
// Make newform 2880.3.e.j in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2880_e();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2880_e_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_2880_3_e_j();".
// 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_2880_3_e_j();".
// 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 := [16, -8, -8, 2, 3, 1, -2, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [24, 8, -24, -17, 7, 4, 3, -1], [-24, -8, 16, -5, -5, -4, -1, 3], [-56, 40, 8, 3, -21, -12, 7, 3], [-104, -8, 48, 15, -1, -20, 3, 7], [10, 10, -1, -4, 1, 3, 0, -1], [-40, -8, 8, 5, -3, -4, 1, 5], [72, 16, -36, -9, 11, 8, -5, -5]];
    Rf_basisdens := [1, 8, 16, 8, 8, 1, 4, 4];
    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_2880_e();"
function MakeCharacter_2880_e()
    N := 2880;
    order := 2;
    char_gens := [2431, 901, 641, 577];
    v := [1, 2, 2, 2];
    // 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_2880_e_Hecke();"
function MakeCharacter_2880_e_Hecke(Kf)
    N := 2880;
    order := 2;
    char_gens := [2431, 901, 641, 577];
    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 := 3;
    raw_aps := [[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, 1, 0], [0, -1, 0, 0, 0, 0, 0, 1], [-2, 0, -2, 0, 0, -1, 0, 0], [0, 0, 4, 1, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 1], [0, -3, 0, 0, 1, 0, 2, -2], [8, 0, 2, -2, 0, -2, 0, 0], [0, -2, 0, 0, -4, 0, -2, -1], [14, 0, -10, -2, 0, 1, 0, 0], [2, 0, 0, 0, 0, 2, 0, 0], [0, -6, 0, 0, -2, 0, -3, 2], [0, -1, 0, 0, 5, 0, 4, 2], [44, 0, 2, 0, 0, 2, 0, 0], [0, -3, 0, 0, 2, 0, 0, 3], [22, 0, -4, 4, 0, 2, 0, 0], [0, 4, 0, 0, -6, 0, -1, -4], [0, 8, 0, 0, 2, 0, 0, 0], [-30, 0, -4, -4, 0, 2, 0, 0], [0, -2, 0, 0, -8, 0, -4, 9], [0, 2, 0, 0, 12, 0, 5, 2], [-10, 0, -44, 0, 0, -2, 0, 0], [54, 0, -12, -6, 0, -2, 0, 0], [-28, 0, -2, 4, 0, 0, 0, 0], [0, 1, 0, 0, -2, 0, 1, -10], [0, -4, 0, 0, 2, 0, 13, -10], [-46, 0, -4, -8, 0, -4, 0, 0], [36, 0, -8, -7, 0, 4, 0, 0], [0, 5, 0, 0, -10, 0, -5, -6], [0, 15, 0, 0, 6, 0, -6, -1], [52, 0, -12, -5, 0, -4, 0, 0], [0, -10, 0, 0, 2, 0, 28, -7], [-84, 0, -2, -2, 0, -2, 0, 0], [0, 16, 0, 0, 8, 0, -6, 1], [6, 0, -54, 6, 0, -1, 0, 0], [0, 18, 0, 0, 0, 0, -25, 10], [0, -15, 0, 0, -11, 0, 12, -6], [-12, 0, -34, 10, 0, -2, 0, 0], [0, -11, 0, 0, 14, 0, 