
// Make newform 7600.2.a.cj in Magma, downloaded from the LMFDB on 06 May 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_cj();".
// 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_cj();".
// 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, 14, 0, -9, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [-3, 0, 1, 0, 0, 0], [0, -10, 0, 9, 0, -1], [0, 14, 0, -9, 0, 1], [0, 6, 0, -8, 0, 1], [6, 0, -8, 0, 1, 0]];
    Rf_basisdens := [1, 1, 2, 2, 1, 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, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [-3, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 1, -1, 1, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0], [0, 2, 0, 0, 0, 2], [-2, -2, 0, 0, 0, -2], [0, 0, 0, -1, 0, 0], [0, 2, 0, 0, 0, -2], [0, 0, -2, -2, 1, 0], [0, 0, 2, -2, -1, 0], [0, 0, -2, -1, -2, 0], [-4, 0, 0, 0, 0, 2], [5, -1, 0, 0, 0, 0], [0, 0, 1, 2, 4, 0], [-8, 0, 0, 0, 0, -2], [0, 0, 3, 1, 3, 0], [-4, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, 0], [2, 0, 0, 0, 0, 2], [0, 0, -2, -1, -2, 0], [1, 1, 0, 0, 0, -1], [0, 0, -3, -2, -2, 0], [0, 0, 3, -2, 2, 0], [0, -2, 0, 0, 0, 0], [0, 0, -1, 2, 2, 0], [0, 0, -2, -5, 0, 0], [-4, -2, 0, 0, 0, 3], [0, 0, 3, 1, -1, 0], [-3, -3, 0, 0, 0, 2], [1, -1, 0, 0, 0, 0], [4, 0, 0, 0, 0, 2], [0, 0, -4, 2, -4, 0], [0, 0, -1, -1, 0, 0], [0, 0, -4, -5, -4, 0], [0, 0, -1, -6, 2, 0], [-4, 0, 0, 0, 0, -2], [-2, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 1], [0, 0, -2, 7, -2, 0], [0, 0, 4, 0, 0, 0], [4, -2, 0, 0, 0, 3], [6, -6, 0, 0, 0, 0], [0, 0, 6, -3, 4, 0], [0, 0, 1, 0, 0, 0], [-17, -3, 0, 0, 0, -2], [0, 0, 5, 9, 5, 0], [-16, -2, 0, 0, 0, -5], [-8, 2, 0, 0, 0, -2], [-8, 6, 0, 0, 0, 3], [0, 0, -2, 1, 2, 0], [0, 0, -2, 4, -1, 0], [4, 2, 0, 0, 0, 4], [5, 3, 0, 0, 0, -3], [0, 0, -3, -5, -3, 0], [-10, -4, 0, 0, 0, -8], [0, 0, 0, -2, -5, 0], [0, 0, -2, 7, -2, 0], [0, 0, -7, 0, -8, 0], [-7, -3, 0, 0, 0, -6], [0, 0, 6, 6, 0, 0], [0, 0, 5, 2, -2, 0], [2, 2, 0, 0, 0, -6], [0, 0, -3, -4, 4, 0], [0, 0, 4, 2, 5, 0], [0, 0, 0, 0, 0, 5], [0, 0, 6, 4, 4, 0], [-19, 1, 0, 0, 0, 2], [0, 0, 5, -7, 4, 0], [0, 