
// Make newform 2736.3.o.p in Magma, downloaded from the LMFDB on 01 January 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_2736_o();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_2736_o_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_3_o_p();".
// 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_3_o_p();".
// 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 := [256, 0, 1064, 0, 345, 0, 34, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 16, 0, -205, 0, -30, 0, -1], [216, 0, -35, 0, -20, 0, -1, 0], [64, 0, 205, 0, 30, 0, 1, 0], [0, 504, 0, 245, 0, 30, 0, 1], [424, 0, 245, 0, 30, 0, 1, 0], [0, -1784, 0, -495, 0, -40, 0, -1]];
    Rf_basisdens := [1, 1, 40, 40, 40, 80, 40, 40];
    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_o();"
function MakeCharacter_2736_o()
    N := 2736;
    order := 2;
    char_gens := [1711, 2053, 1217, 1009];
    v := [2, 2, 2, 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_o_Hecke();"
function MakeCharacter_2736_o_Hecke( : Kf := false)
    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 := ISA(Type(Kf), Fld), 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]];
    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], [2, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, -1, 0, 0, 0, 0], [-4, 0, 0, 0, -1, 0, 2, 0], [0, -2, 0, 0, 0, 0, 0, 1], [3, 0, 0, 0, 2, 0, -1, 0], [-2, 0, 1, 0, 1, 1, 1, 1], [1, 0, 0, 1, 1, 0, 2, 0], [0, 6, -1, 0, 0, 4, 0, -1], [0, 4, -1, 0, 0, 0, 0, 2], [0, 2, 3, 0, 0, 6, 0, 0], [0, 8, -1, 0, 0, 4, 0, 2], [-10, 0, 0, 4, -5, 0, 0, 0], [4, 0, 0, 6, 3, 0, -8, 0], [0, -8, 1, 0, 0, 4, 0, -1], [0, 13, 3, 0, 0, 20, 0, 0], [-18, 0, 0, -6, -5, 0, -6, 0], [0, -9, 0, 0, 0, 16, 0, 2], [0, -16, 0, 0, 0, -16, 0, 2], [-21, 0, 0, -6, 8, 0, 13, 0], [0, -14, -1, 0, 0, 16, 0, 0], [-12, 0, 0, 10, -14, 0, -8, 0], [0, 12, 5, 0, 0, 0, 0, 4], [0, -26, 0, 0, 0, 20, 0, -4], [-14, 0, 0, -16, 4, 0, 4, 0], [0, -18, 0, 0, 0, -36, 0, -2], [0, -11, 1, 0, 0, 4, 0, 8], [0, -2, 3, 0, 0, -28, 0, 1], [0, -28, 9, 0, 0, -16, 0, 2], [0, -34, -3, 0, 0, -20, 0, 2], [54, 0, 0, 0, 1, 0, 8, 0], [113, 0, 0, -2, 12, 0, -17, 0], [0, 0, 0, -4, -19, 0, 30, 0], [32, 0, 0, -4, -17, 0, 14, 0], [0, 30, 4, 0, 0, -8, 0, 8], [54, 0, 0, -14, 0, 0, -26, 0], [34, 0, 0, 6, -12, 0, -14, 0], [0, -14, 7, 0, 0, -12, 0, -8], [0, 