
// Make newform 5925.2.a.r in Magma, downloaded from the LMFDB on 03 June 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_5925_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_5925_2_a_r();".
// 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_5925_2_a_r();".
// 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 := [-13, -10, 21, 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], [8, 0, -7, 0, 1, 0], [8, 4, -7, -1, 1, 0], [6, 12, -2, -8, 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_5925_a();"
function MakeCharacter_5925_a()
    N := 5925;
    order := 1;
    char_gens := [1976, 5452, 2926];
    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_5925_a_Hecke( : Kf := Kf)
    return MakeCharacter_5925_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, 1, 0, 0, 0], [2, 0, 0, 0, 0, -1], [-1, 0, 0, 1, 0, 0], [-2, 0, 0, 0, 0, -1], [0, -1, -1, 0, 0, -1], [0, -1, 0, 0, 1, -1], [2, 0, 0, 1, 1, 0], [0, 1, 1, 1, 0, 1], [2, 1, 0, -1, 1, 0], [0, 1, 0, 0, -2, -1], [-1, 0, -2, 0, -1, -1], [-2, 1, -1, 0, 1, 0], [0, -3, 2, 0, 0, 1], [2, 2, -3, -1, 2, 0], [-2, -1, 0, 0, 1, -2], [4, 2, 0, 0, 1, -1], [4, 1, 4, 0, 1, 2], [3, -3, 0, -1, -1, -2], [1, 0, 0, 0, 0, 0], [-2, -4, 2, -1, -1, 0], [0, 2, 2, -1, 0, 2], [1, 2, -1, -4, 2, 0], [0, 0, -2, -2, 3, -3], [-1, -4, -1, 1, -1, -1], [0, 1, 1, 1, -2, -1], [4, 3, -2, 1, 0, -1], [2, 0, 3, -1, 3, 1], [4, 3, -2, 1, 3, 0], [-2, 1, 4, 1, 0, 3], [0, -4, -4, 1, 0, -3], [-3, 2, 3, -1, -1, 1], [6, 1, 1, -1, 2, -2], [4, 3, 0, -2, 2, -1], [0, 3, -2, 3, -2, -1], [2, -1, -5, 1, -1, 2], [-4, 0, -2, -1, 0, -3], [-2, 3, 1, -1, 0, 0], [4, -1, 1, -4, -1, 0], [-5, 1, 4, 0, 0, -1], [-2, -4, 2, 4, -1, 1], [10, -3, -2, 1, -2, -5], [-2, 2, -2, 1, -1, 2], [3, 3, -1, -1, 0, -3], [-1, 2, 1, -3, 2, -4], [4, 0, -4, -1, 2, 0], [2, 3, -1, 1, -3, 4], [-8, -4, 5, -3, 4, 2], [4, -3, 0, 0, 1, -5], [6, 3, -4, 3, -1, 3], [-4, -1, 2, 0, -1, 4], [6, -4, -2, 5, -4, -2], [2, 7, -2, -4, 2, 1], [12, 4, 2, -4, 2, 2], [2, -3, -2, 3, 0, -5], [2, 4, -2, 3, 4, 0], [-1, 2, 5, 1, 1, 3], [4, -7, -5, 0, -3, -2], [-2, -4, 1, 5, 1, -1], [0, 2, -5, 3, -2, 2], [-3, 1, -3, -3, 1, 0], [6, -9, 1, -1, -2, -3], [9, 3, 2, -1, 4, -3], [0, 0, -1, -3, 5, 1], [-7, 1, -3, 0, 0, 3], [-4, 6, 1, -3, -3, 3], [0, 9, 0, 3, 2, 0], [-6, -3, 5, 2, -7, 2], [8, 2, 1, 3, -5, 4], [8, -3, 4, -3, -3, 