
// Make newform 7245.2.a.bj in Magma, downloaded from the LMFDB on 28 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_7245_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_7245_2_a_bj();".
// 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_7245_2_a_bj();".
// 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, -7, 16, 6, -8, -1, 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], [0, -4, 0, 1, 0, 0], [-2, 4, 1, -1, 0, 0], [2, -1, -5, 0, 1, 0], [-1, 11, 0, -7, 0, 1]];
    Rf_basisdens := [1, 1, 1, 1, 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_7245_a();"
function MakeCharacter_7245_a()
    N := 7245;
    order := 1;
    char_gens := [5636, 5797, 5176, 1891];
    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_7245_a_Hecke(Kf)
    return MakeCharacter_7245_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, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, -1, -1, 1, 0], [-2, -2, 2, 1, 0, 0], [-2, 1, 1, 1, 0, -1], [-2, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0], [0, 2, -2, -2, 0, 0], [-2, -1, 1, -2, 0, -1], [2, 0, -2, -1, -4, 0], [-2, 3, 0, 1, -1, -1], [0, 1, 0, 1, -3, 1], [-2, -4, 2, 0, 0, 0], [-4, 1, -3, 2, -2, -1], [2, 0, -1, -3, 1, 2], [-4, -3, 5, -1, 0, 1], [2, 1, 3, 3, 4, -3], [-4, 2, 2, 4, 2, 0], [-2, 0, 1, 3, -1, 0], [2, -1, -1, -4, 0, -1], [-4, -7, 0, 1, -1, 1], [-4, -2, 6, 0, 0, 0], [4, 4, 0, 2, 4, -4], [-4, -1, 1, 3, 4, 3], [-2, -2, 0, 2, -2, 2], [-2, 4, -4, -4, 2, 0], [-2, -4, 0, -2, 0, -2], [-12, 5, 3, 2, 0, -1], [8, 2, -6, 0, 0, -4], [0, -2, 0, -3, 0, 2], [-4, -1, -1, -2, -2, 5], [2, 1, -7, 0, -2, -1], [-2, -1, 5, -1, -2, 1], [4, 5, -2, -3, -5, 3], [6, 2, -8, -2, -4, 0], [0, -2, -6, -4, 0, 4], [-4, 6, 0, 0, 2, 0], [-4, 1, 3, -2, -2, 3], [-6, -4, 6, -4, -2, 2], [0, 1, -4, 1, -1, -1], [8, -2, -6, -1, -4, 0], [8, 4, -4, 2, 2, -6], [-4, -4, 2, 0, -2, -4], [-6, 0, 6, 0, 6, 0], [0, 5, -2, -3, 7, 3], [0, 1, -1, -3, 2, -5], [-10, 5, -1, 5, 0, -1], [-10, 5, 0, -5, 7, -1], [0, -1, 2, -1, -3, -5], [-12, 4, 4, 0, 2, 0], [-6, 1, 3, 5, 2, 1], [8, 0, -2, -8, 2, 2], [-4, -3, 1, 0, 0, -5], [-12, 2, 10, -2, 8, 0], [-2, 5, -4, 3, -3, 1], [0, -3, -1, 6, 2, 7], [-2, -8, 2, 2, -2, 4], [-6, 3, 4, -3, 7, -3], [-2, -6, -6, -4, -4, 4], [-2, -9, 2, 1, -3, 1], [-8, 3, -4, -1, -9, -3], [4, -5, 1, 2, 0, 3], [-2, 0, 2, 2, -4, 8], [-6, 3, 5, 5, 4, -1], [-4, 1, -7, 3, 0, -1], [6, -6, 0, 3, 0, -6], [-4, -3, -5, 1, -10, 1], [6, 