# Stored data for newform 45.10.e.a, downloaded from the LMFDB on 27 December 2024. {"Nk2": 4500, "analytic_conductor": 23.17661262737429, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [45, 3, [11, 37], [2, 3]], "cm_discs": [], "conrey_index": 16, "dim": 34, "has_non_self_twist": 1, "hecke_orbit": 1, "hecke_orbit_code": 275045679149, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "45.10.e.a", "level": 45, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 5], "level_radical": 15, "minimal_twist": "45.10.e.a", "prim_orbit_index": 3, "related_objects": [], "relative_dim": 17, "rm_discs": [], "sato_tate_group": "9.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "45.10.e", "trace_display": [-16, -285, 10625, 9946], "traces": [34, -16, -285, -3840, 10625, 1635, 9946, 38772, 7959, -20000, -32881, 595719, 100272, -333129, -157500, -292740, -103174, -401577, -1954002, 2400000, 846540, -603517, -2528832, 2610864, -6640625, -11356132, 13389570, 1233322, 4997116, -2246250, 7154764, -3848138, 37701447, -1842211, 12432500, 31228485, -29485864, -27825985, -48378006, 12116250, -1432577, 645597, 30233475, 172245706, -4490625, -38739414, -51256132, -273587937, -97033283, -6250000, 191039205, 170396546, 198356324, 65145240, -41101250, -446494149, -442487301, 199102621, -163581061, 110338125, 263506344, 682090404, -131178564, -504872168, -62670000, -888863958, 624947419, -77685671, 1347472386, 208205625, 520490800, -150538482, -1740248610, -479177876, 12890625, 1071379103, -777961272, 2208863298, 847184266, -365925000, -455780961, -2343238688, -663595350, -1445250609, -32241875, -1041586195, 945629148, 1122086037, 729648408, -437745000, -2090033068, 157159431, -150985728, 3068174993, -610625625, 1273538655, 186406391, -1334731394, -3426367056, 3000000000, -531400980, -4666468287, 1047131618, 5197432578, 1360923750, 10331191748, 5857569810, -7608189420, -1941785116, 377198125, 4533320814, 5058949747, 4151798246, -6107570481, 1580520000, -26825501410, -3133304340, 5793660062, 6186476202, 170105625, -2647356564, 12487882985, -7348278222, 793505422, -8300781250, 9316433394, -8554260060, 5112123294, -1071441597, -3548791250, -1379305860, -12477164511, -3812136628, -9876011436, 5893183125, 13720836090, 2395512531, 8034790203, -2628490879, 385413125, -7642335972, -21258014192, 5431029608, 33675667899, 6246395000, 6984533627, -9206365590, 11278435428, -69266942, -2042578125, 11523295200, 10985001846, 15688502391, -28037346852, -4471727500, -24598888224, -3669868540, -5871891972, -7784537874, 2405086250, -41043056004, 103886307045, -12988587556, -2960725768, 7300089375, 7267437099, -15228725106, -14278466016, -10290809883, -2302763750, 82593776325, -88098011098, -46692527382, -146364307983, 3885156250, 14492234383, -34031977668, 67500713499, 100142402492, 10833673125, -52264189132, 28663675350, -79454974764, 46673284683, -9214332500, -79821700902, 67849085627, 115411359910, 102948839946, -34782481250, -20693939594, -157090773030, 42810874439, 2638052191, 24106890000, 81027015485, 65365562520, 262990881165, -61747795212, -7572656250, -121466211966, 134730319722, -79618844226, -5481852336, 895360625, -38200822784, 137563378902, -405695144356, -65209782109, -49022595000, 163266814538, -53738284412, 80249640918, 178161388878, 37791843750, 330335154288, -325319511880, 87330368149, -214961325171, 53826783125, 3732281192, 28438798836, 177602552882, -199375359942, -5915625000, -711086023180, -41650569011, -426378475692, 127925211418, -12106066875, 58957300566, 281889755949, 115118323974, 505351526250, -64070165000, 279903967321, -234835349778, 548885507136, -33959330170, 48755538750, 200084567139, -535007227238, 4882068855, -879283601098, 60645801875, -452982835254, 325458741436, 31817134050, 203177809800, 3906250000, 37732542858, 953080573239, -810104532108, 76510541855, -63021881250, 472294036636, -61523822751, 4152180096, 564593637674, 212995682500, 