 0], [0, 0, 1, 0, 5, 7], [0, 0, 1, 0, -10, -7], [-16, -11, 0, 5, 0, 0], [26, -1, 0, -5, 0, 0], [0, 0, 7, 0, 5, -6], [0, 0, 7, 0, 5, -3], [-40, 1, 0, -6, 0, 0], [0, 0, 0, 0, 8, -12], [0, 0, -4, 0, 8, 0], [0, 0, 1, 0, 4, -7], [10, 6, 0, 8, 0, 0], [-36, 4, 0, -2, 0, 0], [0, 0, -9, 0, -15, 3], [10, -12, 0, 0, 0, 0], [10, 4, 0, -10, 0, 0], [0, 0, -2, 0, -5, -19], [28, 7, 0, -2, 0, 0], [0, 0, 10, 0, 4, -1], [8, -9, 0, 10, 0, 0], [20, -5, 0, -7, 0, 0], [0, 0, 4, 0, 20, -8], [20, -3, 0, 7, 0, 0], [0, 0, 1, 0, -2, -11], [0, 0, -4, 0, -2, -5], [0, 8, 0, -6, 0, 0], [-18, -3, 0, 5, 0, 0], [0, 0, -11, 0, 3, -2], [2, 6, 0, 4, 0, 0], [0, 0, -8, 0, 14, -3], [0, 0, -2, 0, -5, -9], [-6, -7, 0, 5, 0, 0], [-4, -8, 0, -6, 0, 0], [-26, 8, 0, -4, 0, 0], [0, 0, -13, 0, 8, 5], [0, 0, -4, 0, -4, -11], [0, 11, 0, -8, 0, 0], [0, 0, -15, 0, 1, 5], [-8, 0, 0, -4, 0, 0], [0, 0, -18, 0, 2, -3], [-6, -3, 0, 12, 0, 0], [0, 0, 12, 0, -3, -9], [-32, 4, 0, 4, 0, 0], [4, -12, 0, 0, 0, 0], [14, 3, 0, -5, 0, 0], [0, 0, 1, 0, 6, 1], [0, 0, -7, 0, -2, 19], [-18, -14, 0, 1, 0, 0], [0, 0, 2, 0, -13, 19], [-38, 6, 0, -4, 0, 0], [-28, -2, 0, -2, 0, 0], [0, 0, 4, 0, -8, -1], [30, -5, 0, -8, 0, 0], [0, 0, 15, 0, 1, 6], [-6, 6, 0, -2, 0, 0], [0, 0, 3, 0, 15, 5], [-2, 5, 0, 8, 0, 0], [0, 0, -19, 0, -6, -13], [8, 16, 0, -8, 0, 0], [-12, -10, 0, 2, 0, 0], [0, 0, 19, 0, -10, 17], [0, 0, -4, 0, 4, 20], [-24, -9, 0, 6, 0, 0], [0, 0, 21, 0, -1, 8], [-18, -3, 0, -5, 0, 0], [0, 0, 20, 0, -9, 13], [52, -4, 0, -4, 0, 0], [-36, -11, 0, 2, 0, 0], [0, 0, -10, 0, 6, -1], [0, 0, 21, 0, -3, 13], [0, 0, -6, 0, 18, -6], [0, 0, -18, 0, 6, -21], [0, 0, 16, 0, -16, 9], [6, -4, 0, -11, 0, 0], [0, 0, 5, 0, -3, -7], [0, 0, 16, 0, -21, 17], [-16, -3, 0, -3, 0, 0], [30, 0, 0, 6, 0, 0], [38, 2, 0, 1, 0, 0], [0, 0, -14, 0, 10, -11], [0, 0, -8, 0, 15, -3], [-6, -6, 0, 8, 0, 0], [0, 0, 24, 0, -16, 9], [0, 0, 4, 0, -5, 7], [-4, 15, 0, 0, 0, 0], [0, 0, 11, 0, -7, -13], [0, 0, -7, 0, 11, 2], [0, 0, -7, 0, -2, 7], [-18, 6, 0, 4, 0, 0], [-46, 3, 0, 3, 0, 0], [20, -9, 0, -2, 0, 0], [0, 0, 24, 0, -12, 13], [38, 14, 0, -4, 0, 0], [0, 0, -9, 0, 2, -1], [-6, -6, 0, 2, 0, 0], [0, 0, -15, 0, 4, 15], [0, -1, 0, 6, 0, 0], [0, 0, -8, 0, -13, -11], [0, 0, 7, 0, -3, -1], [2, -7, 0, -6, 0, 0], [-22, 3, 0, -11, 0, 0], [14, 0, 0, -8, 0, 0], [0, 0, -9, 0, 4, -13], [0, 0, 19, 0, 1, 3], [4, -14, 0, 8, 0, 0], [0, 0, -11, 0, -19, 7], [-4, 3, 0, 1, 0, 0], [-40, -21, 0, 11, 0, 0], [0, 0, 12, 0, 15, -19], [8, -2, 0, -2, 0, 0], [0, 0, -1, 0, 4, -13], [0, 0, -10, 0, 5, 23], [0, 0, -19, 0, 5, -9], [-12, 9, 0, 2, 0, 0], [0, 0, -4, 0, 10, -3], [-18, 11, 0, 4, 0, 0], [0, 0, -13, 0, 13, -19], [0, 0, 4, 0, 2, -21], [-18, 8, 0, 4, 0, 0], [10, -13, 0, 8, 0, 0], [0, 0, -8, 0, 8, 16], [0, 0, 1, 0, -12, 17], [32, -7, 0, -5, 0, 0], [34, 10, 0, -4, 0, 0], [0, 0, -10, 0, 6, -19], [0, 0, 23, 0, -3, 28], [-2, -16, 0, 6, 0, 0], [12, -7, 0, -12, 0, 0], [-4, -8, 0, 4, 0, 0], [0, 0, 16, 0, -5, 1], [8, 15, 0, -2, 0, 0], [-12, 5, 0, -5, 0, 0], [0, 0, 8, 0, 7, -13], [-22, 11, 0, -5, 0, 0], [0, 0, 20, 0, 10, 23], [0, 0, 0, 