
// Make newform 483.2.q.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_483_q();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_483_q_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_483_2_q_c();".
// 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_483_2_q_c();".
// 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 := [2374681, 4299390, 3616480, 2029154, 999838, 156742, -101709, -39430, 7852, 7700, 7261, -6446, 4383, -1560, 1777, -575, 295, -117, 40, -8, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [93770066285540040807952715617632715725508147408004736323, 89862666184746648799671364506226255055636290774177848963, 38475419386141141437860844997385153154987572743582018993, 37775873170370357341592915145991591251897612280495356825, -26941962872451432437781916435801938663289943345471863353, 4088642118152892399344021670712560952518517473025408884, -2929494957268101853591580827979029689075922974647162507, 1240662714998527972467340241137422290070657413214039398, 690589749448408572785183184848316037866091507913941213, -834408993093215313810348887955157067037234492066134006, 535999735391939780803209866232563328019313459976447100, -319836164245895282198403909637610147276610419549320366, 217243012400428783947350244293778274406005937169517149, -86573046030193724323881643136385031553307723383648738, 37992888670975622856358346353540279048821157016625383, 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56884817741056200113583339448402966746640552581039572, -100581598113387455901026681388164107869388566517508801, 71924814102659980714965071057181038173007396022440116, -42834972165656672595118572972767246962320387897183944, 21546174355085374740581520156350889802944342397397490, -13174020569239534450970769689112019590402052966416236, 4897316234715507370509636311168878064836887956179766, -2122470353259634395610718168463100137896241036333420, 746341130583188688492712603869440178052939322810004, -214855540570893202756797357017422063300751581329706, 38841916646474011908528568424994957348769735244902, -4250826929010087670388630973563190430537542350255], [-7203830123427116531716149880925295781982973313547998242, -8917538851257459719761709616058422505095851123892815979, -4886914128062307873455165654787895957413234364533003687, -3661971928532541792670969946435090880015230874904898146, -1232155616096944481946507983094748232229320379473802973, 194956593311301139573319950646835508621594144480860117, 241718099988600194939971808420416059072818035205820045, -23478413814399372893215434147016794259122460329033382, 14765779410724773992322095342850159171864437986917669, -81075075188298342418926508692429798661082744008680582, 