206850332022, -729531698868, -380494789742, -670402885977, 61986351250, 538716290604, 42556471812, 861655401994, 219637597928, 18575730000, -955616308620, 111424234117, -241314325164, 623484086325, -12844140625, -1143695845350, 533869653394, -299675632274, 554048495874, -558117686250, 253643439372, -1115136251433, 187136147278, 353247659768, 181857150000, 613287082892, -188701288824, 757962275091, -806699663628, -124439138125, -751750710819, 796062921623, -271221392622, -993106579953, 102238163125, -775613287032, 1410409995849, -745567965938, 24452182134, -163741406250, 694810418408, 41004421160, 362170930356, 825191120411, 329382930000, 3637887984894, -2076109160322, -485017178382, -1393574012388, 213153251250, 355134029916, -1083838594698, 417121706195, -140860520444, 34011585000, -1825797301832, 87365173048, -2068418792730, 917390590612, -157772552500, -1080999672345, 1533943588263, 2084232496934, 3710753684775, -78337500000, 177764421628, -1179288230484, 1161644328678, -302806777446, -39878480625, 508037623780, -228800724126, 1302629003304, -2767799629014, -390592136875, -3209222406375, 655901720265, -1520056562460, -1112689308024, 48553544375, -106363171620, 5325431608326, -1920226749664, -515228847225, 79417451250, 1924824901722, 39980263505, -425215493511, 1215357510990, 260257031250, 4405709836026, -2068168140218, -712773648795, -2920583981625, 162653375000, -179516337417, -2076583162356, 1088726485262, -495606922908, 319942513125, -1830906200424, -182037702215, -2188536563520, 1160719799390, -543827690625, -1662766043319, 472213889554, 3567101413170, 2909939375697, -598972345000, 523410986796, -4475951570646, 1133445679314, 1581915399791, 69580078125, 3833410840725, 1007313510040, 658775988495, -1919492411382, -669611939375, -3734596916124, 2573389022200, -1475981442990, -721083360735, 486225795000, -6353135552702, 1889313729276, -2998546556790, 496377039702, -165195978750, -181932927288, 995528700795, 2780238528108, 1100682546252, 1058980332500, 5777221419591, -4817310880728, -1773585912784, -2932450940124, -114351562500, 1799391386217, 343070312544, 2944341746588, 3157286270364, -1164648690000, 299523272262, 2126154035152, -2385221517459, 2579551288697, -732262090000, -867114911907, -237460095696, 262763121624, 905464715031, -829494187500, 981095334226, 46133412156, 1977537008825, 3289087342, 1848070659375, 3128209992666, -211606479980, -1976247400146, -12998666568672, 20151171875, -592746443466, 3690001669568, -2190233566326, -348197915796, 650991371875, -3125709982608, -747849468600, -2674007917182, 2068791795492, 99641887500, 1336674871665, 2652649089678, 7743908000859, -715588809018, 1402607546250, 3717341822949, -4015296245440, -2232876237219, 4869025391376, 228015127500, -2520149744819, -3761194471866, 1058483834923, -2407275761338, -116724609375, -5304600754910, 2824865163214, 2138885726082, 2271288705055, -653135333750, -652187066445, 3215108611251, -1598490046038, -951868270908, 196449288750, 4246787457402, 1591609414050, 697362318394, 3399597268433, 172212941250, -4625191991265, -8302750731362, -8880813129126, -4188000596860, -1917609370625, 2756693429424, -4522542269409, 541058963405, 10849513239954, 381641015625, -1441045993248, 660747400338, 1812514703708, 2519816037258, 315535599375, 1995028488084, 1210547989772, 2790822021192, 2392014789103, 233007988750, -5390429773779, 7030865581064, 2962297633017, 156678487368, -417103560625, 5042654060905, 55075010487, -3468966684854, -5959889102992, -1497026746875, 5058279181492, -2152500272532, -164118804219, -4523656412277, 937500000000, -6822337058658, -2477682541527, 12080615327404, -4978104292161, -664251225000, 662358639708, 7407482539671, 314742597323, 1718492844542, 259635980625, -2781410671972, 5878771225652, -7277825147688, 23571045517998, -654457261250, 1414089294891, -7758578917552, -7226237725488, -9187419992094, -3248395361250, -8256630900518, -9808690544364, 3798915120072, -6864962032878, 