32, 4, 0, 0, -54, 0, -2], [0, 18, 3, 0, 0, 50, 0, -8], [0, -16, 8, 0, 0, -70, 0, 2], [-127, 0, 0, 3, -18, 0, 0, 0], [0, -66, -1, 0, 0, -56, 0, 4], [66, 0, 0, 18, 8, 0, -10, 0], [85, 0, 0, 13, -32, 0, -6, 0], [0, -29, 13, 0, 0, -52, 0, 10], [0, 28, -3, 0, 0, 44, 0, -4], [0, -13, -13, 0, 0, 20, 0, 4], [190, 0, 0, -10, 3, 0, -10, 0], [24, 0, 0, -22, 11, 0, -20, 0], [-55, 0, 0, 1, -6, 0, -42, 0], [0, 8, 5, 0, 0, 40, 0, 10], [224, 0, 0, -22, -25, 0, 8, 0], [0, 74, 2, 0, 0, 88, 0, -10], [216, 0, 0, 42, -25, 0, -8, 0], [0, -2, -1, 0, 0, 54, 0, 20], [133, 0, 0, -31, 41, 0, -6, 0], [12, 0, 0, 34, -31, 0, 4, 0], [0, 40, -10, 0, 0, -4, 0, -8], [-110, 0, 0, 4, 47, 0, 4, 0], [0, 60, 18, 0, 0, -8, 0, 19], [0, 50, 1, 0, 0, 94, 0, 4], [219, 0, 0, -21, 72, 0, 14, 0], [49, 0, 0, -24, -41, 0, 65, 0], [0, -16, 26, 0, 0, 24, 0, 13], [0, -27, 4, 0, 0, -104, 0, -18], [0, 62, 4, 0, 0, -16, 0, 14], [170, 0, 0, 2, 1, 0, -58, 0], [-28, 0, 0, -24, 29, 0, 2, 0], [-111, 0, 0, -2, -1, 0, 3, 0], [27, 0, 0, -27, 4, 0, -24, 0], [102, 0, 0, -12, -28, 0, 20, 0], [0, -112, 0, 0, 0, 16, 0, -11], [0, 25, -21, 0, 0, -12, 0, 10], [0, -12, 33, 0, 0, 12, 0, 20], [-96, 0, 0, 22, -5, 0, -56, 0], [-196, 0, 0, 2, 9, 0, 68, 0], [0, -70, -25, 0, 0, -76, 0, 2], [0, -14, 17, 0, 0, -28, 0, -4], [-124, 0, 0, -18, 90, 0, -52, 0], [0, -4, 5, 0, 0, -28, 0, 17], [0, -164, -16, 0, 0, -56, 0, 20], [0, -48, -25, 0, 0, -92, 0, 4], [0, 126, -3, 0, 0, -40, 0, 18], [-204, 0, 0, -16, -81, 0, -6, 0], [0, -136, -14, 0, 0, -12, 0, -10], [399, 0, 0, 34, -4, 0, 17, 0], [78, 0, 0, -30, -15, 0, 6, 0], [-236, 0, 0, -14, -11, 0, -24, 0], [-352, 0, 0, 22, 15, 0, 68, 0], [78, 0, 0, -32, -40, 0, 12, 0], [0, -18, 18, 0, 0, -76, 0, -18], [152, 0, 0, 8, 58, 0, 34, 0], [-42, 0, 0, -20, -5, 0, -72, 0], [-123, 0, 0, 39, 57, 0, 4, 0], [0, -8, -18, 0, 0, -54, 0, 14], [0, 8, -19, 0, 0, -4, 0, -46], [0, 125, -17, 0, 0, -20, 0, -42], [306, 0, 0, 8, -53, 0, 4, 0], [0, -40, 28, 0, 0, 66, 0, 26], [-326, 0, 0, -96, 1, 0, -8, 0], [0, -2, -5, 0, 0, -46, 0, -20], [0, 314, 4, 0, 0, 64, 0, -36], [382, 0, 0, -12, 4, 0, -44, 0], [129, 0, 0, 32, 50, 0, -67, 0], [322, 0, 0, -58, -23, 0, 82, 0], [426, 0, 0, 4, 12, 0, 24, 0], [0, 50, -35, 0, 0, 48, 0, -34], [0, 160, -20, 0, 0, 56, 0, -2], [0, 8, 4, 0, 0, 188, 0, -10], [58, 0, 0, 16, -37, 0, 52, 0], [-280, 0, 0, 18, 19, 