55159785154219161408205693332364053037274368684813586, -31667781314165592182704142911283441161502738543641242, 17205866208552023201568788968672095141538091306080530, -11733430951863537892562700288217447920292130832211635, 4342270185367021782053152865649238553347186022094638, -2069389066119516223898827343852215313324257624391071, 788699785095725337258352441133631367751878521882427, -239688459956268677621199395833533504503747572140277, 44602895736053644441006250048234367130686182253475, -4914699392957061819156075052082571427768266403862], [-395774825919874443787069043478028338121357816247186210062, -1047167216289573578034211244634571571161351078777419365334, -472756066516096825981521756474538078362789152593121290006, -297026578376293602711984551776097693301688199727716819846, -110476358216140367113491688926510291838750133274371430846, 21828931930445957470372249062778610541049124810995814650, 20916577060663695168119955828539351521341678002188038791, -13491400057518724393390349086648977931206916899470169622, 14483588290995301545088352697055912392265778794101750742, -16275461779177321245001411178002335075451513776038502764, 10935704941786732592571762032193197426257389194299221172, -6436974156668401932191601051983855131572453422597281314, 3400723704604366203422546019312203503443387690069328290, -1922957208061436296801681848673956870594906224834295094, 755917396159316808750390594456652272463463011741267516, -315722692603297716040201359418375402819754419460538228, 106064630123461263201337856120423380364968168758573942, -28423536284270012274241063607678761796818891632631051, 4880783570816866452761014133961039643194502152915930, -499678099772728813582995402617431528581587257314786]];
    Rf_basisdens := [1, 1, 163818915742802557904989465623005620889077482505027334933, 163818915742802557904989465623005620889077482505027334933, 2445058443922426237387902471985158520732499738881004999, 163818915742802557904989465623005620889077482505027334933, 163818915742802557904989465623005620889077482505027334933, 2445058443922426237387902471985158520732499738881004999, 163818915742802557904989465623005620889077482505027334933, 163818915742802557904989465623005620889077482505027334933, 2445058443922426237387902471985158520732499738881004999, 163818915742802557904989465623005620889077482505027334933, 163818915742802557904989465623005620889077482505027334933, 163818915742802557904989465623005620889077482505027334933, 163818915742802557904989465623005620889077482505027334933, 163818915742802557904989465623005620889077482505027334933, 2445058443922426237387902471985158520732499738881004999, 2445058443922426237387902471985158520732499738881004999, 2445058443922426237387902471985158520732499738881004999, 163818915742802557904989465623005620889077482505027334933];
