# Stored data for newform 38.10.a.c, downloaded from the LMFDB on 25 April 2024.
{"label": "38.10.a.c", "space_label": "38.10.a", "level": 38, "weight": 10, "hecke_orbit": 3, "hecke_orbit_code": 9007199422513190, "dim": 3, "is_polredabs": true, "trace_hash": 2093630468650903410, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [2320596, -40968, -3, 1]]], "qexp_display": "q-2^{4}q^{2}+(1+\\beta _{1})q^{3}+2^{8}q^{4}+(162+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3800, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 19.571361774227178, "hecke_ring_index": 24, "level_radical": 38, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [38, 1, [21], [1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 19], "conrey_indexes": [1], "field_disc": 320998773, "field_disc_factorization": [[3, 1], [359, 1], [298049, 1]], "field_poly": [85948, -4552, -1, 1], "hecke_ring_index_factorization": [[2, 3], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.883", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.747", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "273.508", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "9.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [19, 1]], "trace_display": [-48, 3, 486, -13317], "traces": [0, 3, -48, 3, 768, 486, -48, -13317, -12288, 22896, -7776, 55968, 768, 158181, 213072, 135660, 196608, -629091, -366336, -390963, 124416, -873405, -895488, -924627, -12288, -4805517, -2530896, -6711147, -3409152, -9839019, -2170560, 1364628, -3145728, -30339114, 10065456, -11097570, 5861376, -2289090, 6255408, -18481557, -1990656, -12899580, 13974480, -22378638, 14327808, 13005630, 14794032, 58896366, 196608, 22294974, 76888272, 85869585, 40494336, 8770629, 107378352, -73415802, 54546432, -390963, 157424304, 16426299, 34728960, -126843780, -21834048, -234650088, 50331648, 45269952, 485425824, -288075309, -161047296, 323371803, 177561120, 78122274, -93782016, -557941845, 36625440, 150154413, -100086528, 394013736, 295704912, -320222022, 31850496, -346127013, 206393280, 430491462, -223591680, -383428242, 358058208, -1044099345, -229244928, 437689644, -208090080, -1010450187, -236704512, -2684851332, -942341856, -63336006, -3145728, -384952146, -356719584, 2029897422, -1230212352, 189618606, -1373913360, 43147998, -647909376, -1807947972, -140330064, 2104129989, -1718053632, -568350789, 1174652832, -118221306, -872742912, 1797854514, 6255408, 2858964408, -2518788864, 4086249390, -262820784, 6126682005, -555663360, 6635573109, 2029500480, 1568353200, 349344768, -1152426894, 3754401408, -3167635998, -805306368, 8954682204, -724319232, 7071120390, -7766813184, 1735484757, 4609204944, -842767632, 2576756736, 3766825473, -5173948848, 4519636782, -2840977920, 19924788, -1249956384, 7698227046, 1500512256, -6028828044, 8927069520, 17445176430, -586007040, -10754245494, -2402470608, -11711270034, 1601384448, -23300974188, -6304219776, 2437962288, -4731278592, -11665331346, 5123552352, -21470445933, -509607936, -24037341987, 5538032208, -36299015004, -3302292480, -9963484764, -6887863392, 12183121944, 3577466880, -15856666878, 6134851872, -2983829616, -5728931328, -5933199870, 16705589520, 16508593443, 3667918848, -7443713727, -7003034304, 19297120236, 3329441280, -40915740426, 16167202992, 12215718510, 3787272192, 10540244196, 42957621312, -25580757996, 15077469696, 28013876325, 1013376096, 29144648463, 50331648, -16792426338, 6159234336, 8550078072, 5707513344, 3355570236, -32478358752, -79040265, 19683397632, -33407237403, -3033897696, 81818913045, 21982613760, -11013795084, -690367968, 33318254070, 10366550016, -7293805728, 28927167552, 