0], [-4, 4, -2, -5, 2, -2], [16, -4, 0, 1, -1, 1], [0, -2, -6, -1, 5, -1], [0, 0, -3, 0, -3, -3], [6, -2, 7, 0, -4, 2], [-7, 0, 9, 0, 2, 2], [8, -3, -6, -3, 2, -4], [-12, -5, -5, 4, -4, 1], [2, 1, -5, -2, 1, -2], [-5, -5, -7, -1, -1, -4], [12, 0, -4, -1, 3, 3], [-4, -15, -5, 4, 0, -1], [8, -1, 1, -3, 7, 2], [-2, 3, -4, 6, -3, 0], [-2, -6, 3, 2, 3, -2], [-3, 4, 8, -2, -2, -2], [0, -8, 7, -2, 2, 5], [2, 0, 6, -5, 6, 2], [-18, -5, -3, 0, -7, 3], [2, -7, -1, 4, -1, -1], [-6, -10, 0, 3, -1, -1], [8, -7, -5, -1, -6, -5], [8, 0, 4, -7, 5, 1], [6, 0, 1, -1, 2, 0], [2, -3, 7, -5, 4, -2], [14, -5, 1, 2, -1, 7], [0, -2, 1, 1, 1, 7], [-3, 4, 0, -2, 2, -2], [2, 5, 5, -6, 3, -4], [8, -4, -3, 5, -4, -2], [-4, -8, -8, 2, 1, -6], [-12, -1, -1, 9, -8, 1], [4, -7, 0, 2, -3, -2], [-20, -11, -2, 4, -2, -1], [4, -1, 2, -4, 10, -1], [-2, 7, -3, -3, 8, 1], [4, 6, -3, 4, 3, 5], [4, 0, 0, 1, 2, -10], [-11, 7, 4, 0, 4, 1], [14, -3, 7, -3, 4, 5], [12, -9, 2, 4, -4, 5], [3, -14, -6, -2, -4, -6], [21, -5, -7, -1, -3, -2], [4, -7, -2, -1, 5, -6], [0, -9, 3, -1, -2, -3], [10, -2, 10, 1, 1, 5], [-2, 4, 8, -3, 0, -4], [4, -3, 5, 2, -7, -2], [-4, 3, 5, 0, 0, 7], [-2, 2, -6, -2, -5, -3], [16, -1, -3, -4, 5, 0], [-6, -3, -3, 1, 0, -2], [-3, -9, 11, 5, -7, 6], [-2, 1, 0, 0, 3, 4], [4, -2, 3, -9, 5, 3], [0, -5, -9, 3, -3, -5], [2, 2, -5, 6, -6, -2], [-17, 4, -4, -5, -1, -1], [1, 4, -5, 6, 0, -4], [-8, -10, 3, -5, 7, -6], [16, -3, 2, -3, -3, 2], [13, -2, 5, -1, -4, -2], [10, -2, -8, -1, -1, 1], [-20, -4, -2, -2, 3, -3], [-14, 1, -10, 1, -1, -2], [2, 7, -4, -4, -6, 7], [0, 7, -8, -3, 6, 0], [-14, -12, -7, 5, 2, -2], [6, -11, -2, -5, 0, -7], [-2, -3, 9, 5, 1, 6], [-2, -2, 5, 0, 4, 6], [8, 0, -5, 8, -10, -2], [0, 10, -8, -2, 7, -1], [4, 9, 10, -4, 7, 3], [8, 6, -9, -4, 9, -5], [8, -5, 8, -3, -4, 5], [-1, -4, -6, 9, -7, 5], [4, 6, 10, -2, -3, 2], [11, -3, 6, -1, 1, 0], [6, 1, -7, -7, -4, 2], [15, 4, -5, 0, 5, -3], [-6, 10, 10, 2, 2, 11], [14, -3, 2, 6, -1, -6], [6, 11, 3, -4, 1, 3], [4, -15, 7, 11, -11, 2], [-26, 4, 4, -5, 5, 8], [6, -2, 8, 1, -3, 3], [0, 8, 1, 5, -10, 6], [22, 6, -9, -4, 1, -1], [12, -5, 5, 2, 6, -3], [10, 7, -3, 5, 2, -11], [-10, -7, 10, 6, 2, 0], [4, -11, 2, 7, -1, -8], [0, -7, -3, 1, 0, 9], [16, 9, 3, -5, 0, -1], [4, 0, 0, 8, 5, 5], [-22, -6, 3, 4, -7, 3], [-16, 8, 3, 7, -7, -1], [22, 9, 2, -6, 