
// Make newform 1148.4.a.c in Magma, downloaded from the LMFDB on 04 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1148_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_1148_4_a_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_1148_4_a_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 := [1052740152, -569503386, -2124774315, 672972471, 982943895, -348573059, -96527282, 35401830, 4412670, -1445580, -102669, 28413, 1158, -270, -5, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-37, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [44138218007337133013346446262, -65434904745517893150538905654, -62806101168914843344353670275, 47665182954874774728312792378, 9330511050063895544158597707, -5587014936965800368946069683, -763387222452186575710634392, 233912723074358892673746989, 28607481575866901506310163, -4450629361249791897050810, -511101505131867399986276, 39587463852203404619001, 4291131082125502820078, -134262495291840228778, -13622912474971399956], [733242000996118228383112453164, -874879429687146001663684418160, -481885643369410677241320882762, 419489028798624830328046143192, 95602963325917735716235548393, -45285848499092055402642499616, -9781018569157059526361248833, 1706577216876084445328237763, 411271182357027927862696464, -27359494068305348135776587, -8094591585063448566843333, 181944799186480706904942, 75673306425678721896450, -348332091334274366193, -273432019016249898692], [725880438666290591239900380588, -828658438053862450764304845900, -621453911610180945240307270134, 731066261925307094454333628116, -29909001805826592169239289020, -81282213498693936668978614311, 6781257160364484286373431430, 3562689049462135773766657627, -325372257173627021784336715, -74977992534945396286269524, 7006680453647712466197221, 759930105270878273749381, -71730952784437306089016, -2983092663920387191166, 283855363951690047383], [505937798243852077184991055272, 601796637454815972364829896386, -708560329860923775109486679835, -537609195600467695103990032911, 276274496779639579991491622493, 65191491900212442678033218054, -26241828435397127818542591081, -3333792694527777547593009915, 1051928033583551751266345424, 82273480924339770014179107, -20722172978429459780556828, -959852772538466414942769, 199586679777962533749465, 4238301525158444487300, -754144851620270508298], [468844118229791537342086632300, -646443201785361368117062145004, -682771364381250203314730848668, 440473446592566984372967900308, 130797456822156654471428351577, -52861793688895276593482512465, -12213406888079773747860415417, 2151246055355070756210718496, 489742630075623631524457317, -38460790609888507406070155, -9267948176054550930482978, 311403397523757426196827, 82842365527249854387092, -925786818083763211159, -283197980211650914843], [-53672549436987310516704205104, 100046256239382042873657916296, -30690132233017795411223573217, -101303439053291389389947851377, 51725230554203357070507663291, 10168945713139654092929281986, -6138610428646496058723034883, -515023913982728712280061901, 265418658689424038611279346, 13365101121547537054966493, -5338178657010763159147098, -163621156832708417655449, 51071665416094782947971, 