0, 6, 3, 2, 0], [12, 4, 0, 0, 0, -2], [0, 0, 7, 6, 8, 0], [-6, -6, 0, 0, 0, -3], [0, 0, 1, -5, -5, 0], [0, -2, 0, 0, 0, 0], [-6, 0, 0, 0, 0, -6], [0, 0, 0, 0, 0, -4], [-4, -2, 0, 0, 0, 4], [-14, 6, 0, 0, 0, -2], [0, 0, -5, -6, 2, 0], [6, -6, 0, 0, 0, 4], [0, 0, -6, -12, -1, 0], [14, 4, 0, 0, 0, -6], [0, 0, 1, 1, -1, 0], [-14, 2, 0, 0, 0, -3], [0, 0, 8, 10, 3, 0], [0, 0, -4, 6, 5, 0], [-11, -5, 0, 0, 0, 1], [0, 0, -1, -4, -2, 0], [-8, 4, 0, 0, 0, 4], [-1, -1, 0, 0, 0, -6], [0, 0, -5, -3, 0, 0], [-12, -6, 0, 0, 0, 4], [-2, 0, 0, 0, 0, 6], [0, 0, -6, 9, -4, 0], [3, -3, 0, 0, 0, 6], [0, 0, -8, 5, -2, 0], [0, 0, 3, 13, 1, 0], [0, 0, 2, 1, -4, 0], [-16, -6, 0, 0, 0, 0], [13, 7, 0, 0, 0, 1], [0, 0, 7, 3, 11, 0], [0, 0, -2, 4, 1, 0], [0, 0, 2, 2, -8, 0], [-26, -2, 0, 0, 0, -2], [4, 6, 0, 0, 0, 2], [0, 0, -7, 2, 0, 0], [0, 0, -5, 9, -5, 0], [0, 0, 1, 15, -1, 0], [-3, 7, 0, 0, 0, 1], [-7, -7, 0, 0, 0, 0], [8, 6, 0, 0, 0, 4], [0, 0, 8, 6, 11, 0], [0, 0, 10, 0, 5, 0], [0, 0, 1, -5, -5, 0], [-10, -2, 0, 0, 0, 0], [-12, -2, 0, 0, 0, -4], [0, 0, 1, -2, -2, 0], [0, 0, -8, 5, 4, 0], [0, 0, -8, 3, -6, 0], [-19, 5, 0, 0, 0, 6], [-5, -5, 0, 0, 0, -7], [20, 2, 0, 0, 0, -2], [-1, 7, 0, 0, 0, 4], [0, 0, 0, -8, 3, 0], [0, 0, 2, -14, 4, 0], [-36, 2, 0, 0, 0, -1], [0, 0, -2, 11, -2, 0], [18, -2, 0, 0, 0, 2], [0, 0, 1, -11, -3, 0], [17, -1, 0, 0, 0, 2], [-19, -1, 0, 0, 0, 6], [0, 0, 5, 14, 2, 0], [0, 0, 8, 9, -2, 0], [0, 0, -2, 7, -6, 0], [8, 8, 0, 0, 0, -9], [6, -14, 0, 0, 0, 2], [-14, 6, 0, 0, 0, 5], [0, 0, -2, -10, 5, 0], [0, 0, 10, 17, 6, 0], [12, -6, 0, 0, 0, -8], [-28, -4, 0, 0, 0, 6], [0, 0, 6, 2, 4, 0], [0, 0, 4, 3, 8, 0], [-16, 2, 0, 0, 0, -9], [0, 0, 0, 1, -8, 0], [0, 0, -12, -11, -16, 0], [11, 9, 0, 0, 0, 0], [0, 0, 6, 2, 9, 0], [0, 0, 7, 6, -6, 0], [0, 0, -7, -12, 0, 0], [-2, -2, 0, 0, 0, 8], [4, -8, 0, 0, 0, 0], [24, 6, 0, 0, 0, 6], [0, 0, 5, -5, -1, 0], [10, -4, 0, 0, 0, -4], [0, 0, -9, 9, -4, 0], [0, 0, 6, 5, -6, 0], [0, 0, 1, 3, 4, 0], [-4, 4, 0, 0, 0, 4], [0, 0, 15, -4, 12, 0], [0, 0, -5, -2, 8, 0], [-32, 4, 0, 0, 0, 2], [0, 0, -5, 13, -9, 0], [22, 4, 0, 0, 0, 2], [0, 0, -1, -15, -3, 