9, -2], [20, -5, -9, -3, 7, 0], [12, -1, -8, 0, 7, -5], [6, 8, -5, 3, -7, 1], [9, 5, 6, -2, 7, -6], [-30, 12, 5, 7, -1, 3], [10, 4, 12, -4, -1, 3], [-2, 17, -7, 1, -1, -8], [8, -9, 6, 3, -5, 2], [-10, -8, 2, 1, 1, 5], [19, -3, 10, -5, 2, 1], [-12, -4, 8, 0, 8, -4], [-6, 0, 7, 3, -5, -5], [12, 2, -3, -6, 8, 1], [16, 11, -1, -7, 1, 3], [-4, 18, -4, 0, 4, -4], [-4, -13, 3, 0, 2, 7], [-7, -8, 8, -1, 1, -7], [-27, 4, 9, 1, -3, 1], [-6, 3, -14, -2, -5, 0], [0, 1, -3, -1, 4, 1], [16, -15, 8, -2, -3, -2], [-10, 0, -13, 4, 1, -1], [20, 0, 5, -4, -8, -3], [14, -20, 5, 3, -4, 1], [-4, -5, 2, 2, -11, -4], [-9, 23, -8, -6, 7, -4], [-2, -8, 9, -2, 1, 7], [14, 3, -7, -10, 7, -4], [-6, -11, 7, 9, -3, 0], [2, 5, 10, -10, 7, 4], [-2, -2, -4, 9, -3, -1], [-4, -7, 7, -3, 11, -2], [-21, -3, 1, 8, 2, -3], [10, -5, 0, 4, 2, 3], [4, 6, 3, 2, -6, 10], [12, 10, -9, 3, -4, -6], [-4, 13, -10, -1, 8, 4], [-20, 22, 2, -2, 1, -1], [18, -7, 0, 5, 4, -1], [8, 6, -13, 2, -3, -7], [-6, 4, -5, 0, -4, 2], [-3, -6, -6, -2, 7, 1], [-14, 4, 0, -6, 6, 2], [0, 8, -1, -5, -8, -4], [-6, -9, -16, 3, -5, -12], [-9, -10, -6, -4, -4, -6], [8, -6, -5, -3, -3, 11], [4, 3, 11, -10, 11, 6], [-24, -4, 2, -4, 3, 8], [-23, -12, 3, 2, 2, -6], [18, 15, 17, -8, 2, 7], [16, -4, -8, 9, -4, 7], [10, -12, -7, 11, -8, 6], [6, 13, 3, -11, 12, 2], [-28, -8, 5, -2, 1, -5], [-12, 12, -5, 3, -7, -1], [6, -2, 17, 4, 3, 11], [0, -5, 3, -8, -2, -7], [2, 14, -7, 5, 2, -10], [13, 8, 8, -3, -4, 4], [17, -12, 18, 1, -5, 3], [14, -6, -1, -1, 2, 4], [2, 16, 12, -4, 9, 7], [1, 8, 0, -10, 9, 1], [-8, 8, -16, -6, 8, -8], [-35, 4, 0, -5, 1, 9], [12, 0, 3, -7, 11, -4], [14, -3, -12, -1, 6, 1], [6, 0, 9, 0, -5, 2], [-2, 1, -7, 9, -1, -2], [8, 19, 2, 8, 4, 9], [-28, 17, 15, 1, 2, 9], [2, 7, -9, -1, 3, 6], [30, -5, 5, 8, 0, 3], [16, -17, -3, 9, -4, -5], [-19, 4, -2, 15, -8, 4], [12, -8, -6, -8, 7, -5], [1, 5, 0, 1, -13, -6], [32, -4, -11, 5, -7, -9], [0, 16, -17, -1, 0, -6], [10, -1, 9, 7, 7, 0], [-10, 7, 2, 4, -2, 9], [-6, -11, 1, 4, 6, -7], [-6, 10, 3, -3, 2, -9], [0, -11, 5, -1, -4, -7], [0, 4, 1, -7, 7, 5], [14, 5, -11, 1, 5, -8], [28, -17, 4, -3, -4, -10], [-8, -5, 9, -9, 10, 1], [-24, -17, 0, 1, -2, 1], [12, 4, 19, 6, 12, 9], [-9, -1, -12, 9, -2, -1], [16, 8, 14, 2, 5, 9], [4, 11, -16, 6, -2, -3], [0, -12, 3, -6, 8, 6], [24, -14, 5, 13, -3, 7], [10, -9, 2, -12, 5, 