4, -2, 2, -6, 4], [-4, -7, -1, 4, 6, 1], [4, 2, 2, -1, 0, 4], [-8, 6, 2, 2, 0, 6], [14, -7, 3, -2, 4, 5], [-10, -5, 1, 8, 2, -3], [-8, 7, -5, -3, -6, 1], [6, 3, -3, -5, -6, 5], [-6, 4, 3, 5, 1, -4], [-2, -2, -6, 8, -4, -2], [2, -2, 2, -2, -4, 8], [-14, 0, 8, 4, 6, -2], [0, 0, -6, 2, 4, 4], [0, -4, -4, 1, 0, 2], [-2, -12, 12, 2, 6, -2], [-8, -3, -3, 4, -12, -3], [-10, 0, 6, 8, 6, -4], [-6, -6, -2, -4, -14, 0], [14, -3, 3, -10, 4, 5], [0, -5, 5, 1, 8, 3], [-8, 8, 0, 6, 2, -6], [-10, 11, 4, 1, 1, -1], [12, -2, -10, -14, -4, 0], [4, 2, 8, 4, 4, -4], [-2, 4, 4, 6, 0, 0], [0, 9, -11, -11, 4, -1], [-2, 2, -8, -8, 6, -2], [-8, -5, 17, 1, 8, 3], [-2, -6, -6, -6, 2, -4], [-6, 4, 2, 0, 8, -6], [-10, -5, 0, 9, 5, -1], [8, 0, -10, -4, 4, -4], [-20, -1, 11, 10, 6, 7], [4, -8, -8, 0, -8, 4], [-14, 7, 8, 1, 7, -3], [-2, 1, -1, 6, 2, 3], [6, 6, 5, 5, 5, -2], [22, -6, -12, -4, -4, -2], [-8, -1, 9, -6, -2, 11], [-12, 2, 2, 12, -2, -2], [12, 4, 8, 4, 10, -2], [-24, -11, 3, 9, 2, 3], [8, 6, 1, 3, 5, 4], [-6, -17, 5, 0, -2, 5], [-4, -7, 3, -1, -8, 9], [6, 13, -17, -6, -2, -9], [-26, -11, -1, 9, 2, 3], [-12, 2, -8, -6, 0, 4], [-2, 0, -8, 8, 6, 4], [-10, -9, -7, -7, -4, 3], [18, 5, -15, -6, 6, -3], [-10, -1, -3, 3, 2, -5], [6, 0, -4, 4, 0, 2], [2, 1, 9, 1, -8, -1], [-6, -5, -2, -1, -5, 13], [-10, 7, -3, -4, -8, 1], [-2, 0, -12, 0, -20, 0], [-4, 10, -10, -2, 2, 0], [6, 6, 1, 1, 1, -4], [6, -4, 10, -6, -2, 6], [20, -6, 2, 2, -4, 4], [20, 3, 2, -5, 1, 5], [-4, 12, -8, 6, 0, 0], [12, 1, -3, -12, -10, -1], [16, 4, -11, -7, -5, -2], [2, -14, 2, -4, 0, 2], [14, -9, 9, 7, -6, 3], [-10, 5, 1, 13, 4, 3], [6, 6, -8, -6, 2, -10], [2, -1, -10, 13, -11, -3], [-4, -4, 0, -8, 6, -2], [-14, 5, 1, -10, 2, -9], [8, 2, -6, -10, 6, 8], [-10, -2, 4, 6, 18, -8], [-2, 12, -8, 0, 2, -8], [6, -4, 4, 4, -4, 12], [-4, 2, 12, 2, -6, 8], [-16, -1, 11, 2, 10, -1], [-10, 13, -9, 0, -4, -9], [-6, -1, 1, 0, 0, 7], [16, 9, -17, -15, -2, -3], [14, 6, -2, -8, -4, -4], [-2, 2, -2, 0, 12, -12], [-2, 0, -10, -2, 6, 8], [6, 8, 4, 4, 10, -14], [-4, -13, 2, 9, -7, 3], [8, -16, 1, -3, 3, 0], [-10, -5, -3, 12, 2, -1], [-8, 3, 5, 3, -4, -1], [20, -12, -6, -8, -6, -6], [10, -6, -6, 8, -6, -10], [0, 5, 8, 5, -9, 3], [8, -13, 7, -8, 2, 3], [-8, -14, 10, 8, 8, 4], [-10, 10, -10, 0, -6, 0], [-18, 15, 1, 0, -2, -7], [2, 10, -12, 0, 2, -2], [12, -1, -1, -9, -4, -3], [-16, 15, 11, -6, 18, -5], [2, -6, 16, 0, -2, 4], [-22, 17, -1, 4, 0, 