0, 132, 0], [184, 0, 0, 76, -98, 0, 34, 0], [56, 0, 0, -34, -79, 0, -64, 0], [0, -118, -10, 0, 0, -136, 0, -34], [92, 0, 0, 58, 21, 0, 16, 0], [-301, 0, 0, 15, 56, 0, -38, 0], [-104, 0, 0, -14, -101, 0, 28, 0], [0, 53, -17, 0, 0, -44, 0, -42], [0, 28, 20, 0, 0, -32, 0, 17], [0, 74, 4, 0, 0, -52, 0, -52], [0, 154, 25, 0, 0, 68, 0, -7], [0, 116, -22, 0, 0, 10, 0, 46], [338, 0, 0, -50, 67, 0, 94, 0], [52, 0, 0, 0, 70, 0, 114, 0], [4, 0, 0, -8, -110, 0, -34, 0], [537, 0, 0, 35, -66, 0, 8, 0], [337, 0, 0, 1, -60, 0, 50, 0], [-204, 0, 0, -30, -50, 0, 72, 0], [-590, 0, 0, -38, 51, 0, 10, 0], [0, -92, 17, 0, 0, -196, 0, -2], [0, 112, -8, 0, 0, -52, 0, 26], [66, 0, 0, -54, 111, 0, -58, 0], [-291, 0, 0, 46, 48, 0, -45, 0], [457, 0, 0, 6, 118, 0, 59, 0], [0, -120, 8, 0, 0, 40, 0, 3], [0, -7, -1, 0, 0, 132, 0, 4], [0, -18, 15, 0, 0, 84, 0, -1], [-159, 0, 0, 0, 16, 0, -127, 0], [0, 205, -15, 0, 0, 76, 0, -14], [512, 0, 0, -78, 131, 0, -28, 0], [317, 0, 0, -45, -36, 0, -8, 0], [0, -83, -8, 0, 0, 312, 0, -20], [0, -104, 22, 0, 0, 208, 0, 31], [0, -138, 2, 0, 0, 188, 0, 38], [36, 0, 0, -46, 110, 0, -8, 0], [0, 100, -52, 0, 0, 140, 0, -48], [-646, 0, 0, -28, -57, 0, -4, 0], [0, -138, 5, 0, 0, -244, 0, 34], [0, 26, 12, 0, 0, 56, 0, 1], [-12, 0, 0, 94, 55, 0, 20, 0], [270, 0, 0, 106, -73, 0, 94, 0], [0, 48, -40, 0, 0, -68, 0, -12], [0, -69, 2, 0, 0, -320, 0, 24], [0, -154, -8, 0, 0, -40, 0, -54], [-377, 0, 0, 125, 75, 0, -12, 0], [-211, 0, 0, -100, 47, 0, -27, 0], [-65, 0, 0, 72, 88, 0, -89, 0], [0, -146, -36, 0, 0, -176, 0, 27], [-540, 0, 0, 94, -46, 0, 28, 0], [0, 200, -19, 0, 0, -152, 0, -44], [354, 0, 0, 96, -32, 0, 84, 0], [0, 36, 24, 0, 0, -254, 0, -66], [0, -122, -25, 0, 0, 192, 0, -36], [0, -88, -26, 0, 0, 12, 0, -72], [0, -384, -23, 0, 0, -260, 0, 24], [228, 0, 0, -70, 105, 0, -92, 0], [0, 110, 51, 0, 0, 64, 0, -36], [-20, 0, 0, 78, -89, 0, 116, 0], [0, -71, -58, 0, 0, -88, 0, 36], [0, 6, 23, 0, 0, 428, 0, 1], [-178, 0, 0, -88, -8, 0, 36, 0], [69, 0, 0, -42, 175, 0, 27, 0], [0, -12, 54, 0, 0, 132, 0, 70], [-368, 0, 0, -66, -101, 0, 136, 0], [-662, 0, 0, -26, -196, 0, -38, 0], [-300, 0, 0, 18, 39, 0, 112, 0], [0, -306, -40, 0, 0, 208, 0, -56], [-176, 0, 0, 68, -71, 0, -46, 0], [663, 0, 0, 91, -122, 0, 38, 0], [0, 245, -27, 0, 0, -44, 0, 30], [0, 108, 52, 0, 0, 106, 0, 18], [0, -154, -20, 