4], [8, 7, -4, -7, 1, -4], [-12, 17, 21, -3, 7, 3], [-6, -6, 2, -3, -1, -3], [-10, -9, 21, 0, -6, 15], [-30, 0, -2, -5, 3, -5], [24, -6, -7, 0, -5, 5], [-14, -1, 1, 3, 6, 3], [-22, 9, -1, -7, 3, -2], [-16, -7, 3, 8, -6, -6], [-18, 11, -8, -1, 3, 8], [16, 5, -7, 4, 11, -4], [22, 5, -4, -3, 3, 1], [6, 11, 9, 1, 3, -8], [31, -14, -8, 1, -4, -6], [-22, -2, -10, -3, -5, -11], [-21, 1, 0, 4, -4, 3], [2, 13, 4, 0, -16, -1], [24, 11, 0, 1, -5, 2], [8, 14, -15, 2, -3, -5], [-12, 8, -18, 0, 0, -6], [20, -14, -11, 6, -9, -3], [-2, 3, -9, 7, 6, -11], [34, 11, -1, 0, -6, 7], [6, 11, 15, -7, 5, -6], [22, 15, 2, 0, 4, 0], [12, 4, 4, -7, -7, -5], [-20, 10, 15, -4, 8, 4], [14, 20, -6, -1, -8, -2], [0, -6, 1, -8, -2, -6], [-24, 13, 2, 3, 5, 10], [6, 10, -17, -9, 11, -3], [36, -4, 5, -9, 8, 8], [-11, 13, -19, 0, 8, -13], [18, -3, -15, 9, -5, 4], [-3, -6, -11, 3, 6, 8], [26, -9, 9, 9, 0, 7], [16, -4, 3, -1, 2, 4], [11, 1, -15, -9, 3, -6], [6, -23, -5, 11, -6, 2], [4, -20, 3, -6, -2, -8], [22, 6, 6, -6, 4, 1], [-8, 4, -15, -6, 7, -7], [12, 25, -14, 8, -1, 3], [20, -12, 0, -1, 2, 7], [30, 24, -11, -1, -5, 1], [-4, 6, -28, -2, 4, -10], [18, 14, 3, 2, -15, 5], [-18, 12, 2, -6, 4, 6], [-16, 18, -1, 3, 1, 14], [18, 8, -9, 10, -7, 5], [-34, -1, -2, 5, -3, -8], [-8, -2, -2, 17, -2, 1], [18, 4, -1, 8, 2, -10], [12, -5, -13, 7, 1, 10], [-2, 0, -2, 11, 12, 0], [-28, 3, 11, -4, -1, 0], [24, -17, -7, 6, -5, -2], [2, -3, -4, 14, -17, 4], [36, -5, 15, -6, 0, -5], [11, 29, -7, 10, 7, 2], [-16, -4, -2, -1, 2, -4], [-10, -18, 12, 9, -14, 4], [3, 6, 0, 1, -1, 1], [6, -14, -15, 6, -2, 6], [23, 10, 8, 1, -8, 6], [28, -4, -1, -2, -2, 9], [-1, 22, 3, -7, -6, 4], [22, -26, -4, 1, -2, 0], [14, -5, 10, 7, -2, 9], [-8, 28, 0, -12, 2, 8], [12, 7, -13, 2, -8, -11], [-3, -14, 0, 7, 16, -2], [-11, -1, 23, 0, 1, 6], [-4, -5, -15, 1, -1, -11], [8, 8, 9, -7, 11, 9], [-18, -18, 17, 5, -3, 3], [-28, 9, 6, 2, -11, -6], [-34, -7, -5, 0, 0, -3], [-1, -14, 3, 9, -7, 3], [-4, -18, -1, 4, -1, 5], [2, -16, 15, -7, 0, -8], [-18, 9, -2, -1, 9, 7], [22, 15, -17, -5, -5, 8], [20, -8, 17, -10, 1, 3], [34, 9, 9, -2, 12, 3], [-12, -12, -7, -1, -4, -6], [-38, -6, -7, 2, -5, -7], [-2, -25, 13, 12, -11, 4], [-6, 9, -23, 2, -1, 4], [14, 25, 10, -11, 7, -2], [-20, 3, 3, 16, -10, 6], [30, 0, 4, -19, 1, 1], [53, -6, -10, -4, 5, -5], [16, -9, -8, 4, 7, -21], [-36, 