11], [-10, -5, -5, -14, -10, -1], [24, 0, -20, -4, 2, -6], [16, 8, 7, 3, 13, -8], [6, 6, 4, 5, 4, -2], [2, 5, -15, -6, 6, -7], [-32, -4, 10, 14, 8, 0], [12, 11, -9, -5, 8, -7], [0, -18, -6, -6, -2, 0], [10, 6, -8, 2, 0, -8], [4, 5, -7, -5, 8, 1], [-20, 6, 14, 20, 10, -4], [8, 0, -16, -12, 0, -2], [12, -16, -10, -8, 0, 2], [2, -21, 3, 0, 2, -1], [0, 0, -8, -12, 0, -6], [-16, -20, 8, 10, -8, 6], [6, 2, 8, 4, 2, 8], [-10, 10, -6, -8, -6, 2], [8, -7, -1, 5, 8, -13], [12, 13, -1, -10, -4, 1], [18, 10, -22, -1, -8, -4], [6, 5, -15, 1, 8, -15], [8, 7, -9, 12, 2, -11], [22, 10, -6, -8, -4, -10], [-2, 0, 6, 8, -4, -6], [-18, -5, 0, -5, -5, 13], [24, 0, -2, 2, -4, -4], [22, 4, 2, -5, 0, 4], [10, -5, -6, -3, -7, 5], [4, -16, 2, 6, 2, 2], [6, 15, 1, 3, 10, -3], [8, 3, -5, -6, 4, 3], [-20, 13, -15, -2, -2, 1], [-16, -9, 4, 11, -3, 1], [2, -22, 20, 6, 8, -2], [-30, -1, 11, 6, 14, 3], [2, -11, 8, -3, -3, -7], [2, -7, 10, 13, 1, -5], [28, 8, 2, -2, -8, 0], [-8, -11, 11, 10, 10, -5], [-6, -16, -2, 4, 14, -10], [-14, -9, 2, -5, -3, 7], [-14, -9, -11, -7, -16, 7], [2, 1, -1, -3, -8, 15], [8, -2, 8, 17, 0, -2], [6, -3, 0, -9, 7, -9], [0, -16, 16, 12, -2, 12], [10, 9, 8, -5, 9, -3], [12, -12, 24, 2, 8, -8], [-12, 3, 2, 11, 9, 3], [24, 5, 6, -9, 13, 5], [-8, -5, -11, -5, -4, 11], [-4, -4, 6, -12, -10, -6], [-4, 9, 10, -5, -9, -3], [14, -6, -10, 4, -6, 8], [-2, -7, 8, -5, 7, -3], [-18, -21, 4, 7, -9, 5], [-12, -18, 6, 2, -14, 2], [-40, 0, 28, 12, 2, 6], [-4, 4, -14, 16, -12, -6], [8, 16, 10, 14, 8, -8], [-18, 6, 8, -4, 2, -6], [-10, 9, -1, 4, 2, 3], [-8, 10, -16, -6, 0, 4], [14, -22, 2, 0, -6, -14], [-2, -3, -8, -21, -5, -3], [10, -8, 0, -12, -8, 4], [-20, 5, 5, 10, 6, -5], [44, 2, -2, -4, -2, -2], [2, 6, -27, -7, -15, 0], [-32, 6, 14, -2, 0, 8], [-4, 11, 19, 0, 0, -7], [-28, 19, 10, 1, 9, 9], [-10, 1, 5, 17, -6, -9], [-2, 19, -5, 0, 6, -7], [18, -4, -9, -3, 9, -2], [-4, -5, -3, 3, -18, 1], [20, 2, -16, 10, 6, -8], [18, -5, -11, -10, -6, 5], [-26, -12, 16, 0, 2, 6], [22, 2, -12, 1, 4, -6], [24, 8, -6, 0, 14, -4], [-28, -12, 4, -6, -12, 10], [2, 11, 8, -7, -3, -3], [10, -1, -3, -6, -12, -19], [18, -2, 16, -4, 6, 4], [20, 6, -8, -12, 8, -2], [-6, 10, -10, -4, -16, -12], [-26, -3, 11, 6, 4, -1], [-14, 0, 16, 13, -8, 2], [-6, 7, 1, -13, -4, -5], [-20, -22, 30, 18, 4, 6], [-12, 16, 10, 6, 16, -8], [24, 22, -20, -10, 2, -14], [20, 5, -1, 8, -6, 7], [-4, 1, 19, 1, -12, -7], [54, 1, 6, 5, 11, -1], [-4, -14, -6, -8, 