    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_483_q();"
function MakeCharacter_483_q()
    N := 483;
    order := 11;
    char_gens := [323, 346, 442];
    v := [11, 11, 6];
    // 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_483_q_Hecke();"
function MakeCharacter_483_q_Hecke(Kf)
    N := 483;
    order := 11;
    char_gens := [323, 346, 442];
    char_values := [[1, 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, 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, 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, -1, 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, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 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], [0, 1, 0, 0, -1, -1, -2, -1, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, -2, -1, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1], [1, 1, -1, 0, 0, 0, -1, 1, 3, 0, 0, 0, 1, -2, 0, -2, 0, 1, 0, 1], [1, 1, -1, 1, 0, -1, 0, 0, 1, 0, 0, 1, 2, -2, 0, -1, 1, 0, 1, 1], [3, -1, -2, 3, 1, -1, 0, 1, -1, 2, 1, 1, 1, -1, -1, -1, 1, 0, -1, -2], [0, 0, -1, 0, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 0, -1, 0], [0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 0, 1, 0, 0, 0], [-1, 1, 1, 2, 1, -3, 2, 1, -1, -1, 1, 0, -1, 1, 0, 1, 0, 1, 0, 0], [-3, 2, 0, -2, -1, 0, 0, -1, -2, 0, -1, -3, 0, 4, 2, 1, 0, 1, 0, -1], [-1, -1, -2, 0, -1, -2, -2, 0, 2, 0, 1, 2, 2, -2, 0, -2, 0, -1, 1, 0], [3, -1, 0, 5, 1, 2, 0, -1, -2, 2, 0, 0, 3, -4, -2, -5, 1, 1, 0, 0], [3, -2, 6, 3, 2, -1, 6, 2, -1, 2, 2, 0, -2, 2, -2, 0, 2, 1, -1, -2], [2, 0, 2, -2, 1, 2, -1, 1, 0, 1, 0, 0, -2, -1, -1, 1, 1, 1, 1, 0], [0, 0, 1, -1, 2, 1, 3, 1, -3, 0, 2, 2, -1, 3, 0, 1, 1, 0, 0, -2], [0, -2, 4, -5, 1, 0, 5, 0, -4, 0, 2, -4, -3, 6, 0, 0, 0, 0, -2, -1], [6, -2, -3, 5, 0, -4, -3, 1, 6, 3, 1, 4, 3, -4, 0, -8, 0, 1, -1, -2], [-5, 2, 6, -3, -2, 2, -3, -2, 0, -3, -3, 0, 0, 3, 2, 4, -1, -1, 1, 1], [2, -1, 0, 1, -1, -2, 1, 1, 3, -1, 0, 2, -1, 0, -1, -2, 0, 1, 0, 0], [4, -3, 0, 3, 3, 0, 3, 2, -1, 3, 2, 4, 3, -5, -3, -2, 0, 2, -3, -2], [-2, 2, -3, -1, 0, -1, 4, 0, 3, -2, -2, 0, -1, 1, 4, 2, -2, -2, 2, 0], [0, 1, 1, 0, 2, 1, -1, 2, 3, 2, -1, -2, 2, -3, -2, 0, -1, -1, 0, 0], [2, 1, -3, 2, -3, -4, -8, -1, 5, 0, -3, 1, 1, -2, 3, -2, 1, 1, 3, 1], [-2, 0, 4, 0, 0, 1, -1, -2, 2, -2, 0, 1, 0, 2, 3, 7, 0, -3, 0, 0], [-1, -1, 1, -3, 1, 4, 6, 2, 0, 0, 0, -6, -3, 4, 0, 3, -3, 0, -2, 0], [2, -2, 2, 2, 0, -1, 2, -1, -3, 2, -2, -1, -3, -2, 0, -3, -1, 2, -2, 0], [-3, 2, 1, -3, 0, -1, -1, -1, 1, 0, 0, 1, 