# Stored data for newform 14.10.c.a, downloaded from the LMFDB on 25 April 2024. {"label": "14.10.c.a", "space_label": "14.10.c", "level": 14, "weight": 10, "hecke_orbit": 1, "hecke_orbit_code": 137606725646, "dim": 6, "is_polredabs": true, "trace_hash": 1558695564656874563, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [8143799049, -894217887, 77161662, -2489283, 64198, 233, 1]]], "qexp_display": "q+(-2^{4}-2^{4}\\beta _{2})q^{2}+(78\\beta _{2}-\\beta _{3})q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "c", "char_is_real": false, "Nk2": 1400, "analytic_conductor": 7.210501706294224, "hecke_ring_index": 9408, "level_radical": 14, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [14, 3, [3], [1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [9, 11], "field_disc": -15952633299105075, "field_disc_factorization": [[-1, 1], [3, 3], [5, 2], [101, 2], [127, 2], [379, 2]], "field_poly": [4410000, -2341500, 1245325, -3085, 1116, -1, 1], "hecke_ring_index_factorization": [[2, 6], [3, 1], [7, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.845", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "157.159", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8118.542", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "9.2.3.c3", "trace_display": [-48, -233, -733, 5012], "traces": [0, 6, -48, -233, -768, -733, 7456, 5012, 24576, -15058, -11728, 7339, -59648, 197036, -142576, 738238, -196608, -306665, -240928, -377991, 375296, -1585927, -234848, -2267255, -954368, -142612, -1576288, 21348358, 998144, -13085956, -5905904, -6654517, -3145728, 3747977, 9813280, 22864807, 7709696, -22287969, -6047856, 3151974, -3002368, 68096196, 58323776, -125648280, 1878784, -86300638, -36276080, -52703019, 30539776, 57596070, 4563584, 97736333, -25220608, -12091125, -170786864, 377435398, 20529152, -158517670, 104687648, -12949897, -94494464, -160252153, 212944544, -356021666, 100663296, 334191270, 59967632, -480890225, -78506240, 1131233162, -349171760, -74421440, -61677568, 251382283, -356607504, 16322324, 193531392, -527045155, -100863168, 286494785, -48037888, -2165894587, -544769568, 2295182344, -527183104, -2389185074, 1005186240, 1412199358, 30060544, -901243845, 2761620416, 1026798920, 1160834560, 710456889, -843248304, -887366177, -244318208, 629707876, -2185885296, -1256218868, -36508672, -1615945081, 1563781328, -1163723391, 807059456, 5070999164, 386916000, -452750799, -2732589824, 566523583, -3019483184, 2029968230, -583991296, -2902798012, 1268141360, -3362009009, 1675002368, 2521438332, 414396704, 6273543017, 3023822848, -3743856130, -2564034448, -906484782, -1703556352, -8210714634, -7485405536, -10835319952, -805306368, 8035885700, 5347060320, 14171442749, -1918964224, 12731837125, 15388487200, -12662698277, -1256099840, 4414225175, -9049865296, -11591523272, -266642432, 387767538, 595371520, 14828388750, -986841088, 20466023918, -8044233056, -9270812789, 11411440128, -2335945581, 261157184, 9664354171, -1548251136, -59265093140, -19809947584, -4476620634, 806905344, 5692101987, 4583916560, 26447429409, 1537212416, -11147483347, 69308626784, -7293762459, -8716313088, 7698505943, -18361458752, -42232225672, -6495956992, -9474054710, 19113480592, 24027296254, 16082979840, 9960750767, -45190379456, 8776807620, -961937408, 22758501061, -14419901520, -3588491253, -22092963328, -11988128572, -38612594272, -9760366794, -9286676480, 