0, 0], [-24, -8, 16, 16, 4, 4], [-6, -1, 13, 3, 12, -9], [0, 6, 12, -6, -8, -6], [-4, -9, 2, -15, -11, -5], [26, 10, 2, 16, 2, 2], [6, 7, -1, 6, 12, -11], [24, 1, -7, -22, -10, 9], [20, 13, -25, -7, -6, -5], [4, -3, -13, 5, 10, -15], [-14, 13, -12, -17, 7, 9], [32, -4, 14, 4, 8, -4], [-16, 10, -8, 6, -2, -6], [2, 12, 6, -8, 0, 0], [-22, 5, 21, 18, 20, -5], [-14, -1, 12, 13, 5, 7], [-28, -18, -4, -12, -10, 10], [-32, -11, 4, -3, -7, 7], [-4, 10, 2, -4, -14, -4], [36, 12, -19, -7, 11, -2], [32, 15, -3, -10, 16, 3], [4, 1, -11, -14, -12, 7], [-14, 7, -20, -3, -9, 7], [-2, -3, 12, 19, 13, 15], [14, 17, -16, -5, -5, -3], [-16, 3, 20, 5, 3, -5], [-18, -20, 28, -4, -2, 4], [-2, -6, 20, 10, -10, 4], [-4, -2, -18, 4, -10, 10], [0, -25, 5, -9, 4, -1], [-6, -15, -5, 8, -12, -11], [-4, -5, 5, -10, 4, -5], [-4, 3, 1, 3, -6, 5], [0, 4, 18, -8, 18, 6], [-8, -3, -3, -10, -14, -1], [-14, -15, -5, -22, -10, 15], [6, -31, -2, 5, -11, 7], [32, 5, -19, -2, -2, -7], [10, -8, 0, -10, -8, 16], [-20, -25, 20, 19, 1, -3], [28, 22, -36, -20, -2, -6], [52, -6, -5, -3, 7, -6], [-2, -16, -6, 0, -6, 0], [-10, -2, 8, 12, 16, -6], [26, -15, -8, -13, -3, 3], [38, -13, -10, -17, -3, 1], [-8, 0, 2, -8, -6, -12], [-18, -2, 8, 10, -24, 0], [-12, -11, 24, 13, 19, 11], [20, -10, -12, -7, -8, 6], [14, 2, -14, 0, 8, 0], [10, 36, -4, -6, 6, 0], [0, -6, -6, 20, -4, -18], [30, -5, -26, 1, -7, -5], [-2, 5, -5, -6, -8, 17], [38, -5, -12, -11, 7, -5], [-30, -2, 20, 0, -22, 10], [18, 7, 1, -12, 6, 17], [-30, -16, 0, 16, 16, -12], [-16, -1, -11, 12, -12, -11], [-40, 3, -10, 13, -7, -7], [-6, -2, 14, 8, 10, -10], [54, 13, -19, 2, 0, -7], [-6, -19, 9, 5, -6, 11], [24, 15, -18, -5, 5, -17], [-44, 9, 7, 4, 6, 19], [10, 26, 8, -14, 12, -2], [8, 13, -1, 2, 0, -11], [6, 8, 6, 18, 16, -2], [-14, -6, 10, -4, 8, 6], [-22, 1, 1, 5, -4, 7], [8, 2, 16, -4, -4, -14], [-8, 6, -6, -2, 14, -12], [-12, -6, 10, -14, -2, 24], [-34, -3, 25, -4, 4, 5], [-14, 18, 6, 8, 4, -6], [-14, -21, 5, -10, -6, -3], [-8, -15, 9, -6, -10, -3], [22, 22, 2, 2, -8, 0], [2, 0, -6, 0, 6, -8], [8, 10, 8, -6, -2, 2], [-8, 12, -8, -2, -4, 0], [10, 3, -6, -19, 9, -7], [46, -5, -9, -10, 2, -5], [-14, 6, 0, 30, -6, -12], [22, -16, -2, 2, -4, 10], [-2, 4, 8, -2, 14, -4], [24, -26, -22, -6, -2, 2], [-6, -15, 21, -4, 2, 11], [-4, 14, -16, -8, -6, 6], [-16, -14, 6, 22, -16, -2], [32, 4, -10, -4, 14, -8], [30, 7, -6, -1, 23, 1], [-26, 22, 4, 5, -16, -2], [-16, -17, 