1, -2, -1, 7, 1, 1, -1, 1], [-2, 1, 1, -5, 3, 1, 1, 4, -2, 2, 0, -1, -2, 7, -2, 5, -1, 3, -1, -1], [3, -1, -1, -1, 0, -2, 4, 0, -4, -1, 1, 1, 1, -1, -1, 0, -1, 1, 0, -1], [-5, -1, -2, -1, 2, 3, 4, 0, -4, -1, 1, -1, -4, -2, -1, 2, -1, -1, -2, -1], [-5, 1, 0, -5, 1, -3, 0, 3, 0, 0, 1, 5, 5, 0, 0, -1, 1, 1, 0, -3], [3, 1, 1, 3, 0, -2, 0, -1, 4, 1, 1, 0, -1, 4, 0, 5, -1, -2, 2, 1], [7, -1, -10, 4, 0, -2, -4, 2, 6, 0, -2, 2, 9, -6, 1, -6, -1, 2, 2, -1], [1, 0, 1, 2, 0, -5, 1, 2, 2, 1, 1, -7, 2, -2, 0, -6, 2, 1, 0, 0], [-4, 0, 2, 1, 0, 4, 0, 1, 2, -2, -2, -2, -1, 4, 2, 1, 1, 0, -1, 2], [-5, 1, -1, -5, 0, 5, 2, -2, 1, 0, 0, -3, -3, 0, 1, 5, -3, -3, 1, 2], [0, -5, -1, 6, 1, -1, 7, 1, 1, 5, 1, -5, -3, 3, -1, -5, 3, 1, -3, 0], [0, 0, 6, -6, 1, 0, 1, 1, 3, 0, 1, -1, 3, -2, 0, 4, 0, -3, 0, 3], [-12, 1, 1, -7, -2, 11, -1, -4, -10, -5, 0, -1, -12, 14, 5, 7, -1, -2, 1, 1], [0, -2, 2, 3, -2, 0, -3, 0, -7, -2, -2, 5, -2, -3, 0, 0, -2, 2, 0, 3], [5, 1, 0, 1, -3, -7, -2, -1, 5, -2, -2, 0, -2, 0, 3, 1, -1, 0, 0, 1], [1, 0, 6, -1, -1, 5, -1, -1, -6, -1, 0, -5, -1, 1, 0, 6, -1, 0, 1, 0], [1, 1, -3, 6, 0, -7, -3, 2, 5, -2, 0, 7, 7, -2, -4, -8, 4, 2, 0, 1], [-1, -2, -1, 2, -2, 1, -1, 0, 0, 0, 0, 1, -1, 7, 0, -2, 2, -2, 1, 1], [0, 1, 2, -3, 1, 0, 2, -2, 3, -1, -2, 1, 5, -2, 1, 5, 0, -2, 1, 2], [9, -1, -2, 4, 3, -6, -1, 0, 1, 4, 1, 7, 10, -2, -2, -11, 4, 1, -3, -2], [-5, 2, -5, 3, -3, 0, -9, -1, -1, 0, -1, 0, 3, -2, 2, -5, 0, -2, 0, 2], [-3, -3, 9, 0, 2, 9, 1, 2, -10, 2, 3, -2, 2, -1, -2, 3, 3, 3, 0, -3], [-2, 1, 1, -2, -4, -5, -4, 0, -1, 0, -4, -1, -1, 0, -1, -4, -1, -1, -1, 0], [-2, 4, -7, -5, -2, -6, -9, 1, 3, -2, 1, 7, 1, 3, 0, -4, 1, -2, 4, 2], [-2, 0, 11, -3, 0, 4, 5, 0, -5, 3, 0, -4, -9, 2, -2, 3, 2, 0, 0, 0], [12, 1, -12, 4, -2, -12, -12, -1, 7, 0, 0, 0, 9, -10, 2, -9, -1, -2, 2, 1], [-8, 0, 2, -12, -5, 1, -2, -3, 1, 0, 0, -2, -8, 8, 0, 12, 0, -5, 2, 2], [-8, 2, 5, -8, 3, 6, 11, 3, -5, -2, 1, -6, -7, 7, -4, 2, -1, 1, 1, 0], [-4, 2, -8, -4, -2, -9, -12, 0, 12, -4, -2, 0, 5, -8, 5, 4, -4, -6, 2, 5], [-1, 1, 5, -8, -3, 7, 8, -3, -5, -1, 0, 0, -8, 8, 0, 1, 0, 0, 0, 0], [15, 0, -2, 8, -1, -10, 0, -2, 10, -2, 0, 2, 15, -5, 2, -8, 0, -1, 0, 0], [-5, 0, 6, 6, 0, -6, -3, 1, -1, 5, 1, 4, 6, -6, -1, -6, 1, 0, -1, -5], [4, 0, 2, 8, 0, 2, -5, 0, 3, 0, 0, 2, 8, 0, 1, 3, 0, -1, -4, 0], [6, 3, 0, 6, -2, -6, -6, 0, 11, 0, -2, 6, 6, -11, 0, -1, 2, 2, 0, 0], [-3, 2, -6, 2, 0, -4, -4, -2, -3, 0, -3, 2, 0, -2, 2, 3, -3, -2, 0, -1], [8, 2, -10, 2, 0, -4, -16, 0, 10, -2, -2, 10, 4, -4, 2, 2, -3, -2, 3, 0], [-11, 4, 3, -5, -3, 1, 3, -1, -15, -3, 1, -2, -3, 4, 1, 11, 1, -4, 0, -3], [-3, 0, 8, -7, -1, 10, 1, -5, -9, -5, -3, -6, -7, 2, -1, 7, -1, 1, -5, 