747207209175065060736, -188754145191725828602], [1209019898117190310452857610792, -1050284586304304497574687927376, -1487186936896453987576312839024, 679364010749791013293422124974, 329507977168207567369550705919, -82945679084211790823207684719, -31305697690505169702677740621, 3218372898160810785597865942, 1258968121625952266999481929, -51723319313068345493119571, -24025605319374577083138622, 342244037629480246857313, 218086567993712173651832, -656406606345772289801, -762277040752562776673], [-813783375292297716359750523924, 2332702108702836419562169318602, 362025594376758449046803893203, -1886458414780988505266225644278, 426810417627613986701369761026, 200411456893899168261310659301, -51108719147565034931643164941, -9118169602306886638941114350, 2188911357298631841166909001, 205608292001315816727726673, -44064718347839815708881331, -2241836420922993298039037, 425599098845448067437734, 9401916128147702795161, -1596552392454558885744], [-8278655037263187317118294638472, 2402268938277411603031743478734, 10340486489535288421558206958083, -2141533569601682409135597034743, -2488319243602894107286285714584, 297315836052656009429998871065, 228648067694836347978804504918, -10743607637907724678023833163, -8996748914118652439580081375, 131641389168262586378053260, 170344878119657024194208328, -244548024922891668792822, -1548097536858679736041731, -3179366445402845795991, 5449895643720661482133], [438100329665858200986974195736, -3675219784391619608951555672868, 2356660776197240580523952920518, 3323821807683475741080755957475, -2375583368419942847835370172040, -286013927663580669350882565196, 278652755441659375037034007947, 15169991290747674121539439635, -12003308454213016083930059928, -435573120510405710226519633, 240445960714641899627863485, 5782078358679871696760751, -2290729012492720032835893, -27961582974984248342796, 8433540705207814361759], [4934775671306317877270482552752, -516926130672238956412569336564, -9305548590917618991097089862698, -74552225354556382682120666997, 3709245860508424051386076863207, -106602834719614431446391913703, -394446594147699120351870569052, 739001894419481134301129295, 16449573618603459603799859967, 152890044776736368547613998, -322487755003499360392760013, -3506977133364958509638412, 3011740121870294001725535, 21228407248513082849427, -10865467859215986817970], [-1645896201131900076467588632188, 4126822530115145118142430833920, -2051301060829868803395460817436, -5120382354085924295618740276323, 3058884975958352760235370182338, 472008402059591069441666488180, -360563208416264355843648853695, -23914838541505108559757047991, 15500346002351590895976829020, 645107090212589325503393037, -310085524713649014024305715, -8203935942286157489830983, 2952835807634121021654201, 38609964212747199135780, -10872310162566410243681]];
    Rf_basisdens := [1, 1, 1, 884285865897565381062592302, 7958572793078088429563330718, 2652857597692696143187776906, 5305715195385392286375553812, 1768571731795130762125184604, 884285865897565381062592302, 2652857597692696143187776906, 5305715195385392286375553812, 15917145586156176859126661436, 15917145586156176859126661436, 15917145586156176859126661436, 15917145586156176859126661436];