2357171319, 2245281024, 44831914554, -33666079824, 4082548350, 27488858112, -44343804972, 9093612624, 53153692155, -18794445312, -81268172145, 1891540896, -6722967654, 13963886592, -40667945454, -28765672224, 31307844783, -100086528, 18973033356, -45743430528, 204131938086, 40300621824, -90615822144, -65379990240, 42732743346, 4205132544, 40187273118, -98026912080, 10796953311, 8890613760, 54374920260, -106169169744, 72296593092, -32472007680, 95902816236, -25093651200, -20614306101, -5589516288, -12677530878, 18438830304, 27742511160, -60070422528, -243915191538, 50682175968, -59486575284, 12884901888, -18206218188, -143274915264, -99645090546, 11589107712, -64517080014, -113137926240, 93884591214, 124269010944, -114006406104, -27767756112, 152376551028, -73747279104, 68854409298, 13484282112, -149400407355, -41228107776, 9907973883, -60269207568, -160876985382, 82783181568, -223446731382, -72314188512, 408734150760, 45455646720, 52824974268, -318796608, -71350381560, 19999302144, -17679346860, -123171632736, 155989383540, -24008196096, 106715978472, 96461248704, 174697999842, -142833112320, -483549147333, -279122822880, 32180279148, 9376112640, -169087830858, 172067927904, 43221515625, 38439529728, 76122262074, 187380320544, -85530451290, -25622151168, -16343219622, 372815587008, 383076411516, 100867516416, -157426087698, -39007396608, 55090592883, 75700457472, -159396145431, 186645301536, -66284381322, -81976837632, 112748487387, 343527134928, 317422358874, 8153726976, 699167938575, 384597471792, 81983768211, -88608515328, -267212815329, 580784240064, 574009839909, 52836679680, -593590118682, 159415756224, -72928333383, 110205814272, 291736197288, -194929951104, -223340113368, -57239470080, -79319725356, 253706670048, -202980601734, -98157629952, 735996908232, 47741273856, -379951420911, 91662901248, 366099712968, 94931197920, -263838678300, -267289432320, -953803594296, -264137495088, -375082472151, -58686701568, -614223460347, 119099419632, 165880301724, 112048548864, 138183941169, -308753923776, 200854251429, -53271060480, 50950689123, 654651846816, -1304549181129, -258675247872, -350950686522, -195451496160, -1027706663556, -60596355072, -538637149188, -168643907136, 986464358517, -687321940992, -388908124233, 409292127936, -398602016820, -241239515136, -466340731347, -448222021200, -909948308925, -16214017536, 1027732603770, -466314375408, -174037258026, -805306368, 663263585886, 268678821408, -1093790463246, -98547749376, -109193429592, -136801249152, -858993027849, -91320213504, 702453451788, -53689123776, 64474014168, 519653740032, 141999436254, 1264644240, 113823013005, -314934362112, 1437931885104, 534515798448, 1128425536020, 48542363136, -521149344930, -1309102608720, -477101899608, -351721820160, 1044495457776, 176220721344, 2511309687405, 11045887488, -412869368517, -533092065120, 296633444136, -165864800256, 1681258509000, 116700891648, 1074818958924, -462834680832, 2228836084977, -37714741104, 1350578849598, -35924496384, 990991835289, -717310632864, 595060185780, 538657277184, -3006650081550, -65320773600, 623952563130, -439821729792, -465592913274, 709500879552, -1080113317680, -145497801984, 120498315267, -850459074480, -313877826888, 300711124992, 466730000208, 1300290754320, -847096258248, -30264654336, 868061047104, 107567482464, 1795994814564, -223422185472, 457060825086, 650687127264, -331295684148, 460250755584, 2269178383038, -500925516528, -493931648928, 1601384448, 1330563276519, -303568533696, 1490379016383, 731894888448, 2710283212734, -3266111009376, -817552539318, -644809949184, 183828443808, 1449853154304, -4421286405588, 1046079843840, 