14884847857, 11367310224, 24045869129, 26983945728, 108019576028, 28395717664, -13823401659, -3909091328, 18967732143, -5037663008, 4194050700, 20229570816, -90319496948, 10049750944, -20693380269, -584138752, -21694971107, 51710242592, 5659232488, -50041002496, -16911183534, -18619574256, -110011656530, -6456475648, 153317879138, -52480112944, -41428844760, -3095328000, -33579592624, -7244012784, -25179298700, 87442874368, 41105293565, -18128754656, -66325289231, -48311730944, -76733156514, -16239745840, 256393069296, 4088397824, -17465561936, 23222384096, -15536188509, 20290261760, -53792850389, 107584288288, -9907824563, -53600075776, 48583759591, 40343013312, -7192510029, -3315173632, 66744989370, -57499236928, -4580917896, -24190582784, -91661705613, -59901698080, -165043375280, 82049102336, -151060955017, 29007513024, 68866638106, -27256901632, -49339399900, 65685717072, 359395747200, 210908035072, 9670432946, 86682559616, 110956128011, -12884901888, -168686719353, -257148342400, -179439708245, -171105930240, 274099648268, 226743083984, -38510704761, 15351713792, -278968307082, -756712208, 277123314654, -123107897600, -70230438301, -202603172432, 106272863321, 40195194880, -6960399726, -141255205600, 129142619684, -144797844736, 117581900187, 92732186176, -544753176276, 93654249472, -72148148396, -3102140304, -6110173925, 9525944320, 111436577069, -474508440000, -135538373544, 31578914816, -25221248200, 327456382688, 349966414546, 64353864448, 373582655460, 341946167584, 534170180030, -91291521024, 70265307131, -37375129296, 47173340298, -8357029888, -579067645520, -309259333472, -372615273203, -24772018176, 149910572457, 474120745120, -833291148200, 451882721024, 524497548698, 35812965072, -267467637985, 12910485504, -242207878589, -182147263584, -111443235050, -146685329920, -62839895073, 423158870544, 637955295046, -12297699328, 131387852298, -193590446224, 142595085434, -554469014272, -196544992840, -116700199344, 3689623429, 278922018816, 67035210417, -246352190176, -139738167195, -293783340032, 84607639306, 337857805376, -27813127954, 238894186496, 1086855688532, 75792437680, -351156454142, 305815689472, -205151316291, -768873480128, 43478549660, -514655354880, -771824175547, 159372012272, -69551131689, 361523035648, -893359449668, 182796671232, -67879262724, 7695499264, -217304050833, 364136016976, 67112024704, 461436848640, 698089104265, 114831720096, 44882376437, -353487413248, 229468062606, 95905028576, -1443943943428, 354940984832, -476310130474, 78082934352, 236365655895, -148586823680, 248036852532, -476315131424, 908600302701, -363753927168, 649200438295, 384733906064, 705411905991, -215871565824, 1937975935224, -1023411567472, 1573250192176, -227165741312, 719605091880, -221174426544, 120313070509, 125090922496, -659362416916, -606967428576, 1051315833160, -80602608128, -1899212200729, -33552405600, -1411877340934, 235913502720, -2429773687694, 722555975584, 392300127735, 160796015104, -1190125907437, 662188168608, -569171654996, 18692440064, 582471079095, -347119537712, -237978455330, -413681940736, 3407145748394, -1106017409504, -1694418013618, 400328019968, -68157134649, -270578936544, 470767162861, 595826376192, -370939747367, 3520373008960, 244029223396, -103303610368, -1560852201860, -1226543033104, -1172613483720, -458493978880, 1256301868316, 