
// Make newform 2736.2.f.i in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2736_f();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2736_f_Hecke();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_2736_2_f_i();".
// 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_2736_2_f_i();".
// 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 := [1350, 900, -282, -144, 127, -12, -14, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [-11605830, -5392428, -859412, -196776, -597740, -32796, 23083, 12960], [-38703045, 27915822, 1377653, -5883646, 90395, 544454, 8243, -24310], [-66840945, -16379547, 25205858, -7482925, -1249773, 735426, 178954, -47546], [32190, -9156, -1830, 544, -567, -212, 54, 16], [-147000, -13578, 71453, -21101, -2560, 1969, 233, -200], [83548605, 9710091, -37579915, 13107106, 675757, -1170618, -113379, 108029], [75574110, 17283456, -23614798, 14155124, -930214, -1605973, -86890, 123377]];
    Rf_basisdens := [1, 13725555, 13725555, 13725555, 3405, 32915, 13725555, 13725555];
    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_2736_f();"
function MakeCharacter_2736_f()
    N := 2736;
    order := 2;
    char_gens := [1711, 2053, 1217, 1009];
    v := [2, 2, 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2736_f_Hecke();"
function MakeCharacter_2736_f_Hecke(Kf)
    N := 2736;
    order := 2;
    char_gens := [1711, 2053, 1217, 1009];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0]];
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    values := ConvertToHeckeField(char_values : pass_field := true, Kf := Kf); // the value of chi on the gens as elements in the Hecke field
    F := Universe(values);// the Hecke field
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),values);
    return chi;
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, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, -1, 0, 1], [0, -1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 2, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 3, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 1, 1, 1], [0, 0, 0, 1, 0, 2, 2, 2], [0, 4, -1, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 3, 2, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 4, 0, 0, 0, 0, 0], [0, -2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -6, 0, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 5, 2, -2], [-13, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, -1, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, -3, -4, 3], [0, 0, 0, 6, 0, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, -4, -1, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 2, 5, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-20, 0, 0, 0, 0, 0, 0, 0], [0, 6, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, -3, -3, -3], [0, 8, -8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 3, 3, 3], [-17, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -4, 0, -5, -4, 4], [0, 0, 0, -2, 0, 3, 3, 3], [28, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, -5, -2, 5], [5, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, -6, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, -3, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 1, 0, -1, 6, 1], [21, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -4, 0, 4, -3, -4], [0, 0, 0, -5, 0, -4, -5, 5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, -2, -5, 5], [0, -4, -9, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 8, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [11, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [40, 0, 0, 0, 0, 0, 0, 0], [0, -6, 5, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, -4, -7, 4], [0, 0, 0, -4, 0, 3, -4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 10, 3, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, -2, -2, -2], [0, 10, -10, 0, 0, 0, 0, 0], [0, 8, -3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 6, 0, -6, -5, 6], [0, 0, 0, -3, 0, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [19, 0, 0, 0, -3, 0, 0, 0], [0, 0, 0, 2, 0, -7, 2, -2], [-10, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 2, -7, -2], [-17, 0, 0, 0, -3, 0, 0, 0], [14, 0, 0, 0, 0, 0, 0, 0], [0, 4, 11, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 1, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, -5, 4, 5], [0, 6, 11, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, -5, -8, 5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, 4, 4, 4], [0, -8, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [26, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 13, 0, 2, 2, 2], [0, -12, -5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 2, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, -11, -4, 4], [-25, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 0, 6, 7, -7], [0, 0, 0, 0, 0, 0, 0, 0], [0, -14, 14, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, -11, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, -3, -10, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 0, 8, 7, -7], [0, 8, -8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, -3, 8, 3], [0, 10, -10, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, 5, -6, -5], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, -5, 0, 0, 0], [25, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, -2, 9, 2], [0, 0, 0, -9, 0, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, -12, -5, 5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -8, 0, 8, -1, -8], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 0, 10, 7, -7], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, -5, 0, 0, 0], [-46, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 5, 8, -8], [0, 0, 0, -2, 0, 2, 11, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, 6, -5, 5], [0, 0, 0, -9, 0, 9, 2, -9], [17, 0, 0, 0, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 6, 6, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, -16, 16, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 13, 2, -2], [35, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-68, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -7, 0, 7, 10, -7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 15, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 11, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 4, -9, -4], [0, -2, -15, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 12, -5, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, -6, 7, 6], [-23, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, -3, 0, 3, -10, -3], [0, 0, 0, -5, 0, -14, -5, 5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-19, 0, 0, 0, -5, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -10, 0, 10, 3, -10], [0, 16, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -18, 0, -1, -1, -1], [0, -4, 4, 0, 0, 0, 0, 0], [0, 0, 0, 11, 0, 6, 6, 6], [0, 0, 0, 7, 0, -4, 7, -7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 13, 0, -4, -4, -4], [0, 0, 0, 1, 0, 14, 1, -1], [-21, 0, 0, 0, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -16, 16, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [27, 0, 0, 0, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, -1, 12, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -17, 0, 2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -17, 0, -4, -4, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 15, 0, 0, 0, 0, 0], [0, 16, 11, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 16, 0, -3, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 7, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0], [0, -14, 14, 0, 0, 0, 0, 0], [0, 0, 0, -6, 0, 6, 13, -6], [0, 0, 0, 0, 0, 0, 0, 0], [37, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, -10, 0, 10, 9, -10], [0, -10, -17, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 16, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -10, 0, -7, -10, 10], [0, 0, 0, -4, 0, 7, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -10, 0, -9, -10, 10], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 3, 14, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 15, 0, 0, 0, 0, 0], [0, 18, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-33, 0, 0, 0, 5, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2736_f_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2736_2_f_i();".
// 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_2736_2_f_i(:prec:=8)
    chi := MakeCharacter_2736_f();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(1999) - 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_2736_2_f_i();".
// 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_2736_2_f_i( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2736_f();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![36, 0, 1380, 0, 469, 0, 40, 0, 1]>,<7,R![4, 0, -23, 0, 1]>,<11,R![125316, 0, 31548, 0, 2653, 0, 88, 0, 1]>,<29,R![0, 1]>],Snew);
    return Vf;
end function;