0], [-10, 2, 0, 0, 0, -4], [-30, 8, 0, 0, 0, 2], [7, 1, 0, 0, 0, 7], [0, 0, -8, -12, -16, 0], [12, 4, 0, 0, 0, 4], [41, 3, 0, 0, 0, -2], [12, -12, 0, 0, 0, 0], [25, 3, 0, 0, 0, 6], [0, 0, 14, -1, -2, 0], [-13, -7, 0, 0, 0, -8], [0, 0, 0, 14, 1, 0], [-8, 8, 0, 0, 0, 8], [0, 0, -3, 6, 10, 0], [0, 0, -7, -2, 10, 0], [0, 0, -6, 8, 7, 0], [6, 14, 0, 0, 0, 3], [0, 0, -9, 6, 6, 0], [0, 0, -2, -3, -4, 0], [-32, 6, 0, 0, 0, 6], [4, -4, 0, 0, 0, -8], [0, 0, -8, -9, 4, 0], [0, 0, 0, 10, -1, 0], [-8, 16, 0, 0, 0, 8], [-18, -8, 0, 0, 0, 0], [0, 0, -5, -5, 8, 0], [0, 0, 5, -4, 0, 0], [4, -12, 0, 0, 0, -9], [0, 0, 10, -6, -4, 0], [0, 0, 10, -2, 0, 0], [0, 0, -14, 6, -7, 0], [-12, -6, 0, 0, 0, -16], [0, 4, 0, 0, 0, 6], [0, 0, -9, 0, -16, 0], [16, 6, 0, 0, 0, -6], [11, 9, 0, 0, 0, -9], [0, 0, -9, -7, -5, 0], [5, -3, 0, 0, 0, 0], [0, 0, -1, -2, -4, 0], [40, -4, 0, 0, 0, 1], [8, 12, 0, 0, 0, -14], [0, 0, 14, -10, 12, 0], [-19, -7, 0, 0, 0, -1], [0, 0, 6, 4, 7, 0], [0, 0, 14, -3, 10, 0], [2, 10, 0, 0, 0, -12], [-2, 12, 0, 0, 0, -8], [0, 0, -11, -7, -4, 0], [28, 2, 0, 0, 0, 4], [0, 0, 8, -7, -6, 0], [0, 0, -9, -9, -5, 0], [-46, 4, 0, 0, 0, 4], [20, -16, 0, 0, 0, 2], [26, 4, 0, 0, 0, 0], [0, 0, -14, -8, -9, 0], [0, 0, -9, -22, -2, 0], [20, 4, 0, 0, 0, -9], [0, 0, 5, -14, 2, 0], [-16, 0, 0, 0, 0, 4], [0, 0, 7, 22, 2, 0], [8, 2, 0, 0, 0, -11], [0, 0, -1, -1, -1, 0], [6, 14, 0, 0, 0, 6], [42, -2, 0, 0, 0, -6], [-14, 0, 0, 0, 0, -4], [0, 0, -8, -14, -1, 0], [0, 0, 2, -6, -9, 0], [17, -13, 0, 0, 0, -8], [0, 0, 1, 1, 11, 0], [-29, -7, 0, 0, 0, 3], [-2, 18, 0, 0, 0, 2], [0, 0, 1, 6, 14, 0], [8, 10, 0, 0, 0, 7], [0, 0, -15, 1, 0, 0], [2, 16, 0, 0, 0, 8], [0, 0, 8, -15, 4, 0], [44, 2, 0, 0, 0, 5], [0, 0, -2, 6, -1, 0], [-2, -2, 0, 0, 0, -2], [16, 4, 0, 0, 0, 16], [0, 0, 12, -8, -3, 0], [0, 0, -10, -18, 4, 0], [-6, 2, 0, 0, 0, 7], [0, 0, -9, -3, -12, 0], [-2, -4, 0, 0, 0, 10], [0, 0, -1, -1, -7, 0], [-16, 4, 0, 0, 0, 4], [-24, 8, 0, 0, 0, -1], [0, 0, 7, -12, 6, 0], [0, 0, -4, -11, -8, 0], [0, 0, 2, 12, -4, 0], [0, 0, -3, 10, 10, 0], [0, 0, -4, 11, 8, 0], [-31, -1, 0, 0, 0, -14], [0, 0, 4, 21, 0, 0], [0, 0, 5, -3, -7, 