    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_1148_a();"
function MakeCharacter_1148_a()
    N := 1148;
    order := 1;
    char_gens := [575, 493, 785];
    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_1148_a_Hecke(Kf)
    return MakeCharacter_1148_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 := 4;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 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], [7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [8, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [17, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [-2, -1, -1, 3, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0], [2, -4, -2, 3, 0, 0, 0, 1, 1, 0, 0, -1, 0, -1, -1], [10, -6, 0, 2, 0, 0, 1, 1, 0, -1, 1, 1, -1, 2, 1], [20, -11, 1, 1, 1, -2, 0, 1, -2, 1, 2, 2, -2, 1, -1], [-41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [64, 0, 4, 4, 2, -2, 1, -3, 4, -1, -2, 1, 3, 2, 2], [6, -7, -2, 1, 1, -1, -2, -2, 1, 0, 0, -3, 3, 1, -1], [-26, -1, 0, -2, 1, 2, 0, 0, -1, 0, -3, 2, 0, 4, 2], [-2, -4, 2, -1, 0, 2, -1, -4, 2, -3, -2, 2, 5, 3, 1], [94, 3, 3, -9, -1, 3, 2, -4, -3, 2, -1, 1, 1, 2, 0], [4, -7, -10, 2, -1, -2, -3, 4, -3, 3, 5, -2, -3, -1, -1], [92, -1, 3, 12, 0, -2, 0, 1, 3, 2, -1, 3, 2, 1, -2], [93, -27, -2, -18, 3, 3, 1, 2, 2, -1, -2, -1, 2, 3, 1], [108, -9, 12, -15, -3, -2, 3, -6, -5, 3, -3, 8, 9, 11, -3], [128, 6, -2, 12, -8, 3, 1, 4, -2, -2, 2, -1, -8, -9, 0], [148, -26, -17, -7, 7, 4, -2, 6, 2, -2, 10, -5, -4, -10, 1], [84, -38, -4, -14, -7, -1, 3, -1, -1, 3, 5, 3, -3, 4, -3], [321, -53, 4, -22, -6, 12, 1, -4, 5, 1, -1, 2, -9, -1, -6], [218, 41, -4, -23, -5, 6, 5, 2, 2, -1, -2, -4, 3, 1, -4], [136, 6, -16, -9, 5, -10, -6, 16, 0, -1, 10, -8, -12, -10, 4], [41, -10, -10, -18, 5, 2, 1, 0, 6, -3, -6, 7, 6, 5, 7], [159, 9, 8, 4, 1, 6, -1, -13, 10, 5, -4, 6, 15, 5, 1], [326, 96, 7, 14, 2, -3, 0, 3, -1, 7, 0, -7, -6, 2, 0], [181, 110, 0, 16, 6, -1, 0, -3, 2, -2, -16, 9, 12, 9, 0], [144, 5, -26, 22, -23, 7, 2, -9, 4, -11, -5, 0, 5, 5, -4], [573, 45, 13, 7, 2, -16, -3, 7, -20, -2, 2, -1, -9, 12, -8], [415, 21, 4, -4, 0, 3, 6, -36, 8, -13, 2, 0, 10, 0, 10], [458, 49, -42, 60, -2, 2, -8, -7, 15, -7, -6, -18, 5, -19, -12], [713, -27, 8, -49, 0, -11, -14, 1, 3, 9, 1, -3, -20, -19, -4], [601, 118, -8, -10, -7, 1, 9, -3, -6, 10, 13, 2, 0, -12, -7], [459, 83, 19, 46, 1, 19, 3, -14, -7, -2, -15, 10, -7, 19, 7], [144, 130, -29, 10, 3, 4, -5, 8, 8, -1, 7, -8, 9, -11, 1], [-257, 41, -42, 106, 3, 0, 0, -9, 4, 1, -4, 10, 13, 1, -2], [576, 52, 15, 44, 17, -13, 24, 12, 5, -19, -1, 17, -1, 8, 8], [12, 52, -15, -31, -3, 4, 0, 12, -3, 14, 5, 3, -5, 26, 10], [134, -106, -59, 71, -1, -6, 15, 13, 20, -19, -13, -16, 34, -30, 6], [-161, -28, 21, 24, 18, 20, -15, -6, -6, 3, 1, 6, 9, 5, -5], [450, 142, -40, -51, 4, 4, -20, 3, 0, 1, 11, -12, 27, -20, 11], [261, 99, 23, 47, -4, -4, 23, 0, -30, -24, 0, 15, -6, 25, 1], [184, -11, 1, 37, 2, 33, -2, -13, 3, 1, 8, 29, 12, 7, -14], [280, 32, 9, -35, 8, 23, 21, 11, -4, 21, 49, 8, -42, -16, 5], [895, 79, 4, -103, -33, -2, -24, -15, 15, 1, -1, -13, -20, 1, -30], [-488, -187, 24, 23, 18, 25, 19, 6, -22, 7, -3, 7, -12, 