0, 9, -6, 0, 10], [20, -19, -4, 4, -1, -3], [-6, 3, 4, 0, -13, 2], [-26, -5, -4, 6, 8, 5], [-8, -33, 11, -9, -6, 1], [-8, 11, 19, -2, -1, 4], [19, 1, 22, -12, 5, 8], [-18, 1, 4, -1, -5, 10], [2, 12, 6, -4, 7, 5], [6, -1, 11, 10, 2, 1], [10, -6, -2, -12, 3, -11], [-10, 4, -17, 1, 10, -16], [4, -8, 4, -6, 6, 10], [4, 19, -22, -1, 3, -12], [-10, 24, -3, -2, -3, 11], [-5, 1, -3, 7, -8, 3], [22, 4, -5, -5, -2, -6], [-30, -23, 0, 3, -3, -4], [50, -6, 8, -5, 2, 2], [8, 15, -33, -6, 10, -9], [-18, 20, -6, 2, -4, -10], [-2, 30, 3, -1, -5, 13], [12, -16, 2, 7, 11, -7], [26, -2, 4, 7, -2, -4], [-36, 6, 0, -1, -4, 10], [30, 17, -16, 8, 2, 3], [2, 5, 11, 0, 3, 0], [-26, 13, 8, 0, -4, -8], [0, -8, 22, 3, -11, 7], [-24, 28, -2, -1, 0, -13], [10, 1, 12, -1, -7, 3], [22, -4, 8, 4, 10, -18], [10, 25, -5, -4, 11, 1], [0, 32, -3, -14, 16, -2], [3, 0, 11, 6, 2, -6], [16, -4, -12, 5, -11, -17], [10, -17, 3, 0, -2, 19], [-34, -1, -3, 1, -15, 0], [8, -4, -29, 5, -8, -6], [32, 12, -32, -2, -3, 3], [16, 13, -9, 1, 5, -12], [4, 10, -13, 1, 9, 4], [26, -4, -2, -3, 13, -6], [4, 1, -9, 0, 10, -3], [44, -7, -8, -11, 4, -5], [14, -10, -30, 4, -13, -13], [2, 12, 27, -2, 2, 18], [18, -18, 8, 8, -2, 0], [-16, 8, -10, -1, -3, 5], [-34, -14, -12, 17, -5, -7], [54, -7, -2, -5, 4, -1], [-28, 15, 13, -6, -1, -8], [-13, -14, -19, 9, -2, 0], [12, -31, -8, 2, 3, -3], [12, -6, 8, 9, 9, 5], [-17, -21, 15, 3, -2, 3], [18, 2, 1, 6, 1, -2], [2, 7, -4, -16, -7, 0], [18, 9, 0, -12, -8, -1], [-46, 5, 15, -4, 9, 4], [-22, -4, -9, 12, -6, -6], [-6, 14, -15, 8, 1, -6], [-30, -21, -2, 11, 2, -5], [-18, 8, 16, 13, 3, 8], [12, 8, 2, -1, 5, 1], [2, -14, -11, 5, -17, -1], [31, -17, -12, 10, -14, -13], [34, 10, 18, -2, 6, 1]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_5925_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_5925_2_a_r();".
// 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_5925_2_a_r(:prec:=6)
    chi := MakeCharacter_5925_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_5925_2_a_r();".
// 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_5925_2_a_r( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_5925_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-13, -10, 21, 7, -9, -1, 1]>,<7,R![65, 66, -29, -41, -3, 5, 1]>,<11,R![241, 302, -388, 66, 34, -12, 1]>],Snew);
    return Vf;
end function;