2846770457187, -683723893536, -5026777256922, -67282120704, -3442053294486, -642996369888, 626259780957, 1568430593280, -343216968714, -172751252976, -2289256432860, -142249820160, 649530384570, -869998724160, -4483809548181, 1698706715904, 1635134780400, -1156745489472, 605701740354, 519552122880, 1189922271252, -1534445059776, -2405008204020, 401498419200, 2510459288631, 329828897616, -385281099018, 89432260608, -1610506953966, 202840494048, 4277950475922, -295021284864, -3561597000468, -443880178560, -4918892900499, 961126760448, -1253143544556, 3902643064608, -2672590662216, -810914815488, -4651492944690, 951785204544, 5404614730275, -206158430208, 874603388187, 291299491008, -373811728692, 2292398644224, -316773800826, 1594321448736, -5023531765422, -185425723392, -2585998838148, 1032273280224, 3965751291345, 1810206819840, 100694957085, -1502153459424, -6871310693604, -1988304175104, 4301245066212, 1824102497664, 1862362062414, 444284097792, -1812531823608, -2438024816448, 1574966278116, 1179956465664, 5545277214264, -1101670548768, -8779443711120, -215748513792, 2125723528320, 2390406517680, -697188221322, 659649724416, -675304744560, -158527582128, -5440221422340, 964307321088, -2409686813574, 2574031766112, 1282230795099, -1324530905088, 501010709178, 3575147702112, 1296944389128, 1157027016192, -6823162958094, -6539746412160, -3697776534120, -727290347520, 15488845821882, -845199588288, 1566412892472, 5100745728, -107722490292, 1141606104960, 5830508781171, -319988834304, 4894083713664, 282869549760, 4079910597252, 1970746123776, -7190513051385, -2495830136640, 3145736783103, 384131137536, -4377642695919, -1707455655552, -3069869069502, -1543379979264, -4258538006778, -2795167997472, 11570761487310, 2285329797120, 202713838488, 7736786357328, -2329140282750, 4465965166080, -177839685588, -514884466368, 8477234517216, -150017802240, -1498989244002, 2705405293728, 3103280572806, -2753086846464, -2321000783841, -691544250000, 11381058941304, -615032475648, 1120245833016, -1217956193184, -2795717993814, -2998085128704, 2157271303356, 1368487220640, 3325066183518, 409954418688, 12201642880479, 261491513952, 5342433731064, -5965049392128, 13059494669340, -6129222584256, -1638066731016, -1613880262656, -1632939468564, 2518817403168, -3433782913710, 624118345728, 2709083808585, -881449486128, -9002824409172, -1211207319552, 6068246840463, 2550338326896, 3953823675594, -2986324824576, -5904073376910, 1060550101152, -697439854638, 1311629402112, -18964945193139, -1803975798192, -4991687408196, -5496434158848, 1470112201986, -5078757741984, -905687312040, -130459631616, -246576304866, -11186687017200, 5532732851352, -6153559548672, 529956215076, -1311740291376, -6161584679049, 1417736245248, 1275164637414, 4275405045264, 8359985316924, -9292547841024, -7639916079918, -9184157438544, 3700470949410, -845386874880, -18061108951104, 9497441898912, -6031548281007, -2550652099584, -9952741213989, 1166853334128, 11700020359665, -1763293028352, 1446246419970, -4667779156608, -10035640645635, 3118879217664, -4576822822326, 3573441813888, -6250001574414, 915831521280, -2488723647840, 1269115605696, 10986446088063, -4059306720768, -1253667992949, 3247689627744, -14215669992498, 1570522079232, 3680238049809, -11775950531712, -3258715796796, -763860381696, 4001839413294, 6079222734576, 385080272754, -1466606419968, -11201462895, -5857595407488, 5263931390904, -1518899166720, -6479164897290, 4221418852800, 3320488224678, 4276630917120, 10878542850276, 15260857508736, -5411699302806, 4226199921408, -10982131830936, 6001319554416, 298316497890, 938987225088, 6942624039228, 9827575365552, 