0], [28, 4, 0, 0, 0, 12], [-34, 8, 0, 0, 0, 2], [7, -11, 0, 0, 0, -10], [0, 0, -11, 4, -6, 0], [0, 0, 5, 17, -7, 0], [18, 0, 0, 0, 0, 18], [0, 0, 4, -9, -8, 0], [0, 0, -15, -25, -11, 0], [7, 7, 0, 0, 0, -12], [0, 0, 14, -1, 10, 0], [0, 0, 13, 9, -8, 0], [0, 0, -8, -20, -9, 0], [26, 12, 0, 0, 0, -10], [-28, -2, 0, 0, 0, 2], [-21, -5, 0, 0, 0, 2], [0, 0, 13, 16, 14, 0], [-1, 1, 0, 0, 0, 11], [0, 0, 14, 12, 9, 0], [8, -10, 0, 0, 0, -2], [0, 0, -16, 14, -7, 0], [31, 11, 0, 0, 0, 6], [0, 0, -9, -5, -11, 0], [0, 0, 11, -20, 4, 0], [-24, -2, 0, 0, 0, 11], [-36, -2, 0, 0, 0, -8], [-26, -12, 0, 0, 0, -16], [0, 0, 4, 20, -1, 0], [0, 0, 6, -13, -14, 0], [26, -18, 0, 0, 0, -4], [0, 0, 15, 2, 14, 0], [39, -21, 0, 0, 0, -3], [6, 14, 0, 0, 0, -2], [0, 0, -9, -1, -15, 0], [10, 10, 0, 0, 0, 2], [0, 0, -6, -22, 3, 0], [0, 0, 11, 5, 17, 0], [0, 0, 15, 30, 6, 0], [-17, -1, 0, 0, 0, 4], [0, 0, 18, 19, 22, 0], [48, -6, 0, 0, 0, 3], [0, 0, -15, 4, -12, 0], [0, 0, 6, -7, 14, 0], [-28, -10, 0, 0, 0, 2], [-24, -6, 0, 0, 0, -9], [0, 0, -2, 18, 12, 0], [0, 0, 4, -8, -11, 0], [-7, 5, 0, 0, 0, 7], [-20, 2, 0, 0, 0, 0], [0, 0, -14, -23, -20, 0], [0, 0, 11, 25, 0, 0], [12, -2, 0, 0, 0, 16], [3, 3, 0, 0, 0, -18], [14, -6, 0, 0, 0, 6], [0, 0, -7, 1, 1, 0], [4, 4, 0, 0, 0, 9], [-32, -4, 0, 0, 0, 2], [0, 0, -9, 17, 1, 0], [2, -4, 0, 0, 0, 16], [0, 0, 7, 14, -8, 0], [0, 0, 2, -12, 8, 0], [26, 4, 0, 0, 0, 2], [0, 8, 0, 0, 0, 12], [0, 0, -18, 9, 0, 0], [0, 0, -2, 11, -8, 0], [0, 0, 5, -5, 1, 0], [-11, -1, 0, 0, 0, 8], [0, 0, -5, -2, -14, 0], [5, 11, 0, 0, 0, 5], [0, 0, -10, -2, 5, 0], [-7, 21, 0, 0, 0, 4], [0, 0, -4, 8, -17, 0], [8, -10, 0, 0, 0, -12], [0, 0, 8, 15, 4, 0], [-40, 4, 0, 0, 0, -3], [0, 0, -11, -9, -20, 0], [0, 0, -23, 16, -16, 0], [0, 0, 11, 9, -3, 0], [-38, 0, 0, 0, 0, -8], [-24, 4, 0, 0, 0, 4], [0, 0, -4, 5, -16, 0], [-20, -12, 0, 0, 0, -4], [20, -6, 0, 0, 0, -14], [0, 0, 20, -5, 8, 0], [-24, 12, 0, 0, 0, -8], [0, 0, -3, -9, -5, 0], [-26, -2, 0, 0, 0, -4], [0, 0, 3, 0, 0, 0], [25, 3, 0, 0, 0, 0], [0, 0, -11, -20, -6, 0], [16, 6, 0, 0, 0, 20], [0, 0, 15, 28, 16, 0], [24, 12, 0, 0, 0, 16], [-44, 4, 