8, -11], [82, 0, -52, -4, 0, -8, 0, 0], [0, 2, 0, 0, 4, 0, -10, -6], [-178, 0, -32, -6, 0, 0, 0, 0], [136, 0, 14, -6, 0, 0, 0, 0], [0, -8, 0, 0, 20, 0, 20, 5], [0, -6, 0, 0, -6, 0, -26, 1], [0, -17, 0, 0, -12, 0, -21, 14], [0, -8, 0, 0, 0, 0, 3, 20], [-22, 0, -40, -16, 0, 6, 0, 0], [-72, 0, -8, 11, 0, 0, 0, 0], [0, -24, 0, 0, -2, 0, -10, 10], [34, 0, -72, -16, 0, 4, 0, 0], [0, 29, 0, 0, -12, 0, -28, 9], [-68, 0, -32, 1, 0, 12, 0, 0], [0, -1, 0, 0, -33, 0, 20, -6], [-144, 0, -70, -2, 0, 6, 0, 0], [0, 8, 0, 0, -4, 0, -10, -19], [58, 0, 30, 6, 0, -5, 0, 0], [74, 0, -32, -6, 0, 8, 0, 0], [0, -12, 0, 0, 14, 0, -23, 24], [-64, 0, -50, -6, 0, -4, 0, 0], [0, -8, 0, 0, -16, 0, -3, 30], [0, 8, 0, 0, -26, 0, 0, 10], [174, 0, -40, -10, 0, -16, 0, 0], [144, 0, 14, -2, 0, -16, 0, 0], [0, 16, 0, 0, 50, 0, 26, -1], [90, 0, 4, 4, 0, 2, 0, 0], [0, -22, 0, 0, -10, 0, 1, 12], [-130, 0, -84, 20, 0, 6, 0, 0], [16, 0, 0, -13, 0, -16, 0, 0], [0, 26, 0, 0, -26, 0, -90, -6], [0, -7, 0, 0, 2, 0, -21, 12], [-10, 0, 106, 2, 0, -21, 0, 0], [0, 38, 0, 0, 22, 0, 12, -1], [0, -25, 0, 0, -3, 0, 14, 26], [-96, 0, 10, 0, 0, 24, 0, 0], [266, 0, -86, -8, 0, 3, 0, 0], [102, 0, -72, 14, 0, -10, 0, 0], [-86, 0, -72, -20, 0, 4, 0, 0], [0, -23, 0, 0, 16, 0, -34, 9], [34, 0, 144, 4, 0, 10, 0, 0], [0, 42, 0, 0, 18, 0, 24, -14], [138, 0, -12, 20, 0, 10, 0, 0], [0, 60, 0, 0, 12, 0, 28, -19], [0, 4, 0, 0, 28, 0, 77, -16], [90, 0, -36, -32, 0, 20, 0, 0], [86, 0, -156, -26, 0, -22, 0, 0], [-4, 0, 70, -6, 0, 6, 0, 0], [0, 55, 0, 0, -18, 0, -83, -12], [0, 4, 0, 0, 6, 0, 1, -30], [0, 4, 0, 0, 26, 0, 18, -4], [0, -29, 0, 0, -30, 0, 7, 30], [0, -29, 0, 0, -46, 0, 38, -43], [0, 0, 0, 0, -34, 0, 40, 39], [0, -17, 0, 0, 41, 0, 50, -22], [116, 0, 22, 24, 0, -16, 0, 0], [58, 0, 60, -12, 0, 8, 0, 0], [0, -26, 0, 0, 48, 0, 23, -24], [-102, 0, -28, -24, 0, -20, 0, 0], [0, -14, 0, 0, -14, 0, 11, 14], [-116, 0, -146, -30, 0, -6, 0, 0], [0, -2, 0, 0, 46, 0, 11, 12], [-730, 0, 0, 6, 0, 18, 0, 0], [0, 16, 0, 0, -62, 0, 26, -61], [510, 0, 196, -14, 0, 26, 0, 0], [0, 60, 0, 0, -22, 0, -15, 10], [-148, 0, 24, 45, 0, 28, 0, 0], [0, 66, 0, 0, 2, 0, -50, -54], [-14, 0, -80, 28, 0, 52, 0, 0], [0, 41, 0, 0, -8, 0, -99, -4], [10, 0, 194, -24, 0, 23, 0, 0], [504, 0, 104, -9, 0, -12, 0, 0], [0, 50, 0, 0, 10, 0, -80, 45], [0, -42, 0, 0, -28, 0, -22, 