331430758080, 700399048086, -49525248000, -444636250012, 1074546963968, -793002490861, 231808409088, -269025101310, -402868779200, -1419639222957, -699542994944, 5267259012708, -1201734347968, -3576688685828, 145030037248, 251240240669, -1061204627696, 303170571797, 1545975390208, -1169993199466, 2455461008448, -853523177399, -259835933440, -1595050216443, -2051144554368, 879249503646, 84087406592, -685193587276, 139724495488, -947533880118, 371558145536, 1696966754569, 497158032288, 2821969932390, -649288376320, -352236194573, -860685606224, 2591281503599, -860674306304, 5698869755516, 378593943280, 443885030944, 428800606208, 798883975191, 777340153456, 1646265914645, -1290976425984, 1285330107537, 230160320928, -419144180551, -53042778112, -3297066188620, -533959914960, -1611112438424, -686039221504, -13637659401060, 36647343168, 315217850239, -387049324544, -2062817278466, 2933174579616, 7297760285788, 1916854338560, 434386273538, -2640694004480, 3044867547543, -656392818688, -3787221694750, -1980187938064, 119262197136, -232060104192, -3298218773210, 1101866209696, 4741822410406, 872220852224, 3364322085824, 1578860796800, -3297416086955, 1050971473152, 647955600964, -2875165977600, -8691566259264, -1458264743936, 3384475810958, -77363463568, 2855885706161, 1386920953856, 1810877540523, -3550596096352, -1255949516115, 412316860416, 1496002216025, -2698987509648, 2263916585527, 2057186739200, 1821692994426, 1634101978768, 7098625082854, 1368847441920, 1825871992467, 4385594372288, -894273203199, -7255778687488, 525981917524, 1232342552352, -2912119661127, 245627420672, 881653121930, 2231746456656, -11034182289796, -3247242908672, 237958645512, -2216986517232, -539898587769, -1969726361600, -437751331575, 2247374025632, -2235666964433, 6483301517824, 1356381900779, 1700365813136, -790502599782, -321561559040, -5323757376514, -778034167680, 9733699606832, 1130041644800, 3647009292762, 2066281914944, 3814486722946, 4633531031552, -5565441891835, -3762620805984, -2033491889749, 1483714978816, 345859149023, 4358025410208, -11394488865200, -1430207528960, 2512273182346, 577185187168, 7300403411215, -49634244864, -7005191614606, 195525565600, -4225909161509, -304830218240, -1149517163421, 1782985233104, 5090026810235, 3796067520000, 5974241163474, 1400302285536, -962952713368, -252631318528, -6593135469629, -403539971200, 10821698212229, -10478604246016, 1117406740016, -11198925265472, -2044860552003, 1029661831168, -5694126288060, -2988661243680, -19382163386936, -3097810607360, 8478631750306, -4273361440240, 4137036787334, -1460664336384, 7509578381055, -2248489828192, -10236261712012, 1196004137472, 7017561452225, 754773444768, 6866183862975, 66856239104, 18536233474164, 11658317218240, -3137162972260, 2474074667776, 4235707136626, -5961844371248, -9565477620067, 792704581632, 7478975013482, -4797138318624, -1311239206494, 7585931921920, -1152960286657, 6666329185600, 3431478948324, -2158776954880, -6186490842044, -4195980389584, -14671545439553, 573007441152, -19573898816383, 8558964415520, 3590787204711, -413135536128, 10102487498303, -3875326057424, 944575867573, 1457178108672, 12402998888486, 20537702674048, 32149939780320, 1173482639360, -14721165304108, -1005438321168, 4870385281752, -13541083857408, -13527093028372, -20414569441472, -8726734589120, -196763189248, -309287781485, -1051102818384, 