519897656250, -12897670584836, -5504785220538, 640256610186, -8155787882015, 12913989685000, 5538216045027, 18466521572984, -944760405116, 1603917533106, 1830490565625, 6504734025360, -6308282392296, -3468147992533, 3334255418278, -2887848877500, 18736216680844, -6745449047380, 10775297622606, -14983372234901, -606807848750, -677313608256, -4184647952565, -11612642944146, -4161453884646, 471497656250, -3226789946660, 11871014104143, -13879771488556, -5931031458258, -1752779598750, -18194595116199, 4888219778640, -13699055986650, 20117706740488, -3161843591875, 6257736168477, -4885423798089, -420396514521, 13312337622369, -2594873903750, 17532508262946, -1646418592476, 62647209611928, 10693174481889, 4466180686875, -6009026714125, -7799568771476, 1765104726288, -30095074826013, 1975650000000, -24694692232236, 18052453371494, -10977379914041, 12555051119478, -8382969190625, -9343868185830, 5636696831694, -11998104820942, 7971767387478, -2641506982500, 38259444663660, -5083036093101, 23629319356659, -5477044437742, 1810518769375, -3296052202140, -10032246048876, -2205465839156, -27459777843909, 7733095252500, 8563735865669, 20930410408620, -19992449116230, 3040952393872, -913552734375, -13045922410741, -19641335554656, -8138131168833, 10362342562304, 1654597852500, 15254411032386, -17376638832660, -6976053387539, 15390386890686, -7804926865625, 12993914459228, -41470870787499, 2469424171260, -121160262640, 4059241906875, -9438342609246, 7244648107041, 4676116680024, 5009915017001, 991881777500, -43076847203532, 70190441549484, 12186678479574, 26997553228938, -2593994140625, 95054690803, -12634745085363, -19410387423978, -34486376437472, -3799726936875, -4882248435756, -13593784376304, 28003698806688, -31201913646098, -2673206268750, 6366760226586, -5682185045672, -7914527101808, -39972669803580, 6390154117500, -1860734531457, 33058884625245, 2105137960237, 33627576322059, -8801254340625, -8715195551023, 44955071723804, -55686187682442, 36958234946762, 2217994531250, 58857338704338, -21176631562212, 24221382588658, 28799422207716, 862066162500, -30481663078408, -40762447178811, 47632218083610, -14299895351608, 14456641623750, -14622847024944, -15349557257958, -12412141095348, -29244404865753, -4765170785000, -46922790960768, -23067425562156, 28663368781335, 27849661069494, -3086253573750, 10058455525832, 7033500685359, 3607920161014, -3781670124382, -1547061328125, 82494838762968, 1049323133088, 12693072064674, 2367195967016, 4287761278125, 38368905940497, -34353911004522, -52291721066646, -49636547396625, 2994390663750, -7479153501003, 45750175355448, -20012360862799, -7117697934340, -4279903756875, 9343601957016, 52555629063324, -41406845072508, 3128380116386, 1642806799375, 38420892035838, 26524227947347, 32482898109767, 1481869162035, -240883203125, -11062147220864, -50545878142896, -2387847158640, 28439901849167, 10314962216250, -41844249829257, -26459037217512, 19570922786235, -6986467879428, -26572517740000, -57706316208864, -11564172694854, -4233981065676, -38947514555232, 1697196752500, -36163296189722, 6122051948880, -20913500041728, 32755635429912, 6084852442500, -24715507908832, 10624050333951, 31120731219381, -10893827466915, 1951998437500, 54732792245523, 13739512808, -48684365615100, -14714951995026, 8730667033750, -26725949856253, 56674056565221, 2454725780, 13437741367824, -18664391724375, -33055868358573, 17557564405986, 60369303719544, -9752561170974, -7049022142500, 14179923876780, -33029365519206, -30874067129764, 68654755960236, 43291838750, 37826172258824, -20673022935456, 575386941442, 26877916116786, -399169921875, 22940987902734, -21326751969179, 8157478346361, -13972485000842, 14404119000000, 2164322021976, -2485059808596, 59526033930821, 4535951943672, 3432813076875, -24990743290872, -15744092900394, -228769180408, -39511208689648, 21101794085625, 77158633686672, -82228008902908, -111454763203089, 26633063260532, -8761670891250, -9120604855752, -32383087370829, -12461779437660, 