
// Make newform 2325.2.a.ba in Magma, downloaded from the LMFDB on 10 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2325_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_2325_2_a_ba();".
// 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_2325_2_a_ba();".
// 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 := [-12, -8, 20, 7, -9, -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], [-3, 0, 1, 0, 0, 0], [7, 0, -7, 0, 1, 0], [-7, -5, 7, 1, -1, 0], [-3, 12, 6, -8, -1, 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_2325_a();"
function MakeCharacter_2325_a()
    N := 2325;
    order := 1;
    char_gens := [776, 652, 1801];
    v := [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_2325_a_Hecke(Kf)
    return MakeCharacter_2325_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]];
    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, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [1, 0, 1, 0, 1, 0], [-1, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 0], [2, 1, 0, 1, 1, 1], [0, -1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 1], [1, 0, 0, 0, 0, 0], [-2, 1, 1, 0, 0, 1], [0, -2, 2, 1, 1, 2], [0, 0, -1, 1, 0, 0], [1, 2, 1, -1, 0, -1], [1, -1, 0, -3, -2, -1], [4, 2, -2, 1, -1, 0], [3, 1, -1, -2, -1, -1], [-2, 2, 3, 0, 0, 0], [2, -1, 0, -3, -1, -2], [-2, -2, 2, 2, 2, 2], [3, 2, 1, 1, -1, 0], [4, 1, 0, 0, -2, -1], [2, 2, -4, -1, 1, 1], [-6, 0, -2, 1, 0, 2], [0, 0, 0, 0, 0, -2], [-1, -2, 1, -1, 0, -2], [-1, -2, 1, 4, 3, 3], [-1, -2, -1, -2, -2, 0], [3, -1, -3, -2, 1, -1], [-1, 5, -2, 1, -1, -3], [1, -4, -1, -2, -1, 1], [3, 0, -2, 2, -1, -1], [1, 0, -1, 1, -3, 0], [-2, 0, 0, -3, 1, -2], [3, -1, -6, 1, -1, 1], [-6, 1, 3, 0, -1, 1], [-1, -4, 1, 3, 4, 0], [7, -3, 3, 0, 1, 1], [-1, -3, 5, -1, -2, 1], [3, 2, 0, -1, -4, 0], [6, 1, 1, -2, -4, -1], [4, -1, -6, 4, 2, 2], [-1, -7, 0, 0, -5, 1], [5, -4, -3, 1, 0, 1], [-1, -4, 0, -2, 1, 2], [3, 0, -1, -5, -4, -4], [2, -4, -1, 1, 2, 0], [5, -8, -5, 1, 0, 1], [1, 0, 4, -2, -3, 0], [-7, 1, 1, 2, 1, -1], [3, 5, 0, 3, 0, -1], [10, 1, 3, -2, 0, -5], [7, -1, 4, 1, 2, 1], [9, -3, 3, 1, -2, -3], [-2, -4, 0, 4, 2, 4], [-2, 1, 4, 3, 1, 2], [10, 3, 4, -3, -4, 1], [2, -2, 2, -6, -2, 0], [-3, -5, 1, 2, -1, 3], [-1, -6, 1, 1, -4, 2], [-6, 4, -2, -3, 3, -2], [4, -7, -1, 3, -3, -1], [2, -3, 6, -2, 0, 2], [-5, 2, 0, 4, 1, -2], [16, -2, 0, 1, -1, 2], [5, -6, 