18688800106872, 5951202876416, -25092972101560, -1140760683472, -2722559309409, -8871504228352, -21531909410135, 6289439770880, 3056895280509, 3734406379008, 6560750487231, 59033974864, 8566890072491, -2231376150528, 39360851166524, 2429434696752, -7578156497144, 1970817521408, -12311842722797, -2235810675120, 278255781762, 9401066881024, 5071638243665, -2707444457792, 13389184895890, 5405724886016, -13727704560472, 222505023632, -8252114963298, -2159341993984, 2895824253684, -8694845508256, 887023077692, 1212679002880, -7406287111557, 11237006532544, -29117532146472, -9786102063104, 1338970239105, -3282421060656, 1113739800099, 6150987841024, 32684889397262, 9465547874384, -19674199161746, 4117242839040, -4934356576842, -12349186808752, -16644096887619, -5099904392704, 13700602974296, 2225636214048, -10310084585668, 5784368570368, -4601642706822, 7146875597344, 6549672099302, -5171609490432, -4066480589740, 543034101792, 1407657141651, 123127988224, -1259198705367, 6953729626656, -5992909504295, -11652352543232, 12817120275711, 1073792395264, -11923090328610, -3691494789120, -6083447320878, 6500772301744, 30506186127900, -918653760768, 18189400615284, 718118022992, 21396975278457, 11311597223936, -35701442162603, -7342978003392, -19876176495271, 1534480457216, -8787845113448, 11551551547424, 10489741671808, 4205768376320, 28968587681438, 3810481043792, 7999528036580, 1249326949632, -9881426818513, -7563700988640, 26661695472958, 4754778357760, 2539953775489, 3968589640512, 7289820242771, 3810521051392, 3772056856596, -25965556029504, 3982012273440, 2910031417344, -2923825614579, 10387207012720, 4552665933928, -12311484994048, -17198355363, -22573180991712, 22200659113349, -3453945053184, -26486865258840, -15503807481792, -70591632461626, -11278426383616, -7999585642708, -12586001537408, 6820394401861, -3634651860992, 11208163897807, -23027362940160, 6148806089265, 7077581649408, 9131910514822, 1925009128144, 23926522055814, -1000727379968, -12888791482028, -8555399056624, 25220414688774, 4855739428608, 26505667026935, 16821053330560, 946526756228, 2579283460096, 16440230796556, 60774790423328, -13929768182610, -536838489600, 15304142850128, 11295018727472, -105727052206868, -8953386172416, -12637485718490, 19438189501552, -5608201849273, 11560895609344, 8091447259653, -12553604087520, 669945018904, -5145472483328, -15356499612818, -19042014518992, 33878875290423, -5297505348864, 2693179817244, 3498123323632, 23045235347250, -149539520512, -22765492376190, 9319537265520, 37673084645149, 11107825206784, -13688462972695, 7615310570560, -421345419143, -6618911051776, -15513461176693, -27257165987152, -26879586338360, 16247515035136, -83716434351798, 13555344108944, 25957455878947, 6405248319488, -18141758664900, 2181028308768, 51081321625068, 8658525969408, -11605817137877, 7532274605776, 35577425004607, -4766611009536, 5246845079176, -53467164820160, -4754727832920, -28162984071680, -25523006230577, 3904467574336, 38191898927345, 3305715531776, 49808725531075, 49947270459520, -24104832669652, -19624688529664, 11416752939387, 9380907869760, -9701613906320, 20770812575744, 64354512055082, -10050414946528, 18938719412042, 5302892129280, 47099514511429, -22412769538752, 17555242515678, 1584807936000, -58164838988807, -7114180000192, -9315452270029, -8596375711744, 6472996385436, 17120324866064, -80395070377796, -1854467272704, 