0, 0, -92, 0, -58], [281, 0, 0, -55, 154, 0, 14, 0], [670, 0, 0, -32, 205, 0, -124, 0], [0, -8, -26, 0, 0, -224, 0, -33], [0, -120, -36, 0, 0, -14, 0, 18], [0, -306, -21, 0, 0, -96, 0, 30], [131, 0, 0, 137, -37, 0, 72, 0], [0, -26, -45, 0, 0, -168, 0, -84], [628, 0, 0, 74, -61, 0, 84, 0], [0, 90, 15, 0, 0, -114, 0, -72], [0, 268, 25, 0, 0, -188, 0, -3], [730, 0, 0, 70, 128, 0, 30, 0], [0, -84, -8, 0, 0, -128, 0, -34], [-43, 0, 0, -30, -150, 0, 107, 0], [402, 0, 0, 70, -12, 0, -66, 0], [61, 0, 0, -156, 111, 0, 189, 0], [839, 0, 0, -73, -84, 0, -82, 0], [0, 224, 16, 0, 0, -38, 0, -26], [0, -192, 19, 0, 0, 284, 0, 64], [0, 260, -59, 0, 0, 116, 0, 5], [0, 250, -25, 0, 0, 340, 0, 22], [792, 0, 0, -66, -194, 0, 88, 0], [-28, 0, 0, 152, -93, 0, -362, 0], [259, 0, 0, 85, 158, 0, 20, 0], [0, 255, 49, 0, 0, 172, 0, 8], [-111, 0, 0, -192, 168, 0, 81, 0], [0, 55, 111, 0, 0, 292, 0, -8], [267, 0, 0, -94, 109, 0, 33, 0], [864, 0, 0, -46, -274, 0, 136, 0], [-1324, 0, 0, 42, -259, 0, -80, 0], [0, 257, -39, 0, 0, 100, 0, 88], [0, 184, 59, 0, 0, -112, 0, 40], [0, -70, -33, 0, 0, -388, 0, -24], [-271, 0, 0, 73, -59, 0, -298, 0], [0, -92, 0, 0, 0, 380, 0, -34], [0, 394, -25, 0, 0, 100, 0, -60], [306, 0, 0, -8, -247, 0, 184, 0], [0, -80, -34, 0, 0, -78, 0, -34], [0, 228, -3, 0, 0, -416, 0, 16], [0, 242, 43, 0, 0, 348, 0, 50], [1579, 0, 0, -35, 142, 0, -12, 0], [0, -43, -7, 0, 0, -148, 0, -10], [1178, 0, 0, 56, 19, 0, -260, 0], [0, 32, -86, 0, 0, -12, 0, 100], [0, 188, 57, 0, 0, -216, 0, -30], [0, 288, -92, 0, 0, 240, 0, -82], [-426, 0, 0, -74, 285, 0, -114, 0], [90, 0, 0, -114, -97, 0, -158, 0], [0, 319, -56, 0, 0, 320, 0, -74], [0, 62, 55, 0, 0, -432, 0, 40], [0, -118, -74, 0, 0, -520, 0, 48], [-992, 0, 0, -2, -31, 0, 0, 0], [-739, 0, 0, 119, -70, 0, 120, 0], [400, 0, 0, 138, -115, 0, -112, 0], [-270, 0, 0, 234, -19, 0, -230, 0], [-140, 0, 0, 6, 26, 0, 100, 0], [0, -6, 109, 0, 0, -24, 0, 54], [0, 184, 2, 0, 0, -98, 0, -26], [810, 0, 0, -30, 235, 0, -86, 0], [1355, 0, 0, -103, -265, 0, 204, 0], [0, -92, -60, 0, 0, -512, 0, 51], [0, 130, -9, 0, 0, 596, 0, 26], [412, 0, 0, -122, 35, 0, 336, 0], [-696, 0, 0, -262, 121, 0, -4, 0], [0, 214, 57, 0, 0, 74, 0, -56], [0, 52, 82, 0, 0, -266, 0, 18], [-315, 0, 0, -21, 26, 0, 196, 0], [-728, 0, 0, 182, 106, 0, -120, 0], [879, 0, 0, -132, -146, 0, -49, 