12772911623745, -5589659375000, -9689352564315, 52641255266928, -29613141880491, 15917568234409, -46471229486250, 29320457119558, 168372795506436, 42292677712824, 29479479935966, 2293667837500, -51722839238022, 20751006996018, 58508557500108, 20695635074604, 3669932482500, 35034700044312, 70629404725080, -2711079381608, 7183518128546, 20899210162500, -14906900843584, -71016886976840, -31309943099436, 41460809993198, 3006357812500, -46727229124080, 20764152302934, 3627492775841, -129308088890637, -12825955001250, -520266346632, -86834616670950, -8344448615382, -14857982295482, 64964112030000, 569990690254, -50283779301687, -48175869669504, -36745919187716, -4058933611250, 17887727499429, 30268589448343, -149385106799258, 1890846413622, -3700907210000, -39356194927098, -90335549881116, 41906781735452, -4623677179296, -10164571875000, -15126281560350, 144222558742832, 198582262535925, -119527002221564, -4542148186875, -15820028193366, 5696729176674, 69266653211503, 81036875693283, 9517953191250, 36858805896742, 40385779750746, 10265387278588, 9289636915120, 23619017435625, 46595439095811, -21627477020236, -138892296043692, 41658568638846, -12863512353750, 132878069854122, -113227447983668, 24258656299132, -20233339714890, -719613671875, -55938181067406, -119259038587842, 69181304059120, -87056434158570, 27357694783125, -56748895637016, -2408085449470, -224116420241136, 68512368267333, -27530628468125, -24163677075834, 13880423895426, -2752271699372, 89962664318226, -58365659227500, 20945668878341, 95489602762722, 51059469935084, 82271933717298, -59629421426250, 55819883527334, -30830204721666, 133839397619430, 84584178854292, -2428222656250, -137339355782772, 76815548175910, 51154580252858, -62386019764398, -9057646489375, 61437229633520, 213619354674261, -213012373230550, 67091151385984, 7827372766875, -42412226887602, -66229891121916, 76334591320020, 50908599898430, 84375891873750, 66428741539917, -123251256360930, 81107168985080, -283935067764987, 31294500778750, 77414350029243, -106175725709436, 31932560762405, -205114758487884, -5427581250000, -231598046889556, -119932994964473, 88756069450842, 105223422356058, -16332559103750, 109088035699194, 116731198015591, -99970062385726, 75249544927284, 35829594187500, 13205218630658, 25387655907135, 101459941093188, 109928735831993, -102884753966250, 12248790640039, -41286413618400, 68048451225387, -329953618427220, -29170802926875, -36820561593435, 63963106443345, 13124800523464, 212128733848968, 5758957812500, -58076650041600, 82594642402968, -149495500887946, 62926614991690, -20952860782500, 194451703088155, -158370907678749, -23075753963580, 104609991006583, 84811357033750, 145943847215676, -100360777364876, 78677140147365, 15433485968973, 36066049971875, 54846813637858, -54046592538330, 141801380420850, -326940995662826, 42951223350000, -314374553820526, -72452922595575, -249784849327248, 156610922308168, -10869525390625, -151515229838424, 192232970366304, -176381863746550, 17344978482594, -25867424492500, 7485482815858, 151200426234276, 13144734305736, 50279244942948, -62420602134375, 149623010945383, 323673891345280, 38685464157717, -48273148937896, -26756796524375, -484804621554840, 93185207483636, 171936118540395, 26579192889513, -1648782619375, 163487550080244, 106469234072253, -394984144146520, 140454073578526, 33964464843750, 123282070355573, 32522731769879, 362395984432872, 263844886923708, 101283769356250, 76445151438858, -105517650990554, 42124735437174, -583463646997245, 20426738287500, 53748696849310, -454678606301940, 77464074080568, -262042260964188, 44190496027500, -187885807743808, -181706498642190, -165120682331340, -34129222104762, -19296186003750, 113157387961227, 153415596236446, -58830399518446, 206095245969024, -9465820312500], "weight": 10, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_cutters": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}