31, -6], [-88, 50, 56, 101, -3, -6, -7, -30, -24, 2, -6, 25, -32, 23, 3], [425, -67, 13, -58, 6, -8, 6, -15, 49, -15, 7, -19, 10, -17, 8], [709, 301, 15, 66, -2, -23, -45, 21, -17, 23, -7, 0, 14, -32, -24], [293, 162, 51, 69, 11, -6, 18, 10, 2, 31, -9, 9, -57, -10, 15], [932, 52, 58, 50, -17, -17, 13, -53, 19, -5, -10, -11, 31, 22, -5], [-867, -112, -70, -51, -6, -38, -30, 46, -8, -13, 8, -48, -18, -44, 4], [280, 129, 46, -76, 17, -21, -10, -27, -11, 15, 10, 44, -25, 51, -1], [1076, -252, 150, -103, 10, 23, 11, -13, -49, -12, 5, 26, -14, 66, 7], [-654, 249, 8, 104, 1, 9, -10, 37, -35, -11, 26, -16, -15, -11, 17], [946, 37, 28, -79, 3, -45, 9, -49, -36, -12, -11, 24, 26, 4, 5], [-113, -153, 13, -38, -5, 43, 49, -26, 12, -30, 2, 23, 70, -27, 22], [1221, 311, 12, -62, -29, 36, 30, -30, -16, -27, -19, -15, 27, 40, 10], [108, -90, -68, -92, 23, -20, 25, 17, 47, -35, -34, 4, 65, -43, 9], [-478, 151, 21, -152, 3, -42, 34, 48, -51, 0, 28, 7, -62, 19, 41], [-1013, -219, -46, -22, 2, -5, -25, -37, 43, 2, -8, 11, 65, -36, 4], [1156, -283, -122, -153, 3, 43, 21, 109, -28, -6, 39, -30, -72, -106, 25], [-1778, 122, -39, 74, 6, 106, 26, -22, 3, 17, 0, 56, 16, 38, -16], [599, 41, 22, -3, 41, -51, -42, 2, 25, 46, -30, -18, -36, 18, -14], [285, -229, -113, -44, -8, -19, 9, 3, 37, 17, 20, -33, -35, -56, -13], [-1725, -289, -24, -79, -44, 23, 14, -65, 56, -35, -51, -5, 22, 55, -6], [1311, -224, -22, -97, -25, 36, -26, 8, -11, -10, 13, -3, 30, -36, 23], [322, -103, 18, -164, -29, 53, 41, -78, 21, -10, -49, 5, 72, 23, -20], [216, 17, 40, -193, 26, 59, -15, 45, -56, 45, 13, -20, -50, 30, -19], [-1688, 380, 36, 4, -20, 30, 26, 28, -25, 24, -15, 29, -81, 46, 14], [736, 437, 106, 132, 56, -32, 2, -39, 26, -11, 31, 9, 10, -1, 12], [-682, -239, -37, 53, 36, -7, -39, -5, 53, -22, 15, -96, 51, -58, 20], [-1092, 645, 66, -31, -31, 70, 24, -43, 23, -12, -68, 45, -34, 9, 18], [-1345, 32, 77, 330, 2, 43, 40, -49, -17, 14, 13, 86, -89, 58, 13], [-2261, 154, -160, 235, 15, 42, -24, 24, 33, 50, 18, 12, -38, -60, -12], [987, 609, -99, 111, 27, 21, -56, -6, 30, -15, 10, -69, 7, -36, 15], [-2433, 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452, 200, 221, 154, -179, -457], [-29320, 4271, -956, -37, -252, 557, 144, -247, -101, -216, 271, 54, 29, -769, -232], [2891, 4569, 1121, 869, 11, -253, 104, 245, -1081, 89, -158, 322, -13, 327, -2], [36015, 4833, -1172, -404, -184, -536, 289, 155, 490, 69, -531, -724, 593, 96, 578], [-13090, -8640, -645, 468, -561, 1019, 296, -595, -162, -11, 81, -149, 44, 105, -192], [-13966, 5567, -101, 591, 363, -860, -44, -575, -439, -663, -413, 482, 199, 1289, 354], [4801, 5163, 99, 1457, -330, -179, -94, 177, 212, 404, -110, -154, 153, 377, -456], [19797, 1104, 1275, 75, 116, 653, 624, 212, -390, 39, -369, 287, 741, 290, 162], [15914, -1140, 703, -1202, 287, 24, 462, -363, -137, -447, -135, -384, 21, 676, 570], [6487, -780, 478, 1148, 462, 9, -471, -584, 614, 245, -471, -662, 615, -523, 31], [24702, -7990, 880, 359, -176, 474, 235, 696, -405, 455, 597, -28, -929, 177, -172], [6958, 4867, 1388, 834, -78, 48, -733, 84, -390, -352, -435, -2, -199, 551, 23], [-1543, 1878, 592, -1694, -67, -306, -1, -152, -597, -207, -201, 