0, 0, 0, 8], [0, 0, -13, 17, -15, 0], [0, 0, 4, 1, -16, 0], [0, 0, 3, -3, -17, 0], [-23, 13, 0, 0, 0, 3], [0, 0, 3, 12, 14, 0], [34, -6, 0, 0, 0, -6], [0, 0, 4, 2, -7, 0], [0, 0, -9, 10, 22, 0], [0, 0, -8, -6, -16, 0], [0, 0, -11, 4, -6, 0], [-18, 0, 0, 0, 0, -2], [-59, -9, 0, 0, 0, -7], [-2, 14, 0, 0, 0, 16], [0, 0, 4, 8, 9, 0], [30, -12, 0, 0, 0, 0], [56, 6, 0, 0, 0, 1], [0, 0, 11, 5, 7, 0], [2, -14, 0, 0, 0, -6], [-40, 0, 0, 0, 0, 8], [0, 0, 3, -9, 3, 0], [-6, 14, 0, 0, 0, -3], [0, 0, 6, 7, 14, 0], [-22, -4, 0, 0, 0, -12], [0, 0, 15, 15, 9, 0], [0, 0, 18, -18, -1, 0], [0, 0, 3, -21, 9, 0], [20, 0, 0, 0, 0, 14], [0, 0, 19, 20, 24, 0], [-33, 1, 0, 0, 0, -17], [0, 0, 2, 12, 20, 0], [0, 0, 22, -6, 9, 0], [0, 0, 3, -4, -14, 0], [50, -4, 0, 0, 0, -4], [0, 0, -13, 10, -14, 0], [-40, 8, 0, 0, 0, -8], [0, 0, -18, 12, -11, 0], [-76, 0, 0, 0, 0, 6], [0, 0, -15, -2, -14, 0], [-4, -8, 0, 0, 0, 16], [14, -8, 0, 0, 0, -4], [14, -10, 0, 0, 0, 0], [-12, 26, 0, 0, 0, 10], [-10, 0, 0, 0, 0, 22], [0, 0, -3, -15, -23, 0], [0, 0, -6, -7, 18, 0], [0, 0, 1, -6, 6, 0], [-50, 8, 0, 0, 0, 2], [-12, -14, 0, 0, 0, -5], [0, 0, 19, 1, 1, 0], [42, -8, 0, 0, 0, 4], [0, 0, -2, -11, -16, 0], [0, 10, 0, 0, 0, 21], [0, 0, 10, 21, 18, 0], [0, 0, 11, -1, 7, 0], [0, 0, -11, 4, 6, 0], [-3, -11, 0, 0, 0, -14], [0, 0, 14, -8, 20, 0], [-20, 14, 0, 0, 0, -2], [16, 20, 0, 0, 0, -20], [0, 0, -20, -15, -26, 0], [0, 0, -2, -24, -4, 0], [0, 0, 13, 4, 22, 0], [-48, -2, 0, 0, 0, 4], [0, 0, -8, 9, 4, 0], [0, 0, -10, 10, -13, 0], [24, -16, 0, 0, 0, -10], [0, 0, 9, -20, -4, 0], [0, 0, -3, -20, 8, 0], [0, 0, -2, -27, -8, 0], [-5, -11, 0, 0, 0, -16], [-32, -2, 0, 0, 0, 5], [-55, -7, 0, 0, 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_cj();".
// 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_cj(: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_cj();".
// 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_cj( : 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, 36, 0, -14, 0, 1]>,<7,R![-64, 0, 104, 0, -27, 0, 1]>,<11,R![-28, 14, 9, 1]>,<13,R![-64, 0, 108, 0, -26, 0, 1]>],Snew);
    return Vf;
end function;