11482580175870, -1905590714112, -3870572999958, -2654084827584, -4406429352780, -1792776781824, 10814134001556, -2210943058704, -3186117088584, 4940062780416, -28061399075553, -3213668022864, 2581476118659, 852336967680, 2671667666382, -815211025968, 33695597804952, -10474429549056, 12644919107451, 20872786898064, -1483963472445, 4138803965952, -9765224567433, 5615210984352, 18173927418714, 3127223938560, -27054755064948, 16443306616896, 13976517420888, 969541681152, 12158307935826, 8618194387008, 11067707787642, 2698302514176, 2408534989797, -15783429736272, 15601879241580, 10997151055872, -562043302242, 6222529987728, 11063254989708, -6548674046976, -17498822368635, 6377632269120, 8975125357968, 3859832242176, 11602430253714, 7461451701552, 4828317525228, 7171552339200, -39300114563736, 14559172942800, -11895490028958, 259424280576, 29663718245133, -16443721660320, 11802697463979, 7461030006528, -220153835466, 2784596128416, 5365424449731, 12884901888, -16963990273917, -10612217374176, -16897146346788, -4298861142528, -2627008906449, 17500647411936, -4440332008692, 1576763990016, -11155388468922, 1747094873472, 1681086165180, 2188819986432, -18557341753704, 13743888445584, 20385205511661, 1461123416064, -6464563912812, -11239255228608, -32695944626001, 859025980416, -11239506744084, -1031584226688, -5219597709534, -8314459840512, -10578111368634, -2271990980064, -15803739359160, -20234307840, 56651617281, -1821168208080, -31147812893466, 5038949793792, 5719344597576, -23006910161664, -15318196632144, -8552252775168, -19278222912072, -18054808576320, -36891512345034, -776677810176, -8591475247305, 8338389518880, 23885737620045, 20945641739520, 19552615743027, 7633630393728, 2737024213752, 5627549122560, 2916406482798, -16711927324416, -18003922663122, -2819531541504, 5167931705994, -40180954998480, 30238328867601, -176734199808, 50215350074046, 6605909896272, 32066990102919, 8529473041920, -47329450584621, -4746135106176, 46741068517044, 2653836804096, -22125487763934, -26900136144000, -5868609560124, -1867214266368, -6161099741100, -17197103342784, -25714914226140, 7405354893312, 11701555289490, -35661377359632, 10029934382424, 603435857664, -3336614969910, -21609261593568, -48145502153259, 574791942144, 30793090287150, -15855869364624, 36762238149162, 11476970125824, 21930505215774, -9520962972480, -1694906707230, -8618516434944, 13100971537128, 48106401304800, -14524147491444, 1045132377600, 7194832026192, -9983241010080, 39232357922982, 7037147676672, 4758021869268, 7449486612384, -48003911757816, -11352014072832, -23129359798908, 17281813082880, -15832088221641, 2327964831744, 20834013028644, -1927973044272, 34039279376250, 13607345191680, -35325903247869, 5022045230208, 16698149493957, -4811377999872, 47314600570392, -7467680003328, -31189764862668, -20804652069120, 4095707912784, 13553540131968, 9151074215766, 484234469376, 65031841398930, -13888976753664, 31376791393704, -1721079719424, -7675433313486, -28735917033024, 10984437467748, 3574754967552, 33068366505087, -7312973201376, 5309995541220, -10410994036224, 20604069191583, 5300730946368, -39802154547060, -7364012089344, -12300323312916, -36306854128608, -4120779076155, 8014808264448, -22416369477768, 7902906382848, 11916999365364, -25622151168, 2207220843516, -21289012424304, -4440473448708, 4857096539136, -52765903885122, -23846064262128, 53460664380783, -11710318215168, 37296249176772, -43364531403744, -741587595930, 52257776150016, 8166001929270, 13080840629088, 9888783200496, 10316959186944, 72636216428781, -2941255100928, -2905503306654, -23197650468864, 10924565919495, 70740582489408, 18127911231774, -16737277501440, 