181, 296, 199, -342], [5412, 249, -363, 1605, -276, 350, -348, -460, 606, 54, -168, 69, -141, 648, -352], [39502, -4515, 495, 2297, -243, -1218, -88, -227, -216, -359, -197, 452, 459, -95, -78], [-7919, 1373, -1435, 1014, -374, -789, -372, 788, -364, -463, 399, -556, 150, -883, -407], [19355, 2594, -968, -2103, 475, 75, 37, 1220, -247, -192, 201, -368, 313, -861, 113], [2037, -6995, 844, 1898, 176, 526, -355, 237, -912, 931, 331, 400, -735, 856, -530], [23545, 3597, 917, 2957, -350, -379, -181, 351, -118, 271, 47, -208, -486, -610, -139], [13688, 405, -197, -1847, 55, -590, -628, 540, 282, -465, 196, -774, -78, -1114, 208], [5991, 3385, -1597, 3267, 80, 1558, -321, 91, -230, -222, 526, -257, -757, -16, 224], [18780, -2840, 989, -352, -383, -286, 63, -278, -1035, 140, 55, -73, -919, 434, -356], [3883, -1689, -480, 12, -698, -445, -53, 141, -497, -188, -137, 340, -196, 476, -791], [-3408, -2848, -200, 166, 77, 83, -664, -710, 592, -700, -25, 1, 272, -84, 100], [15421, 1483, 160, -842, 255, 662, -293, 381, 394, 435, 644, -28, -269, 103, -373], [22065, -306, 512, -277, 510, -121, 709, -95, 359, 211, -344, -363, -465, 538, 477], [12105, -2438, 119, 1185, -27, -157, -45, -724, 489, 283, -434, 713, 4, 869, 27], [7776, -6253, -1541, 2103, -352, 163, -700, -29, 132, -57, -338, 26, 925, -113, -336], [16297, -6092, 582, -535, -72, -12, -95, 456, 343, 244, -276, 209, 6, -959, -485], [-6165, 1990, -891, 821, 233, 1218, -961, -16, -173, -230, -64, -445, -250, 457, 153], [27989, -4293, -1058, -1550, -61, -204, 39, 957, -485, -332, 575, -522, -1856, -990, -30], [-16363, 886, -1372, 312, -289, 798, -527, -583, 503, 78, -76, -470, 183, -77, -173], [37107, -1700, -487, -1135, -221, -1114, -591, 45, 453, -398, -279, 65, 578, -172, 186], [6959, 5169, -702, 1531, -566, 1399, -570, -87, -144, -511, -112, -511, 310, -1047, -229], [22959, -3354, 987, 357, 7, 280, 910, -622, 277, 121, -457, 69, 123, 658, 812], [-5818, -2767, 1193, -2049, -27, 133, 189, -349, -21, -551, -625, 1, 45, 1022, 518], [-18195, -3340, 1032, 1351, -55, 719, 481, -794, 289, -299, -542, 643, 1221, -8, -350], [23348, 2078, 944, 1533, 115, -512, 232, -568, -501, -303, -381, 356, 352, 1326, 193], [-19613, 7788, -96, 2588, 683, -503, 766, 82, -250, 153, 150, 1050, 52, 446, 199], [-9188, -233, 1438, 3885, 71, -143, -19, 175, 160, 508, 293, 266, -1258, -388, -419], [-28148, -1989, -310, -2942, 644, -505, 481, -127, 236, 682, -88, 284, 839, 1005, 427], [17853, -3218, 2225, -1682, -100, -17, 104, -387, -913, -245, -677, 615, -84, 965, -186], [17698, -112, -1254, -393, -52, 493, 251, 452, 88, 442, 827, -398, 469, -723, 471], [2301, -2767, -2473, -756, -97, 792, -16, 378, 866, -379, 280, -437, 555, -307, 469], [-32643, 8234, 991, 1906, -32, -849, 353, -126, -2, 347, -491, 319, 603, 94, -419], [9936, -9304, -553, -726, 658, 251, -769, -97, -14, 479, 413, -202, -48, -492, -271], [33995, -5927, -470, 581, 41, 2, 164, -831, 311, 173, -792, 72, 1691, 377, -112], [22362, -647, 151, 1992, -218, 430, -514, -225, 9, 588, 259, 51, -364, 331, 132], [4683, 8100, 1061, -460, 730, -606, -199, 316, 204, -355, 123, 250, 207, 259, 77], [-32526, -6147, -1623, 2119, 283, 683, 