2, 0, 3, 2], [-4, 1, -1, -4, 0, -3], [9, 0, -2, -5, -2, -2], [-8, -7, -1, 4, 3, -1], [-5, 3, -8, 3, -2, -1], [-1, 7, -1, -2, -3, 1], [3, -3, 4, 3, 5, 3], [-19, 1, 5, 3, 1, 1], [-6, -5, 5, 3, 1, 3], [0, 4, -3, -1, -1, -6], [-3, -1, -3, 0, -3, 3], [9, 7, -6, 4, 3, 1], [1, -6, 1, 0, -5, -4], [1, -3, 5, -8, -3, -3], [0, -7, 2, -1, -1, 2], [-10, -3, -8, 2, -1, -1], [-1, 9, 7, -2, -3, -1], [-11, 9, 1, 6, 3, 3], [1, 2, 6, 1, 6, 0], [3, -6, 1, 2, -1, 5], [-13, 7, 3, -1, -2, 0], [-3, -4, 0, -8, -3, -6], [-11, 0, -3, 4, -1, -2], [-10, 0, 7, 5, 6, 4], [6, 7, -8, -3, -3, 0], [-3, -6, 3, -5, -2, -1], [-10, -3, 0, 5, 0, 7], [9, -4, -3, -4, -1, 0], [14, 1, 0, -3, 0, 1], [12, -1, -6, 1, -5, 0], [1, 9, -2, 3, -2, -1], [-4, 2, 2, -3, 5, 2], [-1, 5, 6, -5, -1, -1], [-3, -7, -3, -3, 1, -5], [7, 5, -8, 4, 1, 1], [4, -6, 6, 1, -1, -1], [18, -3, 0, -2, -2, 0], [3, -8, 7, 6, 3, 2], [-4, 6, -6, 2, 2, 2], [-5, 4, -1, 4, -2, 2], [6, 11, 0, 0, 0, 3], [9, -3, 5, -3, 0, -1], [-21, -4, 5, 4, 7, 5], [6, -9, 11, 2, 6, 5], [-1, -3, -2, -2, -1, 5], [1, 9, -13, -8, -5, -5], [23, -5, -3, 1, 0, 1], [12, -14, 1, 1, 2, 2], [-6, -5, 2, 5, 0, 1], [7, -3, -4, 7, 2, 1], [6, -9, -2, -7, -2, 1], [-5, 4, -5, -4, -3, 4], [0, 0, 2, -7, -1, 2], [5, -5, -5, -4, -5, -5], [-9, 9, 1, -7, -3, -5], [-20, -5, -1, 2, -4, 5], [12, 0, -1, 4, 4, 3], [-3, 12, -3, 7, -2, -3], [13, -6, 3, 1, 0, 4], [3, 5, -3, 3, -6, 1], [-4, -5, 5, -2, -8, 1], [4, 2, -4, -4, 0, 0], [2, 9, 1, -1, -3, -5], [-17, -2, 0, 4, 4, 6], [0, -5, 4, -11, -4, -5], [13, 2, 1, 0, 1, -2], [-14, -16, 3, -2, 0, -2], [6, 5, -7, 2, 4, -3], [27, 3, 0, -2, -5, -6], [0, -12, -2, -1, -6, 4], [-3, -1, -3, -7, -4, 2], [0, 4, 4, -4, -2, -6], [19, 2, -2, -3, -2, -4], [1, 8, -14, 2, -3, 1], [17, 16, -6, 1, -2, -4], [-19, 4, 1, 2, 7, 4], [8, 16, -8, 4, 2, -2], [3, -1, 6, -7, -4, -5], [1, -8, -2, 6, -1, 6], [7, 4, -9, -5, -4, -7], [-15, 2, 1, -4, -2, -2], [22, 2, -8, -5, -1, 0], [29, -3, -4, -5, -5, -1], [15, -3, -3, -4, -1, -7], [-11, -5, 4, 1, 7, 3], [12, 15, -4, 5, -1, -4], [-5, 4, 2, -4, 5, 4], [-14, -1, 0, 4, 8, 2], [-7, -10, 11, 1, 2, 0], [10, -2, 5, -3, 1, -4], [2, -2, 7, 2, -4, -2], [-7, -15, 0, 1, 0, -1], [3, 2, -1, 11, 10, 2], [2, 4, 0, -1, 1, 1], [-18, 3, 8, -4, -4, 1], [3, 5, -9, 8, 5, -1], [1, 4, 6, 6, 9, 8], [10, 7, 8, -4, -6, 0], [4, 0, 8, 3, 1, 4], [7, -7, 12, -5, 8, 1], [-4, 5, 4, 5, 2, 5], [-5, -13, -8, 4, 1, 1], [14, 4, -8, 