5], [-106, 0, 180, 18, 0, -8, 0, 0], [0, 94, 0, 0, -20, 0, -101, 50], [0, -27, 0, 0, 39, 0, -66, 50], [32, 0, -30, -36, 0, -8, 0, 0], [0, -17, 0, 0, 30, 0, -40, 65], [-426, 0, 84, -8, 0, -6, 0, 0], [210, 0, 340, 8, 0, -30, 0, 0], [640, 0, 114, -20, 0, 24, 0, 0], [0, -64, 0, 0, -14, 0, 51, -6], [0, -92, 0, 0, -26, 0, -26, 63], [268, 0, -170, 56, 0, 36, 0, 0], [178, 0, 200, -12, 0, -42, 0, 0], [0, -56, 0, 0, 28, 0, 56, -34], [0, 55, 0, 0, -6, 0, 19, -18], [298, 0, 254, -6, 0, -1, 0, 0], [0, -120, 0, 0, 6, 0, 60, -13], [0, -27, 0, 0, -9, 0, 84, 58], [0, 90, 0, 0, -8, 0, -6, 43], [18, 0, 334, 30, 0, 23, 0, 0], [-22, 0, -244, 48, 0, 4, 0, 0], [-366, 0, 320, -8, 0, 8, 0, 0], [-664, 0, 134, 26, 0, -4, 0, 0], [0, 22, 0, 0, 0, 0, 5, -64], [732, 0, -114, 34, 0, 2, 0, 0], [-706, 0, -340, 14, 0, -44, 0, 0], [0, -106, 0, 0, 50, 0, 134, -3], [-256, 0, 210, -14, 0, 22, 0, 0], [0, 65, 0, 0, -68, 0, -37, -38], [0, 12, 0, 0, 40, 0, 119, -64], [-230, 0, -28, -12, 0, 32, 0, 0], [0, -10, 0, 0, -2, 0, -110, 58], [-318, 0, 82, -64, 0, 3, 0, 0], [696, 0, 68, -35, 0, 0, 0, 0], [0, -82, 0, 0, -74, 0, 0, -13], [0, 33, 0, 0, -67, 0, -82, 46], [358, 0, 10, 10, 0, 19, 0, 0], [-306, 0, 116, -96, 0, 26, 0, 0], [0, -26, 0, 0, 8, 0, 51, -46], [0, 73, 0, 0, 33, 0, -12, -122], [0, 66, 0, 0, 66, 0, -53, 40], [0, -14, 0, 0, -34, 0, -104, 16], [0, 42, 0, 0, 28, 0, -92, 55], [122, 0, 500, -20, 0, -4, 0, 0], [426, 0, 56, -32, 0, 24, 0, 0], [-1232, 0, 50, -20, 0, -16, 0, 0], [0, 2, 0, 0, 10, 0, -151, 28], [-172, 0, -204, -25, 0, -72, 0, 0], [0, 7, 0, 0, 56, 0, 41, 14], [0, -99, 0, 0, -60, 0, -160, 45], [472, 0, -4, -95, 0, 24, 0, 0], [0, -55, 0, 0, 15, 0, -40, -26], [0, -44, 0, 0, 60, 0, 98, 35], [586, 0, 254, 20, 0, -55, 0, 0], [242, 0, 24, -24, 0, -20, 0, 0], [-172, 0, -106, 30, 0, 38, 0, 0], [0, 57, 0, 0, 146, 0, 124, -29], [-218, 0, -392, -24, 0, 44, 0, 0], [0, 164, 0, 0, 104, 0, 46, -40], [-378, 0, 256, 34, 0, 36, 0, 0], [0, -58, 0, 0, 92, 0, -4, 77], [-58, 0, 252, 28, 0, 70, 0, 0], [0, -10, 0, 0, -62, 0, 26, 31], [812, 0, -58, 82, 0, -2, 0, 0], [0, 21, 0, 0, -8, 0, 95, -28], [-354, 0, -80, -88, 0, -20, 0, 0], [0, -11, 0, 0, 24, 0, 25, -150], [0, 45, 0, 0, -184, 0, -128, 19], [270, 0, 146, 36, 0, -27, 0, 0], [676, 0, -432, 105, 0, 40, 0, 0], [0, -121, 0, 0, -15, 0, -34, -18], [-696, 0, 522, -4, 0, 0, 0, 0], [738, 0, 