3], [0, 0, 8, -11, 1, 9, 9, 0, -13, 0, 1, -7, -12, 12, 0, 9, 0, 0, 0, -1], [-9, 4, 2, -14, 0, 6, 5, -5, -5, -5, -1, -6, -7, 5, 5, 14, -5, -5, 1, 4], [-8, 0, -1, -7, -5, 1, 0, -6, -3, -6, -5, -5, -7, 1, 3, 2, -5, -3, 5, 5], [6, 2, 1, 5, -1, 0, -4, 0, 12, -1, 0, 6, -1, -4, 0, -6, 0, -2, 0, 1], [-5, -1, 2, -2, -2, 1, -2, 0, 2, -2, 1, 6, -3, 2, 3, -4, -2, -4, 2, 3], [8, -3, 4, 1, -1, 2, 11, -1, -4, 3, 2, 5, -1, 1, -7, -3, 1, 2, -1, 0], [10, -3, 0, 10, 2, -5, -2, 3, 3, 0, 2, 11, 11, -3, 0, -7, 0, 0, 0, -3], [3, 0, -11, 1, -1, 5, -4, 0, 17, 0, 0, 16, 1, 0, 1, -10, -1, -1, 3, 0], [0, 2, -6, -8, -3, -6, -9, -4, 3, 0, -5, 6, 0, 5, 0, -6, -4, 0, 2, 3], [-5, 0, 7, -8, 0, -8, 6, 5, -2, 0, 2, -4, 2, -8, -2, -2, 2, 0, -5, 0], [-2, 3, -6, -2, 1, -1, -3, -3, 1, -3, -3, 0, 0, 4, -1, 8, -4, -3, 3, 4], [5, 4, -10, 2, -5, -6, -1, -5, 10, -4, -3, 9, 1, -1, 8, 4, -7, -3, 7, 0], [-8, -1, 4, -4, 2, 5, 3, 2, -4, 1, 2, -9, -6, 6, 0, -1, 2, 2, -2, 0], [9, -2, 1, 6, 3, -16, 2, 5, 14, 5, 0, -1, 9, -18, -5, -6, 2, 3, -2, -2], [-3, 2, 1, 18, -2, -5, -11, -4, 2, -5, -2, 9, 5, -5, 2, -5, -2, 0, 4, 5], [7, -2, -4, -5, 0, -3, -1, -1, 2, 0, 1, 3, -4, -5, 8, 4, -8, -1, -1, -2], [1, -4, 4, -3, 0, 8, 4, -2, -15, 1, -1, -11, -15, 3, 0, 7, -2, 1, -4, 0], [6, -7, -5, 2, 7, -12, -4, 3, -1, 4, 1, 5, 5, -12, -1, -5, -1, 0, -3, -4], [9, 2, -7, 9, -4, -3, -13, -3, 22, 0, -4, 9, 9, -15, 7, -12, -1, -1, 7, 3], [-2, -6, 13, -7, 1, 0, 14, 3, -8, 1, 3, -8, -3, 7, -6, 8, 0, 0, -1, 0], [4, 1, -5, 3, -2, 1, -7, 0, 7, 3, -1, 9, 2, -5, -3, -12, 3, -6, 2, -3], [5, -1, 1, 0, 0, 0, 9, 3, 0, 0, 3, -8, -9, 12, -1, 4, 0, 4, 0, -4], [0, 0, -19, 6, 1, 3, 0, 0, -3, 1, 0, 19, 0, 8, -1, -6, 0, 1, 0, 0], [-4, -2, -14, 4, 0, 1, -1, -1, 1, 2, 1, -1, 15, 6, -1, -4, 1, -1, -1, -2], [4, -1, -6, 12, 0, -8, -12, -3, 2, 1, -1, 8, 5, -3, 1, -2, -1, -3, 1, -1], [-17, 0, 7, -6, 0, 6, 16, -1, -10, -1, -1, -10, -6, 0, 0, 7, 0, 0, -1, 1], [0, 4, -4, 5, 0, 9, -4, 0, -5, 0, 0, 4, 0, 9, 0, -5, -4, 0, 4, 4], [6, 1, 3, -4, -2, 0, -7, -3, 9, -2, -3, -2, 9, 2, 1, -4, 0, -2, 2, 2], [-10, -3, 14, -11, 8, 0, 17, 10, -12, 0, 10, -9, -11, 8, -3, 15, 0, -1, 0, 1], [2, 0, 2, 8, 3, 1, 5, 0, -7, 0, 5, 0, 8, 5, -2, 0, 3, 2, -3, -5], [-7, 3, 8, 1, -3, -1, -7, 1, -1, 4, 1, 8, -1, -1, -1, 1, 6, 0, -1, -4], [-15, 5, -3, -15, -2, 7, 3, -1, -6, 0, -2, -18, -18, 9, 3, 11, 0, 0, 3, 1], [-4, -1, -1, 1, -4, 0, -1, -4, 1, 1, -3, -5, 6, -6, -2, -1, 3, -3, -3, 0], [-5, -2, 1, -2, 5, 4, 11, 5, -1, 2, -4, -7, 5, -5, -7, -2, 4, -4, -4, 0], [5, -7, 5, 5, 6, -1, 4, 0, -13, 0, 6, 9, 9, 8, -5, 2, 2, 2, -5, 0], [3, -1, -4, 6, 1, -8, -1, -2, 1, 0, -1, 0, 6, -8, 1, -6, -1, 0, 2, 0], [0, -3, 18, -2, 0, 12, 8, 2, -2, 5, 5, -12, -15, 