0, 6, -2], [-4, 3, 6, 11, 7, 8], [11, -3, -1, 16, 9, 5], [-22, 2, 4, 2, -4, 4], [1, 3, -11, 6, -5, 1], [-20, -1, -1, 4, 1, 1], [19, -7, 7, 0, 5, -3], [-13, -13, 1, 4, 3, 3], [0, -3, -5, -3, 7, -5], [-12, 12, 2, 5, 11, 6], [6, 7, -12, 3, -1, 1], [-11, 5, 1, 12, 11, 1], [-25, 13, 4, -2, -1, -1], [18, -10, -1, -5, -5, 0], [-4, -12, 8, -7, 0, -4], [9, -5, -6, -1, -4, -1], [26, 3, 0, -4, -14, -4], [14, 5, 3, -8, 0, -6], [14, 18, -2, -3, -2, 0], [14, -7, 11, 1, 5, 3], [0, -5, -5, 2, 0, 5], [11, 6, -7, -6, -1, -5], [0, -17, -9, 4, -6, 3], [-10, -12, 6, -5, -3, -4], [11, -10, 6, 2, 5, 0], [7, -13, -7, 8, 3, 3], [-21, -9, 3, 8, 11, 9], [15, -1, -5, -7, -4, -8], [-13, 14, 4, -4, -1, -4], [16, 0, -5, 1, 4, 4], [1, -11, -5, 6, 1, 1], [-24, -4, 2, 3, -3, 6], [-9, 1, 1, 6, -3, -3], [-9, 0, -6, -12, 1, -8], [6, -13, -7, 1, -9, -3], [0, -9, 7, -2, -1, -5], [22, -9, -4, -3, -5, 2], [1, -8, -1, 7, 2, -1], [11, 2, -7, 5, 8, 4], [-10, -2, -9, 7, -3, 6], [-26, -2, 0, -4, -6, 0], [-7, 7, -12, -8, -5, -5], [-12, -15, -3, 0, -10, -9], [3, 6, 1, -7, 8, 7], [-5, -2, 3, 5, 8, 6], [-22, 0, 0, 9, 5, -2], [-1, -3, 2, -5, 0, 3], [18, 17, -15, -6, -11, -7], [-8, 16, -3, 0, -6, -4], [3, 9, 3, -7, -10, 3], [-29, -8, 7, -12, -5, -6], [12, 24, -6, -2, -2, -12], [-3, -17, -7, 4, 5, 1], [31, -13, -6, -6, -7, -1], [-6, -6, 10, -6, 0, 2], [16, 6, -3, 6, 6, 4], [-29, 1, 1, -10, -3, -5], [15, 21, -5, 0, -5, -5], [7, -1, -1, 7, 8, -5], [-28, 9, 2, -8, 0, -3], [19, 7, -10, 11, 5, 5], [19, -8, 11, -4, 3, -5], [-1, 16, -4, -6, 1, 0], [18, 7, 1, 5, -3, 5], [-19, 7, 6, -8, 1, -1], [5, -4, -4, -1, 4, -8], [11, 4, -9, -5, -1, -6], [-24, -11, 4, -8, -8, -7], [-15, 21, 3, -7, -3, -1], [35, -1, 1, 7, 0, 1], [10, -5, -4, -12, -8, -7], [-10, 6, -11, 3, 5, 6], [17, 10, -3, 6, 5, -5], [27, -8, 3, 1, -1, -2], [21, -2, 4, -2, -9, 0], [1, -17, 13, 6, 5, 7], [15, 3, 7, -3, -12, 2], [6, -12, -2, -3, -3, -2], [-7, 2, -7, -5, -13, -2], [20, 4, 3, 5, 1, -4], [-8, 17, 2, 1, -6, 3], [13, 13, -3, -4, 9, -1], [29, -8, 1, -7, -6, -12], [9, -1, 3, 5, 2, 1], [-35, -1, 6, 3, 10, 5], [-32, -15, 2, 0, 11, 9], [-8, 6, -2, 6, -2, 0], [-9, 14, 11, -1, 8, 1], [-12, 22, -2, -5, -4, -6], [-1, -2, -7, 9, 1, 10], [-2, 14, 14, -4, 6, 2], [4, -7, -2, -2, -5, 7], [-3, 4, 0, -7, -8, 4], [-3, 19, 8, 1, -2, 5], [-3, -3, -3, 2, 3, -3], [23, 2, -9, 1, 2, 4], [-17, -14, -1, 8, 9, 8], [-17, 4, 14, -13, -2, -4], [3, 