57769598594139, -45548327314992, -43165363565469, 10939582296576, 21084511733577, 80428436110752, -27696756043656, 1076513931264, 22002490345680, 55072852711776, 8471698946160, 10287941918208, -65030927164659, -10020156495312, 66020718452481, -25094889492480, -57683652119682, 5491471499424, -32239247682378, 2764020047616, 96833276736450, 36628102925760, -35591817969735, 2275997122560, 68124229824723, -10392486153120, -38450694868542, 13919979586560, -29737466466144, 71740952770896, -68964301245312, -27179307454464, -11190610186785, -26162156486400, 46704027345516, 18507927831552, -35885305101930, -9691227845664, 43100384171673, -8312833966080, 6358307879820, -19038756340032, -71693799382104, 24551120956416, -92481767001630, 38480131264320, -47632262486682, -6423974707200, 24578043397116, -40167348618096, -54423511788924, -5277262361856, 19070214988320, 6164497584288, -32663920291392, -1430916169728, -70300636681089, 25768111263456, 10338152900406, -3245447904768, 48455812647090, -68447207614752, 5862702681882, 4720340557824], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "38.10.a.c", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [-16, 0, 0], [1, 1, 0], [256, 0, 0], [162, 2, 1], [-16, -16, 0], [-4439, -14, -10], [-4096, 0, 0], [7632, -72, 27], [-2592, -32, -16], [18656, -386, -43], [256, 256, 0], [52727, -204, 67], [71024, 224, 160], [45220, 319, 129], [65536, 0, 0], [-209697, 858, -564], [-122112, 1152, -432], [-130321, 0, 0], [41472, 512, 256], [-291135, -6447, -1128], [-298496, 6176, 688], [-308209, 5110, 3289], [-4096, -4096, 0], [-1601839, 2040, 425], [-843632, 3264, -1072], [-2237049, 1386, 81], [-1136384, -3584, -2560], [-3279673, -13893, -3628], [-723520, -5104, -2064], [454876, -29685, 8839], [-1048576, 0, 0], [-10113038, 33805, -13647], [3355152, -13728, 9024], [-3699190, -24136, -6301], [1953792, -18432, 6912], [-763030, 3757, 14761], [2085136, 0, 0], [-6160519, 87920, -483], [-663552, -8192, -4096], [-4299860, 13925, -15333], [4658160, 103152, 18048], [-7459546, 106246, -9441], [4775936, -98816, -11008], [4335210, 21654, -1395], [4931344, -81760, -52624], [19632122, 15016, 44215], [65536, 65536, 0], [7431658, 242228, 84492], [25629424, -32640, -6800], [28623195, -443223, -19134], [13498112, -52224, 17152], [2923543, -299391, -106356], [35792784, -22176, -1296], [-24471934, -131576, -31053], [18182144, 57344, 40960], [-130321, -130321, 0], [52474768, 222288, 58048], [5475433, -71558, 55609], [11576320, 81664, 33024], [-42281260, 143100, -21479], [-7278016, 474960, -141424], [-78216696, 113274, -61839], [16777216, 0, 0], [15089984, 113280, 27084], [161808608, -540880, 218352], [-96025103, -461027, -162254], [-53682432, 219648, -144384], [107790601, 315328, 384645], [59187040, 386176, 100816], [26040758, 583150, 105562], [-31260672, 294912, -110592], [-185980615, 492830, -464234], [12208480, -60112, -236176], [50051471, -1621984, 86955], [-33362176, 0, 0], [131337912, 2609040, 350123], [98568304, -1406720, 7728], [-106740674, 517415, 65849], [10616832, 131072, 65536], [-115375671, -896508, -487944], [68797760, -222800, 245328], [143497154, -44200, 330414], [-74530560, -1650432, -288768], [-127809414, -757656, -103821], [119352736, -1699936, 151056], [-348033115, -3364768, -647211], [-76414976, 1581056, 176128], [145896548, 2108807, 726611], [-69363360, -346464, 22320], [-336816729, -28980, -463013], [-78901504, 1308160, 841984], [-894950444, 5300098, -138570], [-314113952, -240256, -707440], [-21112002, -260642, -130321], [-1048576, -1048576, 0], [-128317382, 2792874, 1872892], [-118906528, -3875648, -1351872], [676632474, -9118206, 735579], [-410070784, 522240, 108800]]}