3, -3, -4, 3, 2, -5, -3], [-3, -8, 11, -6, 0, 2, 11, -2, -15, -3, 2, -1, -15, 6, 0, 5, -2, -3, -8, 0], [1, -5, 3, 1, 1, 9, 15, 3, -4, 0, 1, -5, -5, 1, -3, 11, 1, 1, -3, -3], [2, 2, 5, -6, -3, 4, 2, -3, -5, -2, 5, 4, 5, -5, 2, 2, 4, 5, -4, 0], [-4, 0, 1, 3, 6, 1, 3, 0, -3, 3, 0, -3, 2, 1, 1, 0, 3, 5, -6, 1], [5, -4, -6, 10, 5, 0, 1, -1, 0, 4, -1, -10, -1, 7, -4, -4, 0, 1, -4, -1], [-4, -1, -1, -11, 4, -1, 13, 4, -5, 4, 4, -15, 4, 9, -4, 4, 4, 1, 0, -6], [-4, 0, -13, -7, -4, 8, -1, -4, -1, -4, -1, -2, -7, 3, 4, -9, -4, -4, -3, 1], [7, -1, -20, 13, 0, -12, -12, -1, 19, 5, 1, 12, 20, -6, 0, -20, 0, -1, -1, -1], [2, 1, 3, -12, -2, 4, 1, 1, -2, 2, 3, -3, -4, 10, 0, 2, 1, 2, 1, 2], [-7, 5, 9, -14, -2, 5, -3, -5, -10, -2, -2, 0, -1, 6, 2, 8, -2, 2, -2, 2], [14, -5, -9, 14, 4, 0, 6, 4, 6, -1, 4, 13, 4, -9, -5, -2, 0, 3, 1, -3], [-1, 5, -4, -10, -6, 0, -18, 0, 18, -10, -5, -1, -10, -4, 7, 11, -10, -3, 6, 7], [5, 1, 2, -3, -5, 0, 3, -7, 7, -2, -7, 3, -6, -2, 1, 5, 0, -1, 2, 1], [8, -3, 1, 8, 3, 2, -5, 2, 7, 3, -5, 5, 3, -7, -2, -8, -5, 3, 0, 4], [7, 0, -10, 5, -2, -11, -2, 3, 7, 3, 2, 9, 5, -1, -3, -13, -2, 3, 0, -2], [-6, 0, 10, -2, 0, 3, 5, 3, -4, 2, 4, -1, -8, 3, -4, 8, 1, 0, -3, -2], [-4, 7, 1, -21, -7, 1, 10, 0, 3, 5, -3, -13, 2, 1, 3, -2, 3, 0, 0, -5], [12, -4, -10, 10, -2, -14, -9, 4, 14, -2, -2, 0, 5, -9, 2, -7, -2, -3, 3, 2], [0, 1, -2, -7, -2, 2, -2, 1, 0, -2, 0, 2, 0, 3, 2, 7, -1, -2, 2, 2], [-27, 3, 8, -2, -1, 5, 5, 0, -5, -2, -3, 9, -7, 8, -3, -7, -2, -1, 1, -3], [-3, 2, -5, -3, -5, -4, -12, -3, -7, 0, -5, 3, 3, 12, 5, 13, 0, 0, 5, 3], [1, 2, -7, -6, 0, -1, -1, -1, 2, 3, -2, 1, 2, -3, 5, 5, -5, -1, 2, 2], [-20, 11, 17, -6, -11, 7, -1, -2, 3, -5, -3, -2, -7, 7, 3, 7, -1, 0, 2, 5], [15, -7, -18, 19, 9, -14, -1, 5, -4, 9, 4, 10, 9, -6, -5, -15, 4, 7, 0, 0], [-8, 4, 0, -4, 0, 0, -4, 0, 0, -5, 0, -2, -21, 3, 4, 4, 0, -4, 5, 4], [-11, 5, 5, -10, -6, 0, -5, -2, -5, 0, -2, -10, -14, 9, 5, 1, 0, -1, 0, 1], [-9, 4, -3, -2, 2, -11, 1, 0, 10, -2, 0, 3, -9, -1, 2, 2, -4, 2, -1, -1], [18, 0, -10, 0, 2, -8, -17, 3, 10, 3, 0, 8, 0, -3, -1, -11, 2, 1, 1, 0], [0, 3, 1, 0, 3, 13, 4, -4, -14, 0, -4, -8, -11, 3, 0, 13, -4, 0, 3, -3], [5, 1, -2, 7, 5, 9, 3, 8, -11, 5, 7, -2, -6, -2, 0, 4, 8, 5, 1, -5], [-8, 4, -1, -4, -9, 1, -4, -4, 8, -7, -7, 0, -8, 8, 9, 11, -3, -6, 6, 3], [-12, 1, -4, -7, -1, -6, 1, 1, -18, -1, -4, -6, -1, 0, -1, 12, -4, -1, 0, -2], [-14, 5, 14, -9, -3, 4, -5, -3, -14, -5, -2, -9, -12, 12, 1, 5, -1, -2, 1, 0], [14, 0, 5, 6, 3, 3, -10, 2, -6, 2, 2, -4, 6, 0, -2, 3, 3, 2, 7, -2], [-15, -3, 13, -1, 0, 9, 8, 4, -15, -1, 5, -9, -9, 18, -4, 8, 4, 4, -5, -3], [0, 0, 3, -13, 0, 2, 12, -2, -3, 4, 3, -9, 2, 2, -3, -2, 