0, -20, 2], [-30, 7, 0, 5, 0, 0], [16, 9, 0, -11, 0, 0], [0, 0, -18, 0, 2, -27], [0, 0, 16, 0, 12, 15], [0, 0, 6, 0, -3, 23], [-2, 2, 0, 1, 0, 0], [0, 0, -15, 0, 5, -5], [-38, -4, 0, 10, 0, 0], [0, 0, -13, 0, -18, -3], [-8, 15, 0, 6, 0, 0], [0, 0, 11, 0, 0, 7], [30, -1, 0, 13, 0, 0], [0, 0, 9, 0, 13, -1], [-12, 9, 0, -4, 0, 0], [0, 0, -5, 0, 9, 16], [0, 0, 5, 0, 11, -19], [0, 0, -10, 0, 1, 15], [22, 5, 0, -7, 0, 0], [20, 17, 0, -7, 0, 0], [0, 0, 9, 0, 9, 5], [32, 1, 0, 1, 0, 0], [-14, 14, 0, -2, 0, 0], [0, 0, -8, 0, -8, -23], [12, -5, 0, 15, 0, 0], [0, 0, -2, 0, 15, -7], [-48, 3, 0, 1, 0, 0], [0, 0, 21, 0, -17, 27], [54, -6, 0, -3, 0, 0], [0, 0, 12, 0, -4, 21], [-14, -8, 0, -6, 0, 0], [0, 0, -19, 0, -1, -29], [16, 12, 0, -4, 0, 0], [-28, -22, 0, 10, 0, 0], [0, 0, 18, 0, -7, 19], [0, 0, 6, 0, 6, 19], [0, 0, 4, 0, -3, 13], [-8, -5, 0, -7, 0, 0], [0, 0, 12, 0, -4, 23], [32, 0, 0, -8, 0, 0], [0, 0, 11, 0, 6, -1], [0, 0, -21, 0, 3, -9], [0, 0, -16, 0, 8, -30], [0, 0, -4, 0, 4, 17], [18, -1, 0, 5, 0, 0], [22, 24, 0, -10, 0, 0], [32, 13, 0, -9, 0, 0], [0, 0, 1, 0, 8, 5], [-26, -21, 0, 11, 0, 0], [46, 5, 0, 0, 0, 0], [0, 0, 4, 0, -3, -11], [32, 2, 0, 10, 0, 0], [32, 6, 0, -2, 0, 0], [0, 0, -4, 0, 13, -1], [-8, 7, 0, 8, 0, 0], [0, 0, 7, 0, 9, 7], [30, 0, 0, 0, 0, 0], [0, 0, -2, 0, -3, -15], [0, 0, 5, 0, 2, 23], [0, 0, 24, 0, -1, 13], [28, -5, 0, 1, 0, 0], [0, 0, 2, 0, 16, -3], [-18, -6, 0, 4, 0, 0], [0, 0, 18, 0, 2, 6], [0, 0, -25, 0, 6, -19], [0, 0, 12, 0, -8, 11], [26, 13, 0, -7, 0, 0], [0, 0, 1, 0, -3, 27], [-12, 2, 0, -18, 0, 0], [0, 0, 19, 0, -10, -17], [-4, 2, 0, -8, 0, 0], [0, 0, -31, 0, 9, -19], [-20, -13, 0, -5, 0, 0], [30, 16, 0, -12, 0, 0], [-16, 11, 0, 5, 0, 0], [66, -2, 0, 6, 0, 0], [18, 5, 0, -5, 0, 0], [0, 0, 18, 0, -3, 17], [0, 0, 10, 0, -4, -5], [0, 0, -11, 0, -7, -7], [10, -11, 0, -1, 0, 0], [-22, 9, 0, -10, 0, 0], [0, 0, 6, 0, -15, 3], [-14, -6, 0, 14, 0, 0], [0, 0, 10, 0, -18, 25], [-22, -7, 0, 16, 0, 0], [0, 0, 5, 0, 3, 5], [0, 0, -6, 0, -21, 7], [0, 0, 10, 0, 14, -19], [4, 15, 0, -12, 0, 0], [0, 0, -24, 0, 8, -18], [26, 0, 0, 4, 0, 0], [-28, -17, 0, 7, 0, 0], [0, 0, 4, 0, 14, -23], [0, 0, -6, 0, -6, -14], [0, 0, -12, 0, 24, -23], [-50, -11, 0, 11, 0, 0], [0, 0, 5, 0, 9, 29], [0, 0, -29, 0, 12, -21], [0, 10, 0, 0, 0, 0], [0, 0, 15, 0, 25, -15], [0, 0, 5, 0, 11, 21], [0, 0, 22, 0, 18, -7], [14, 16, 0, 1, 0, 0], [-54, -21, 0, 10, 0, 0], [20, -15, 0, 4, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_7600_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_7600_2_a_ck();".
// 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_7600_2_a_ck(:prec:=6)
    chi := MakeCharacter_7600_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_7600_2_a_ck();".
// 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_7600_2_a_ck( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_7600_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-16, 0, 60, 0, -16, 0, 1]>,<7,R![-144, 0, 104, 0, -19, 0, 1]>,<11,R![-12, -16, 1, 1]>,<13,R![-576, 0, 236, 0, -28, 0, 1]>],Snew);
    return Vf;
end function;