0], [673, 0, 0, -101, 149, 0, -260, 0], [0, -368, 35, 0, 0, 72, 0, 40], [-702, 0, 0, -66, 261, 0, -146, 0], [1128, 0, 0, 234, -10, 0, -60, 0], [-808, 0, 0, 72, -175, 0, -66, 0], [0, -334, 57, 0, 0, -566, 0, 48], [0, 158, 97, 0, 0, 458, 0, 64], [522, 0, 0, -124, -136, 0, 364, 0], [0, 192, 75, 0, 0, 620, 0, 44], [0, -72, 8, 0, 0, -458, 0, 66], [1356, 0, 0, 20, -139, 0, -10, 0], [0, -34, 58, 0, 0, 400, 0, -71], [124, 0, 0, -22, 199, 0, 248, 0], [0, -727, 62, 0, 0, -384, 0, 12], [0, -96, 1, 0, 0, -412, 0, -51], [-651, 0, 0, 30, -56, 0, -181, 0], [0, 475, 111, 0, 0, 92, 0, 52], [-214, 0, 0, 40, 161, 0, 96, 0], [0, 188, 5, 0, 0, 44, 0, 67], [0, -319, -84, 0, 0, 216, 0, -32], [295, 0, 0, 48, -152, 0, -25, 0], [-1053, 0, 0, 99, -126, 0, -318, 0], [0, 284, 91, 0, 0, -112, 0, 6], [211, 0, 0, -5, 171, 0, -122, 0], [160, 0, 0, 204, -77, 0, -86, 0], [0, -72, 157, 0, 0, -68, 0, 51], [0, 150, -84, 0, 0, -452, 0, 14], [964, 0, 0, 24, -73, 0, -158, 0], [0, 108, 44, 0, 0, 444, 0, 2], [-481, 0, 0, 7, 223, 0, 70, 0], [-1905, 0, 0, 25, 192, 0, -24, 0], [0, -640, -44, 0, 0, -72, 0, 77], [-784, 0, 0, -88, -275, 0, 90, 0], [2316, 0, 0, -78, 3, 0, -228, 0], [-707, 0, 0, 24, 270, 0, -39, 0], [0, 528, 34, 0, 0, -42, 0, 34], [1149, 0, 0, -47, -120, 0, 22, 0], [0, 618, 74, 0, 0, 0, 0, 18], [546, 0, 0, 282, -176, 0, -82, 0], [-1574, 0, 0, 22, -111, 0, -38, 0], [0, -540, 50, 0, 0, -176, 0, 102], [0, -156, 162, 0, 0, -70, 0, 110], [0, 20, 70, 0, 0, 230, 0, 130], [242, 0, 0, -80, -100, 0, 116, 0], [0, 512, 78, 0, 0, 116, 0, -34], [-844, 0, 0, -28, 43, 0, -158, 0], [0, -239, 134, 0, 0, -376, 0, -20], [468, 0, 0, 18, 413, 0, 176, 0], [-392, 0, 0, 54, -307, 0, 100, 0], [0, -364, 2, 0, 0, -416, 0, 97], [843, 0, 0, 31, -470, 0, 278, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2736_o_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2736_3_o_p();".
// 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_3_o_p(:prec:=8)
    chi := MakeCharacter_2736_o();
    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_2736_3_o_p();".
// 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_3_o_p( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2736_o();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<5,R![-352, 256, -34, -7, 1]>,<7,R![338, -221, -99, -3, 1]>],Snew);
    return Vf;
end function;