17934008564715, -4304401620960, -16885092405879, 12891800934400, -9284016575274, 45428455134624, -7034165824207, -11192687919104, 2439167380001, -42138072101664, -6392220016624, 8704794414848, -69408154656030, 28613509486624, -22034619599594, 2320480595968, 91038296037332, -8039687701408, 4001306423268, 33958548086272, -26292965090837, 4850729148752, -28172093190486, -12367803121664, -6103393753044, -56589480785824, -71609420562360, -19643688067584, 34133273590795, -13656370838384, 1339796065533, 8314749870080, -17017433163808, 51041606926176, 15967066805371, -32818312869888, -19707134384943, -7033996029168, 22073462856582, -2392028348416, -7977104592492, 5481548698208, 4785626483382, 2235591927808, -59189967859503, 30321084163776, 49589150873500, -11889860657152, 52392524865954, 27151468073104, -14975517963865, -3977264258304, 140394972315212, -37169306304480, 6411865266336, 5194307010560, 15984562760852, -5635779113168, 1371400548531, 27541939399168, 9141665492449, -82921008115168, 21649036094773, -13770788900864, 25895509848796, -45590958044128, 21635999110656, -3521100004352, 23276570462584, -3551080247552, -45571961987906, 6860809699328, -28657112192133, -25564287206112, -51839255863731, -24874884910592, 9811023140221, 26340254634320, -77229399585889, 10327811407872, 41780855166876, 1826704848192, 56908000041358, -1841282567424, 51443788203323, -6706306888816, -16497046175106, 1697368899584, -69570281598937, 105506118035840, 54051280963613, -8543358639360, -23018108010170, 12888899507392, -24518047276986, 25696432197632, -19391343136076, 109101275208480, -27654337031421, 586357490688, -29829220270342, -10086971207648, -55825189339031, 12385578385408, 35496140282266, -33005076455456, -10212232719954, -23465396636928, -36480358842434, -67999256502800, 18211359659232, -15334834708480, -19456068737447, 6950180376608, -51902227127259, 84502208143360, 104631415747152, -97435761521376, 2957192808360, -10502285099008, -53920496693361, 30297773558000, 89063471767302, 70354611493376, 9098646832364, -954097577088, 89285132535051, -3712961667072, 7024002367414, 105543000742720, 21947853480588, -35259718710272, 60364444208060, 75869158566496, 24568646522031, -6977766817792, -130325170838398, -45920600658688, -115117151633354, -12630886374400, -73205909874477, -52758657391280, -54615090014305, -33631087140864], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "14.10.c.a", "char_is_minimal": true, "conrey_index": 9, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-16, 0, -16, 0, 0, 0], [0, 0, 78, -1, 0, 0], [0, 0, 256, 0, 0, 0], [-246, 5, -246, 5, 2, -1], [1248, -16, 0, 0, 0, 0], [134, -31, -1423, -1, -3, 8], [4096, 0, 0, 0, 0, 0], [-5103, 251, -5103, 251, 2, -1], [0, 0, 3936, -80, -16, 32], [0, 0, -2475, 86, -51, 102], [-19968, 256, -19968, 256, 0, 0], [32789, 151, 0, 0, 73, 73], [-24912, 480, -2144, 496, -80, -48], [123471, -1294, 0, 0, 13, 13], [-65536, 0, -65536, 0, 0, 0], [0, 0, 101526, 2087, 145, -290], [0, 0, 81648, -4016, -16, 32], [-125285, -2136, -125285, -2136, 686, -343], [62976, -1280, 0, 0, -256, -256], [52791, -579, 635823, -5954, -173, 151], [-39600, 1376, 0, 0, -816, -816], [-758040, 6865, -758040, 6865, 312, -156], [0, 0, 319488, -4096, 0, 0], [0, 0, 47494, 130, 626, -1252], [-524624, -2416, -524624, -2416, -2336, 1168], [3567735, -29026, 0, 0, -233, -233], [364288, 256, 398592, -7680, 