23, -5, -7, -4, -3], [-6, -4, 0, -15, -9, -2], [-22, -2, -5, 4, 2, -8], [10, 0, 8, -3, -5, -8], [-5, 9, 1, -11, -3, 1], [8, -10, 8, -4, 6, 4], [12, 1, -9, -4, 4, 5], [14, -6, -9, -5, -14, -2], [-6, 0, -3, -13, 4, 6], [-30, -9, 10, 3, -7, 5], [34, 9, 0, 0, -2, 0], [-24, 12, 18, -4, 0, -2], [-6, -4, -4, 0, -8, 2], [37, -20, -11, 4, -1, 2], [-8, 9, 6, -9, 1, 4], [-27, 3, 0, 4, 5, -1], [10, 14, -2, -1, 9, 2], [-3, 6, 9, 2, 0, 10], [-18, -12, -3, 0, 8, 0], [-24, 15, -11, -9, -3, -7], [-13, -15, 13, 6, 1, -1], [-7, 8, 12, -4, -5, -7], [4, 9, -12, -7, -11, -7], [-40, 1, 13, 0, -4, 2], [-18, -20, 6, 2, -4, 4], [-5, -4, -1, 5, 0, 1], [1, -8, 19, -4, 9, 0], [-7, -5, 1, 14, 1, 3], [13, 3, 7, -10, -1, -5], [1, -6, -14, 10, -7, -1], [-23, 12, 5, 1, 9, -2], [-15, 17, 9, -8, -5, -1], [20, 3, -2, 12, -4, 1], [14, 13, -12, -13, -12, -9], [-20, 6, 4, 19, 10, 10], [-6, 0, 8, 5, -1, 5], [-27, 2, 2, 6, -5, 0], [12, 4, -10, 1, 1, -8], [-9, -3, 18, 5, 9, 9], [-26, 13, -8, -12, -9, 1], [-9, 4, -11, -2, 1, 10], [-14, 8, -4, 7, 12, -6], [-4, 17, 2, 4, -6, 1], [11, 1, -3, -1, -3, 1], [16, -10, 19, 3, 7, 0], [1, -20, 9, -1, -6, 1], [-10, -8, 10, 11, 1, 10], [-12, -5, 16, -9, -4, -5], [13, -9, -3, 14, -3, -1], [-3, 2, 10, 0, 7, 2], [-4, -4, -5, 11, -5, 4], [7, -19, 1, -10, -9, -13], [-1, -5, -20, 2, 3, -3], [-27, 10, -3, 1, -2, 3], [-13, 21, -6, -7, -1, 3], [8, -8, -22, 6, -8, 0], [-9, 17, -3, 5, 8, -3], [29, -23, -6, 6, -5, -1], [-15, -3, -5, 2, 11, 7], [-32, -10, 2, 6, 8, 4], [-3, -6, -2, -13, -6, -6], [13, 11, -14, -4, 5, -1], [-6, -5, 5, 13, 1, 5], [-5, -9, 8, 5, 12, 7], [-1, 19, -5, -13, -7, -3], [22, -8, 0, -14, -4, -14], [-6, -3, 8, 11, 3, 5], [-1, 5, -18, -3, 2, 3], [2, 21, -4, -5, -5, 3], [-19, -7, -1, 6, 5, -3], [8, 28, -2, 4, 4, -4], [-18, -8, 6, -10, -4, -4], [-16, -4, 6, -11, -8, -10], [16, 4, 13, -5, -8, -10], [18, 4, -10, 6, 2, 6], [22, -7, 20, -11, 5, 0], [14, -5, 6, -19, -11, -10], [-12, -5, 6, 11, 6, -3], [-16, -28, 6, -6, -10, -8], [-8, 1, -2, 11, 3, 10], [-15, 6, 5, 11, -6, -4], [11, -17, 0, 13, 5, 3], [-3, 20, -3, 6, 15, -4], [-11, -1, 1, -1, 0, 11], [13, -12, 6, 10, 9, -4], [0, -3, 5, 6, 8, 5], [-12, 0, 8, -2, 4, -4], [17, 18, -9, -3, -5, -2], [-1, 19, -10, -4, -1, -5], [30, 1, 8, -9, -15, -10], [1, -5, -8, -7, 12, -5], [25, 9, -1, 2, -9, 3], [-7, -14, 4, 12, 5, 1], [15, -18, 7, -4, -1, 9], [-25, 8, 5, 13, 8, 4], [-17, 6, -17, 2, 3, -8], [-5, 