228, 350, 498, -700, 9, -696, 102, -238, 452], [20819, -4434, 699, -2803, 163, -336, -726, -578, -695, 449, -489, 231, 1239, 210, -678], [-10715, -9123, -1159, -2041, -284, 815, 169, 370, -471, 1247, 108, 95, -414, 177, -174], [-23979, -3628, -228, 1205, 296, 151, 42, -296, -680, 30, 359, 513, -695, 1046, 580], [24624, -954, -306, 449, 377, -894, 575, 445, -407, -616, -101, -282, 388, -224, 394], [-14329, -1563, -1195, -3053, -505, -788, 372, 885, -99, -140, 224, -506, -277, -417, -382], [24529, 6765, -4806, 1437, -215, -85, -77, 653, 420, -725, 314, -647, 693, -1870, 352], [5596, 760, 1330, 2006, 668, 22, 58, 415, 68, 298, -335, -467, 244, -201, 144], [5006, -6646, 919, 1461, -606, 162, 569, -1120, 835, -363, 7, -401, 320, -362, -258], [-12441, 761, 741, 705, -356, -923, -388, 31, -299, 164, -179, 168, 635, -875, -733], [-13984, 9698, 944, 1270, 697, -1226, 175, 256, -157, -126, -150, 302, -1131, 273, 19], [18406, -1037, 1035, 212, -54, 978, 173, -841, -599, -67, -558, -359, -1103, 988, 195], [24289, 6086, -2165, 1085, 218, -173, -123, -317, 803, 340, 376, 474, 110, 400, -314], [12246, -8789, 474, -2992, 67, -947, -283, 203, -540, 8, 793, 248, -1780, 188, -19], [60971, -353, 1517, 136, -197, 621, -206, 298, -646, 167, -458, 814, -220, 264, 478], [-45255, -202, -277, -2832, 156, -1256, -1286, -88, -565, 726, 11, 356, -661, 64, -210], [30223, -3982, 361, 528, 144, -525, -20, 867, -1235, 273, 269, -179, -1546, 351, -38], [22516, -3444, -1025, -487, 313, 1340, -308, 226, 267, -464, -255, 58, -654, 452, 503], [-21269, 3482, -835, -2197, -30, -1069, -965, -231, 748, -498, -410, -749, -1300, -1120, -180], [-3815, 4321, -848, 1690, -556, -457, 313, 129, -531, -546, 307, -564, -1310, 256, 119], [27095, 1272, -386, -1115, -210, 617, -386, -290, -96, -564, -269, -523, 605, -274, -588], [-5582, 1740, 2535, -3300, -418, 1166, 465, -285, 278, 242, -172, -33, -611, 1056, -63], [30825, 2864, -583, 1750, -491, -388, 614, 41, -401, -203, -263, 225, 1074, 347, 19], [-13685, -4708, 1979, 1959, 417, -1030, -98, -256, -1386, -101, 71, 648, -1580, 1752, 412], [21179, -3552, -813, -1799, -25, -579, 660, -501, 492, 238, -550, -268, 683, -145, -469], [28282, -2455, 251, -1614, 147, 929, -461, -510, -328, -193, -475, -421, 1178, 935, 94], [2767, -1704, -1173, -1339, 194, -417, -732, 290, 193, -491, 11, -173, 1069, -910, 511], [9956, -4424, -1763, 1136, 21, -1004, -538, -657, 208, -204, -119, -656, 1101, -415, 19], [31033, -6953, 879, 1162, 560, -848, 904, 129, -126, -571, -371, 141, -738, 829, 656], [31519, 5976, 1218, -1511, -238, -749, -3, -517, -197, 815, -240, 739, -99, -74, -91], [30873, 279, -2238, 1762, -527, 1455, -1195, 711, -818, 491, 970, -177, -182, -796, -528], [2765, -522, 889, 3340, 658, -805, 1136, -3, 711, -382, 634, 1196, 560, -18, 290], [24000, 5176, -992, 1737, -620, 859, 306, 172, 717, -1207, -383, -289, 385, -550, -114], [-6248, -616, -2, 56, -430, -374, 180, 148, 389, -586, 357, -819, 1017, -1380, 26], [-1297, -9542, -2398, -210, -615, 703, -732, -375, -115, 751, -387, 137, 130, 193, -748], [3326, 4530, 26, 824, -615, -1637, -541, -1045, 503, -167, -123, -1088, 278, -462, 334], [10377, 1476, -876, -3138, 