29, 9, -8, 11], [-28, 13, 23, 17, 10, 1], [-14, 1, -23, 14, 2, -7], [-8, -11, -24, 1, -7, 11], [-12, 22, 8, -18, 20, 8], [-16, 13, -7, -4, 16, 1], [12, 9, 10, 15, 11, -19], [-4, 4, 4, -8, 6, 28], [-38, -20, 16, 18, -4, -2], [-28, 11, 11, 16, 12, 19], [18, 13, -30, -19, -15, -1], [-10, -11, 15, 19, 18, -1], [10, 11, 14, 9, -11, 7], [22, 14, -6, -4, 0, -16], [0, -10, -32, -5, 12, 2], [-10, -11, -15, -2, -18, 5], [26, -20, -14, -10, 0, -6], [6, -8, 34, 16, 0, -6], [-10, -22, 1, -7, -7, -2], [-26, -2, 26, 6, -8, 18], [20, -17, -11, 2, 4, 1], [48, 2, -24, 2, 0, -6], [16, 15, 0, -11, -5, -9], [-10, -23, 12, 13, 5, -3], [-4, 18, -2, 8, 12, 2], [-8, -12, 8, 20, 0, -8], [14, -10, 3, -17, -9, -2], [4, 27, -2, 21, 9, -9], [18, 3, -3, 7, 16, -11], [2, 18, -28, -4, -14, 6], [74, 11, -21, -8, -2, -5], [-4, -12, 34, -20, 8, 0], [-24, 21, 11, -3, 18, -5], [-42, -23, 21, 2, -6, 13], [-12, 14, 9, 7, 9, 16], [4, -11, -1, -5, -12, -7], [-30, 0, 20, 18, 0, -6], [-8, -11, 13, 30, -2, 5], [8, -4, -14, 8, -8, -2], [16, -6, -2, 6, 18, 14], [-6, 1, 3, 7, -4, -3], [44, -19, -8, -15, 1, 5], [30, 20, -28, -16, 16, -8], [-8, -5, 33, -3, 28, 3], [4, 23, -3, -10, -10, -3], [4, 6, -3, -17, 9, -4], [18, -10, -12, -14, -28, 2], [4, 16, -12, 6, 18, 0], [-20, 13, 27, 10, 28, -7], [24, -15, -23, -10, -6, 9], [10, -15, 23, 11, 0, 13], [16, 4, 12, -8, 4, 4], [28, -7, 5, -18, 2, 13], [30, 0, -2, 7, 8, -12], [-18, -6, 30, 4, 16, -6], [-4, 0, 6, 4, -20, -4], [-4, 1, 28, 13, 1, 3], [-2, 3, -5, -15, -4, -3], [-12, 16, 8, -12, 12, 8], [-38, -1, 12, 9, -1, 1], [-70, 2, 16, 24, 12, 0], [-4, -13, 1, -25, 14, -5], [36, 16, -10, -7, 8, 4], [26, -8, -25, -3, -11, 8], [-56, 5, 3, 14, 2, -7], [-20, -4, 4, 24, 0, -2], [44, -18, -16, -6, -10, 4], [46, 9, 1, 10, 26, -7], [6, 16, 1, 11, 3, 6]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_7245_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_7245_2_a_bj();".
// 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_7245_2_a_bj(:prec:=6)
    chi := MakeCharacter_7245_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_7245_2_a_bj();".
// 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_7245_2_a_bj( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_7245_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![3, 9, 0, -14, -4, 3, 1]>,<11,R![270, 360, -45, -118, -15, 6, 1]>,<13,R![698, 1276, 183, -174, -31, 6, 1]>],Snew);
    return Vf;
end function;