242, -6, 0, 45, 0, 0], [0, -76, 0, 0, 142, 0, 129, 50], [-270, 0, 64, 84, 0, -52, 0, 0], [0, 2, 0, 0, -100, 0, -126, -58], [-418, 0, 448, 18, 0, 8, 0, 0], [0, 86, 0, 0, -62, 0, -137, -72], [0, 82, 0, 0, 46, 0, -50, -55], [-60, 0, 182, -74, 0, -106, 0, 0], [0, -178, 0, 0, -100, 0, 11, -10], [-516, 0, 72, -59, 0, 28, 0, 0], [-134, 0, 248, 28, 0, -4, 0, 0], [190, 0, -370, 80, 0, 7, 0, 0], [-52, 0, 456, 89, 0, 0, 0, 0], [0, -47, 0, 0, -77, 0, -24, -34], [-640, 0, -174, -20, 0, 56, 0, 0], [0, -126, 0, 0, 36, 0, 242, -75], [806, 0, 134, 0, 0, -17, 0, 0], [-886, 0, 264, 128, 0, 8, 0, 0], [0, 39, 0, 0, -112, 0, 74, 27], [408, 0, -98, -38, 0, 56, 0, 0], [0, -102, 0, 0, 44, 0, -124, 147], [0, -46, 0, 0, -34, 0, -145, 52], [22, 0, 340, -80, 0, -66, 0, 0], [0, -4, 0, 0, -10, 0, 118, 57], [38, 0, 96, -42, 0, -40, 0, 0], [-44, 0, -106, -122, 0, 70, 0, 0], [0, -203, 0, 0, 98, 0, 289, 2], [0, -116, 0, 0, 60, 0, 183, 68], [0, 26, 0, 0, 92, 0, 84, -112], [-38, 0, 88, -40, 0, 0, 0, 0], [0, -167, 0, 0, -10, 0, -45, 144], [-698, 0, 64, 26, 0, 22, 0, 0], [0, -141, 0, 0, 49, 0, -36, 178], [-732, 0, -162, 66, 0, -50, 0, 0], [-94, 0, 320, 68, 0, -14, 0, 0], [0, -212, 0, 0, -96, 0, -76, -19], [-1470, 0, -248, -32, 0, 54, 0, 0], [0, -5, 0, 0, -74, 0, 41, -104], [0, 168, 0, 0, 14, 0, -207, -10], [-786, 0, 216, 8, 0, 32, 0, 0], [-1044, 0, 120, 41, 0, -16, 0, 0], [0, -248, 0, 0, 0, 0, 88, 118], [0, -153, 0, 0, 10, 0, 251, 36], [0, 197, 0, 0, -30, 0, -158, 49], [438, 0, -162, -80, 0, 11, 0, 0], [0, 46, 0, 0, -106, 0, -144, -39], [0, 52, 0, 0, -28, 0, 54, 41], [906, 0, -456, 26, 0, 4, 0, 0], [0, 82, 0, 0, 56, 0, 195, -52], [0, -243, 0, 0, 53, 0, 184, 110], [386, 0, -328, 4, 0, 48, 0, 0], [-928, 0, -278, 56, 0, -16, 0, 0], [0, -197, 0, 0, 140, 0, 258, -41], [0, -68, 0, 0, 18, 0, 172, -172], [0, -26, 0, 0, 42, 0, -113, -8], [0, 68, 0, 0, -50, 0, 58, 115], [0, 29, 0, 0, -184, 0, -109, 26], [254, 0, -220, -8, 0, 70, 0, 0], [-176, 0, -624, 7, 0, 44, 0, 0], [0, -102, 0, 0, -120, 0, 204, -124], [0, 49, 0, 0, 150, 0, -109, 136], [0, 225, 0, 0, 14, 0, 22, -289], [0, -180, 0, 0, -2, 0, 16, 17], [0, 145, 0, 0, 5, 0, -214, 42], [-570, 0, -358, 100, 0, 13, 0, 0], [-1098, 0, 176, -136, 0, -36, 0, 0], [0, 75, 0, 0, 155, 0, -2, 22], [-774, 0, -400, -68, 0, -40, 0, 0], [340, 0, 426, 36, 0, 38, 0, 0], [0, 83, 0, 0, 138, 0, 