396, -166, 92, 290, -136, 613, 3, 352, 878, 1000, -382], [15209, 2314, -1288, -1131, 71, -635, -460, 547, -32, 750, 1311, -361, -1257, -1858, -300], [1344, -3321, -916, -814, -703, -773, -627, 230, -412, -284, 215, -1374, 1856, -1039, -792], [38789, -7349, 730, -383, 107, 117, 228, 2, 75, 372, 1000, 228, -1938, 302, -4], [9249, 7323, 398, -1996, -199, 3353, 357, -332, -397, 595, 335, 300, -463, 107, 187], [23759, -7271, -12, 2076, 130, -85, -527, 1181, -1002, 771, 808, 616, -593, -853, -800], [12969, 6658, 322, 1676, -136, -493, 332, -791, -49, 186, 185, 607, -1252, -147, 577], [-1001, 5652, -824, -224, -356, -606, 193, -451, 94, -966, -260, 1170, 1040, 708, 204], [2657, -4730, -145, 2477, 501, -1205, 1102, 367, 838, -480, -320, 854, 69, 969, 221], [1027, 681, -756, -762, 235, -520, 294, 104, -239, 339, -418, -475, 577, 264, 775], [9744, -554, 360, 1964, -292, -1004, 376, 340, 796, -282, 176, 26, -842, -108, -6], [24416, 3702, 3781, 1365, 595, 1476, 457, 59, -240, 599, 186, 587, -763, 992, -137], [-24432, -159, 2141, 4921, 7, -1834, 52, -309, -350, -355, 41, 30, 1113, 207, -338], [-15623, 4008, -2787, 422, 496, -336, -251, 981, -652, -429, 47, -800, -22, -176, 761], [27290, 3120, 1405, 257, -697, -964, -609, 111, -905, 629, 361, -1362, -1506, -746, 266], [49706, 2450, 2249, 3360, -376, 822, 649, -379, 116, 606, 36, 223, 901, 320, 81], [45939, -707, 1393, -289, -527, 1271, 825, -1187, 429, -209, -251, 340, 281, 1357, 11], [25872, 1324, 897, 2608, 196, -512, -283, 303, 340, 418, -460, -65, 1101, -172, 537], [9748, 5985, -1893, 2581, 478, -759, -94, -658, 916, 685, 773, 83, 847, 404, -90], [-33025, -4715, 63, -2877, 125, -900, -32, 5, 102, 764, -655, 305, 806, 1157, -12], [14566, 2523, 731, 3446, -211, -1689, 451, 1077, -1282, -535, 572, -175, 383, -148, -525], [39911, -4543, -704, -973, -493, 638, -100, 705, -1449, 723, 641, 505, -1322, -159, -40], [22312, -5774, 1383, -696, -630, 1286, -1227, -1005, -732, 380, -70, -392, -656, -50, -3], [11097, 8349, -2593, -6798, -219, -690, -193, -107, -173, 596, 50, 10, 1437, -839, -703], [-12680, 12388, 819, 1213, 442, 447, -156, -260, -1020, -628, -1221, 530, 800, 2140, -29], [-14872, 12270, -2590, 3320, -604, -1002, 524, 750, 254, -850, 434, -598, -365, -948, -84], [16351, 5511, 342, 1235, 97, 237, 104, -824, -1397, -570, -946, -270, 6, 1630, -552], [47452, 2743, 853, -2787, 614, -1152, -8, -52, 685, -36, -257, 123, 2645, -600, 165], [-65495, 6344, 906, 2834, 843, -1833, 509, 561, -242, -520, -889, -252, 704, 1134, -217], [-73354, -8339, 8, 264, 384, 430, -819, 388, 3, 94, 546, 164, -267, -901, -10], [21877, 2268, 2099, 1637, -138, -619, 877, -1363, 1260, -268, -478, 403, 756, 1138, 72], [-23259, -3023, -1073, 2272, -323, -1207, -861, 1872, -1670, 896, 1277, 340, -583, -2389, -817], [-10081, 1820, -1655, -665, 794, 1, 887, -161, 948, -200, -1029, 151, 1465, 724, -118], [30468, 3377, 786, -3054, -787, 1444, -458, -1714, 983, -954, -179, 196, 1956, 924, -778], [-39674, 1029, -1188, 3039, -585, -761, 84, 59, 385, -311, 515, -45, 144, -573, -122], [-21229, -3299, -2151, 2655, -279, -64, -919, -902, 1049, -387, -335, 356, 99, -1375, -14], [-41090, -3132, 1177, 587, 498, 