9, 5, 16, 17, 3], [-13, -10, -1, 3, 2, -9], [31, 2, -2, -11, -14, -10], [4, -4, 6, -4, 8, 4], [31, 3, 13, 2, 9, 9], [55, -2, 4, -2, -5, -6], [-22, 21, -1, 1, 1, -3], [-26, -2, 24, 3, 1, 2], [25, 4, 0, -1, -14, -8], [-10, -3, 6, 1, -3, -8], [-2, 0, 4, -8, 2, 8], [-40, 15, 3, -5, 7, -3], [15, -21, 13, 0, 11, 1], [39, 0, -1, -8, -5, -6], [-1, 5, 19, -4, 7, -1], [-6, 3, -7, -11, 3, -11], [-2, -20, -8, 0, -2, 10], [15, 24, 4, -2, -3, 0], [17, -2, 18, 2, 1, 5], [-5, -9, 12, 6, -5, 6], [16, -1, -2, -3, -6, -9], [-5, 3, 8, 7, 8, 13], [26, -10, -10, 8, 8, 0], [27, -16, 9, -10, 5, -9], [12, 17, 2, -7, -3, 1], [-1, -4, 8, -14, -13, -10], [8, 1, -8, 1, -10, -5], [15, 7, -5, 18, -9, 5], [10, 14, -12, 2, 4, -10], [34, 10, -15, -4, -18, -7], [4, 1, -12, -1, -15, -4], [-10, -4, -5, 10, 8, 0], [-6, -19, -4, -1, -7, 10], [-28, 15, -15, -13, -15, -1], [0, -6, 14, 18, 16, 4], [-11, -15, -1, 8, 9, 1], [1, -20, 2, -10, 1, -8], [14, -6, 2, -3, 11, 5], [-13, -6, 4, -20, -5, 0], [2, -6, 0, -6, 2, -4], [-18, -17, -10, 7, -3, 9], [45, -1, -1, -3, 0, -1], [3, 10, -26, -2, -5, -7], [-8, 25, -19, -11, -9, -19], [-1, -13, 14, 11, 3, 1], [24, 7, -14, 7, 1, 6], [-17, -16, -14, 8, 11, 10], [-28, -8, 9, -15, -7, -8], [7, 1, 17, -16, -1, -5], [63, -3, -5, -10, -7, -9], [25, -15, -5, 20, 3, 9], [39, -13, 8, -13, -3, -13], [-22, -9, 20, 2, 3, -1], [-33, -3, -1, -6, 9, -5], [33, -13, 0, -13, 2, -9], [-10, -10, 7, 6, -2, -2], [13, 17, 9, -3, -2, -5], [-23, 25, 7, 0, 1, 3], [11, -5, 0, 9, 8, -9], [30, -11, -9, 14, -2, 9], [-20, 3, 9, 15, 1, 9], [-3, 16, 7, -3, 6, -9], [-15, -2, 9, 16, 18, 14], [31, 25, -13, -2, -1, -9], [17, -10, 3, 6, -1, 1], [25, 4, -7, 1, -4, 5], [12, 10, -11, 13, 8, 8], [15, 4, -14, 21, 6, 6]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2325_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2325_2_a_ba();".
// 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_2325_2_a_ba(:prec:=6)
    chi := MakeCharacter_2325_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_2325_2_a_ba();".
// 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_2325_2_a_ba( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2325_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-12, -8, 20, 7, -9, -1, 1]>,<7,R![64, 64, -96, -108, -12, 6, 1]>,<11,R![852, -332, -432, 217, -5, -9, 1]>,<13,R![64, 96, -48, -108, -24, 4, 1]>],Snew);
    return Vf;
end function;