6, 0, 2, -4], [8, -2, -11, 10, -1, 6, -4, -1, -2, 4, 0, 11, 8, -12, -4, -10, 2, -1, 4, 4], [-6, 7, -2, -10, -4, 3, 3, -4, 2, -7, -6, 1, 3, -3, 14, 7, -6, -6, 6, 0], [-10, -1, 11, 5, 5, 21, 16, 0, -16, 5, 1, -11, -16, 11, -6, 6, 5, 3, -5, -6], [-15, 3, 21, 1, 0, 17, 7, 0, -7, 1, -3, -8, -16, 21, 4, 7, 1, -6, 0, 4], [12, -3, 1, 12, 3, -12, -11, 0, 13, 0, 3, 25, 25, -14, -1, -6, 4, 4, -1, 0], [1, 2, 0, 9, 4, 8, 4, 0, -8, 1, 10, 6, -4, -5, 0, 7, 0, 1, 2, -4], [-1, 2, -3, -6, -2, 4, 1, -5, 4, 1, -4, -5, 7, 4, 4, -7, -1, 0, 5, -1], [2, 0, -6, 11, 0, 1, -5, -5, -4, -5, -1, -2, 11, 4, 2, -4, 0, -2, -1, 1], [-20, -1, 3, -20, 3, 21, 27, 3, -33, 0, 3, -16, -16, 30, -3, 8, -1, -1, -3, -3], [-8, -3, -2, 5, 4, 0, -13, -1, -8, -1, -1, -1, 8, -1, -3, -13, 0, -3, 1, 3], [-13, -2, -2, 1, -2, -9, 1, 2, 8, -2, 0, 2, -13, 4, 2, -1, 2, -2, -1, -1], [22, -5, -3, 17, 9, -1, 4, 7, 1, 9, 0, 8, 9, -3, -7, -22, 0, 5, 0, -2], [3, -10, 15, 10, 12, 2, 13, 10, -8, 5, 5, 0, 5, 6, -12, 0, 6, 1, -1, -6], [14, -1, -11, 3, -1, -15, -6, 1, 7, -1, -1, 0, 2, 3, 1, 6, -3, 8, -8, 3], [-3, 8, -5, -6, -5, -3, -27, -7, 1, -5, -9, -1, -5, -20, 7, 3, -9, -8, 0, 5], [-2, -6, 8, 3, 9, -1, -8, 0, 8, 3, 6, -1, 4, 8, -8, -2, 3, 1, -9, -8], [15, -4, -10, 9, 6, -9, -12, 5, 9, 6, 3, 3, 6, -17, -5, -15, 3, 4, 0, -3], [-6, 0, -1, -2, 0, -6, -1, -2, 7, -3, -7, -6, 11, -6, 7, -11, -7, 0, 2, 3], [5, 1, 9, -16, -3, -5, 6, 5, -1, 5, -1, -14, -4, 13, 0, -10, 5, 5, 1, 3], [12, 1, -9, -2, 0, -13, 5, 4, -1, 3, -6, 13, 13, -13, -4, -2, 4, 4, 6, 1], [-2, -3, 12, -12, 2, 4, 0, 3, -17, 2, 2, 0, 5, 11, -2, 8, 3, 7, -7, -3], [10, -9, -4, 7, 8, 14, 5, 0, -5, 7, 9, 4, -7, -4, -6, -11, 7, 5, -8, -6], [-19, 7, -13, -2, -10, -5, -7, -10, 13, -7, -8, -12, -4, 4, 13, 7, -8, -8, 8, 0], [2, 1, 6, 2, -3, -11, -4, 1, -1, 0, -3, 11, 11, -5, -6, 3, 2, 2, -6, -1], [11, -5, -13, 18, 5, 4, 1, -2, 2, 2, -2, -3, 5, 4, 2, -5, 2, 0, 2, -2], [5, 5, -5, -5, 2, 14, -3, 1, -6, 5, -4, 6, -4, 7, 0, 9, 1, 5, 5, -2], [14, 0, -4, 23, 12, -17, 11, 9, -3, 9, 14, 13, 23, 5, -11, -15, 12, 11, -3, -14]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_483_q_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_483_2_q_c();".
// 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_483_2_q_c(:prec:=20)
    chi := MakeCharacter_483_q();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(997) - 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_483_2_q_c();".
// 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_483_2_q_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_483_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1, -5, 3, 7, 20, 10, 16, 8, 4, 2, 1]>],Snew);
    return Vf;
end function;