2048, -1280], [-2185725, 14197, 0, 0, 3387, 3387], [-1975536, 20704, -1975536, 20704, -416, 208], [0, 0, 2210729, 22330, -729, 1458], [0, 0, 1048576, 0, 0, 0], [1251999, -8020, 1251999, -8020, -2008, 1004], [1624416, 33392, 0, 0, 2320, 2320], [2636136, 60385, -2319945, 32614, -1775, 5452], [1306368, -64256, 0, 0, -256, -256], [-7425827, -10488, -7425827, -10488, -8004, 4002], [0, 0, 2004560, 34176, -5488, 10976], [0, 0, -1052889, 6693, -1163, 2326], [-1007616, 20480, -1007616, 20480, 8192, -4096], [11338167, 33597, 0, 0, -4477, -4477], [9328512, -86000, -844656, 9264, 352, -2768], [-20962888, 64524, 0, 0, -14236, -14236], [633600, -22016, 633600, -22016, 26112, -13056], [0, 0, 28849059, -246539, 18155, -36310], [0, 0, 12128640, -109840, -2496, 4992], [-17543715, -71874, -17543715, -71874, 7862, -3931], [5111808, -65536, 0, 0, 0, 0], [-2320038, -181783, -23931530, -85274, -14007, -26789], [759904, 2080, 0, 0, 10016, 10016], [32674131, -286060, 32674131, -286060, 1046, -523], [0, 0, 8393984, 38656, 18688, -37376], [0, 0, 3866913, 490386, -2500, 5000], [-57083760, 464416, -57083760, 464416, 7456, -3728], [62775900, 389999, 0, 0, 15916, 15916], [548864, -126976, -5828608, -4096, -12288, 32768], [-26480103, 181474, 0, 0, 8310, 8310], [34971600, -227152, 34971600, -227152, -108384, 54192], [0, 0, 4156638, 479983, -97084, 194168], [0, 0, 31608576, -331264, 3328, -6656], [-53318603, -296344, -53318603, -296344, -45308, 22654], [35371664, 357280, 0, 0, -11664, -11664], [-131462955, 1095139, -143825463, 910603, 107026, 53857], [16777216, 0, 0, 0, 0, 0], [111244863, 456681, 111244863, 456681, 153942, -76971], [0, 0, -20031984, 128320, 16064, -32128], [0, 0, 160205648, 273281, 10814, -21628], [-25990656, -534272, -25990656, -534272, -74240, 37120], [189196938, -1974233, 0, 0, -4057, -4057], [-79297296, -444336, -42178176, -966160, -58832, -28400], [-12174294, -687838, 0, 0, 63998, 63998], [-20901888, 1028096, -20901888, 1028096, 8192, -4096], [0, 0, -83252491, -1624810, 160486, -320972], [0, 0, 118813232, 167808, 64032, -128064], [5470626, -89554, 5470626, -89554, 22276, -11138], [32072960, 546816, 0, 0, -87808, -87808], [-254287791, -1207305, -333233190, -1396631, -35918, -199901], [-16846224, 107088, 0, 0, -18608, -18608], [95137612, 1081949, 95137612, 1081949, -309752, 154876], [0, 0, 16121856, -327680, -65536, 131072], [0, 0, 723195342, -3691439, -5149, 10298], [-181410672, -537552, -181410672, -537552, 143264, -71632], [382307766, 667874, 0, 0, 74126, 74126], [-162770688, 1524224, -149256192, 1376000, 38656, 5632], [-398372985, 526418, 0, 0, -351908, -351908], [335406208, -1032384, 335406208, -1032384, 455552, -227776], [0, 0, -472486995, 5261627, -46769, 93538], [0, 0, -10137600, 352256, -208896, 417792], [-300776163, 1084644, -300776163, 1084644, 486272, -243136], [461584944, -3944624, 0, 0, 290480, 290480], [-40023767, 174867, -421551452, -1937432, -495453, 503839], [194058240, -1757440, 0, 0, -39936, -39936], [237325281, -1518954, 237325281, -1518954, -70904, 35452], [0, 0, 280699440, 1149984, -62896, 125792], [0, 0, 294681606, 3321359, -176630, 353260], [-81788928, 1048576, -81788928, 1048576, 0, 0], [102649241, 6906215, 0, 0, -385911, -385911], [-345783872, 1544144, 37120608, 2908528, 652736, -224112], [-209746629, 1130453, 0, 0, 993781, 993781], [-12158464, -33280, -12158464, -33280, -320512, 160256]]}