390, -757, 558, -1264, -401, -1340, -286, -10, -2, 214], [-9318, -1437, 2451, 2382, -46, 837, 746, -1530, -767, -50, -126, 823, 228, 2295, 381], [33824, -1636, -1345, 424, 285, -470, -381, -1059, 338, 5, -660, -161, 733, 342, -497], [356, 4263, 2434, -169, 610, -1256, 720, 1525, -1414, -278, 706, 295, -2781, 932, 124], [9717, 518, -581, 1948, 95, -147, -890, 1280, 441, 16, 326, -922, 830, -1408, -434], [-9871, 3617, -1772, 4658, 236, -908, -504, 557, -1195, -54, 116, -432, 79, 353, 166], [32703, -2530, -2350, 994, 152, -778, -1128, -240, 932, -439, 681, -781, -1112, -1900, -57], [-56930, 4794, -261, 1491, 409, -755, 240, 217, -790, -1085, 319, 659, -868, 295, -448], [-50794, 2021, -1509, 7270, -583, -611, 752, 101, 1119, -878, -1258, -392, 1115, 671, 264], [11875, 4707, -4821, 2790, -154, 320, 593, -266, 1343, 118, 679, -820, -61, -2825, 137], [9271, -2313, 948, -2922, -614, -2333, 219, 1181, -415, 180, -199, -504, 968, 252, -711], [-3452, 1597, 211, -2209, -877, 1183, -149, 656, -272, 1025, -481, 1092, -1449, 5, -423], [20869, 5701, -223, -3704, 111, -1119, -691, 2, -400, 994, -1626, 911, 832, 957, 18], [-60636, -4109, 2431, 466, 684, -1441, 265, -110, 81, 556, 565, 206, -739, 27, 741], [-3051, 9772, 62, 1528, 1294, -1012, 997, -381, 1291, -84, 45, 236, 745, -98, 449], [46674, -699, 16, 793, 807, 1194, 272, 258, -279, 1072, 631, -763, -405, -278, -240], [-61, 10436, 443, 2747, -278, -955, 984, -786, 1088, -99, 291, 1493, -251, 142, 243], [7386, 3411, 441, -667, 272, 3785, 378, -235, -245, 865, -218, 535, -594, 775, 184], [-13970, -6463, 91, -6785, 180, -293, 373, 793, -629, 112, 777, 234, -1373, -292, 746], [-21435, 1266, 446, -779, 787, 296, 547, 157, -744, 1235, 351, 569, 879, 1922, 730], [-4757, 7760, -1510, -428, -785, 296, 210, 1317, -276, 169, 1128, 46, -1933, 64, -200], [9173, 5269, 2343, -673, 405, -1370, 328, -389, 1101, 692, -1404, 66, 2125, 173, 52], [-50627, 3917, 2914, 8167, 106, 659, 880, -2523, -42, -855, -1171, 1503, 1900, 2021, -166], [21893, -14209, -774, -6596, -1118, 665, -63, -127, -413, 1224, 261, -228, -1450, -1434, -319], [28097, -8626, 3585, -2020, -321, -1362, -545, -428, 708, -144, 99, -854, -1075, -873, 659], [4219, 219, -2955, 6100, 83, -955, -1725, 1332, 102, -444, 46, -1009, -1792, -1695, -156], [45635, 5049, 1425, -1099, -281, 458, -955, -536, 1099, -555, -763, -244, 1536, 477, 254], [-39913, 1750, 839, -4801, -357, 203, 1924, -785, -821, -347, -716, 613, -73, 1086, 472]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1148_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1148_4_a_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_1148_4_a_c(:prec:=15)
    chi := MakeCharacter_1148_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 4));
    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_1148_4_a_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_1148_4_a_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1148_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<3,R![392425976, -920987876, -1670116586, 545760711, 853830440, -131515024, -145574546, 16161411, 8312370, -852850, -207080, 20794, 2352, -235, -10, 1]>],Snew);
    return Vf;
end function;