24, -31], [-38, 0, -180, -32, 0, 48, 0, 0], [0, -172, 0, 0, -162, 0, -17, -74], [212, 0, -590, -112, 0, 30, 0, 0], [642, 0, -636, 68, 0, 22, 0, 0], [0, 59, 0, 0, -128, 0, 107, -22], [0, -146, 0, 0, -50, 0, 173, -116], [618, 0, -104, -36, 0, 18, 0, 0], [1662, 0, -322, -74, 0, -35, 0, 0], [468, 0, 196, -125, 0, -108, 0, 0], [0, 188, 0, 0, 66, 0, -172, -53], [-720, 0, -14, 24, 0, -68, 0, 0], [1594, 0, 588, 38, 0, -70, 0, 0], [0, 242, 0, 0, -104, 0, -157, -172], [-896, 0, 250, 0, 0, 32, 0, 0], [518, 0, -192, -4, 0, -12, 0, 0], [0, 156, 0, 0, -36, 0, 5, 82], [510, 0, -960, 14, 0, -4, 0, 0], [0, -30, 0, 0, -36, 0, 116, -123], [-114, 0, -720, 82, 0, 40, 0, 0], [0, -27, 0, 0, -54, 0, 101, 142], [0, -86, 0, 0, 242, 0, 73, 48], [-442, 0, -516, 96, 0, -66, 0, 0], [34, 0, -120, 156, 0, 64, 0, 0], [0, -181, 0, 0, 110, 0, 266, 135], [0, -49, 0, 0, -73, 0, 4, 30], [0, 4, 0, 0, 36, 0, -238, -117], [0, -79, 0, 0, -1, 0, -54, -106], [-426, 0, -208, -20, 0, 60, 0, 0], [0, 94, 0, 0, 130, 0, 43, -116], [0, -58, 0, 0, 264, 0, 102, -86], [570, 0, -608, 80, 0, 84, 0, 0], [1432, 0, -38, 56, 0, -12, 0, 0], [0, -140, 0, 0, -4, 0, -168, 115], [-366, 0, 364, 26, 0, -70, 0, 0], [-744, 0, 50, -168, 0, 24, 0, 0], [0, 274, 0, 0, 20, 0, -229, 58], [-1296, 0, 80, 79, 0, -4, 0, 0], [0, -263, 0, 0, -118, 0, -74, -55], [-226, 0, 374, -106, 0, 25, 0, 0], [-468, 0, -370, 62, 0, -34, 0, 0], [0, -142, 0, 0, 172, 0, 326, -39], [-84, 0, 458, -104, 0, -66, 0, 0], [0, -41, 0, 0, -164, 0, 138, 103], [0, -46, 0, 0, -14, 0, 127, 54], [1270, 0, 720, 10, 0, 68, 0, 0], [280, 0, -438, -32, 0, -132, 0, 0], [0, 196, 0, 0, -216, 0, -216, -115]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2880_e_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2880_3_e_j();".
// 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_2880_3_e_j(:prec:=8)
    chi := MakeCharacter_2880_e();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 3));
    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_2880_3_e_j();".
// 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_2880_3_e_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2880_e();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<7,R![65536, 0, 188416, 0, 12032, 0, 224, 0, 1]>,<13,R![-12464, -5792, -472, 8, 1]>,<17,R![-8816, -3840, -424, 0, 1]>],Snew);
    return Vf;
end function;