# Stored data for newform 19.8.a.a, downloaded from the LMFDB on 25 April 2024. {"label": "19.8.a.a", "space_label": "19.8.a", "level": 19, "weight": 8, "hecke_orbit": 1, "hecke_orbit_code": 134217747, "dim": 4, "is_polredabs": true, "trace_hash": 841420501517287312, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [3240, -396, -234, 9, 1]]], "qexp_display": "q+(-2+\\beta _{1})q^{2}+(-4-\\beta _{1}-\\beta _{2})q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1216, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 5.935315484198314, "hecke_ring_index": 6, "level_radical": 19, "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": [19, 1, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [19], "conrey_indexes": [1], "field_disc": 688233996, "field_disc_factorization": [[2, 2], [3, 4], [937, 1], [2267, 1]], "field_poly": [500, 475, -255, -1, 1], "hecke_ring_index_factorization": [[2, 1], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.819", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "40.625", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "675.799", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[19, -1]], "trace_display": [-9, -14, -222, -1246], "traces": [0, 4, -9, -14, 37, -222, -603, -1246, -3555, -4898, -6444, -8718, -6281, -4480, -1935, -2760, 19393, -4440, 52722, 27436, 81228, 34124, 115182, -30528, 90135, -23906, 28521, -74942, 37439, -254244, 11340, -303460, -49059, -362364, 240309, -563862, -153410, -270460, -61731, -270304, 230868, -828564, 728307, 37454, 38874, 146694, 1909269, 335670, 1366243, -67560, 815013, 1047318, 1737887, 76728, 775215, 1008918, -973953, -96026, 1613565, -3191334, 669180, 346550, -4678848, -24766, -1917383, -4512972, -2532006, -270322, -9125409, -1452456, 235836, -2066124, 3929670, -416044, -8358894, 5984890, 253783, -3350514, 1418859, 16025864, -622428, 2742268, 7006752, 8524128, 1508165, 4323186, -9139572, 10085136, 4902930, 2899092, 10474488, 23189218, -24380829, 12902348, -9682776, -1522698, 514647, -4766908, 10655118, 25556322, -25161881, -21936864, -1102113, 6248864, -28854153, -16928400, -33750063, -22023810, 23557381, -11304496, 19753416, -17540632, 14387483, -35005440, -4135977, 8009244, -38137125, 7697816, 70637085, -43226718, 7288380, -12744674, -11584098, 9557040, 6673640, -65617878, -20528226, 60946820, 70585605, 49872992, -10188324, 45582618, 21905526, -8546314, 52534017, 21472140, 107682039, 5954640, -40543281, -2693554, 74615028, -86912292, -29021778, 9497508, -83286818, -121518432, 120733479, 27999300, 187210046, -135585726, 57840255, -26403520, -24383745, 4539678, -67315374, 165711768, 18092381, -279797956, -31555350, 17950728, -90169740, -144932742, -161231049, -29002708, -155312016, 55616580, -117588402, 258961500, -108226755, -438738, 73395612, -33595382, -61381180, 25701948, 127731735, 261224984, -216928518, -101486886, 128064960, 61541028, -164258016, -132178132, -79456473, 66736220, 252610011, 254703300, 126463824, -7376166, 506701536, -24096016, -44199396, 119271882, -128130197, 343475480, 334257498, -105758220, -302021718, 111395052, -127932156, 1527002, 47481399, -306120310, -471704778, 504315462, -40916667, 248167980, -267954930, 200042064, -28282861, -59796762, -46725660, -174743494, 351111063, 332040408, -787832757, -94403658, -172586475, -246078020, 72270855, -196298110, -400294512, -588929352, 8114022, 183042392, 379881711, -121276628, 7184970, -261352050, -43081379, -273954310, 283534668, 168651960, 225981315, -239796966, 9643086, 149598666, -480596433, -156271432, 253383651, -102727398, -170894580, 196672748, 77494743, 545826652, -7794982, 33229044, -43935696, -30728320, 726822360, -54872952, 539944344, -134808054, -79278070, 504873324, 446486886, 163208160, -439617887, -536035284, 437585364, -100532312, 709412748, 62610252, 392862132, -546412986, 241551990, 692000820, -13272165, -126962268, 337588187, -60736728, 67467060, -733487536, -31947933, 572755750, 604382625, -672430776, 6827337, -397525522, 144027000, -80939296, 8233308, -412433004, -350912088, 236312858, -613873614, -18930840, -17954622, -1072197876, -8769978, 101329168, 374539356, -942715444, -697124491, -151141584, -79181334, -293439600, -932276610, 939656424, -220349880, -1278829710, -155308235, 632610886, -825768018, 217045428, 133016587, -729029694, -824711274, -165579544, 1860414, 1044586892, 444320496, -1275760938, -333174555, 1698694502, 1257465690, 1130840214, 683160326, -1501954932, 360261459, -619437816, -34654236, 910691838, -138389733, -30453960, 690576229, 1369037384, -2267863128, -386038216, 2741963040, 622529382, 344389320, 506966306, 1312004658, 330830708, -242014860, 1176537012, -848448655, 2778143060, -452810628, 1734992196, -1951550604, -304618656, 361620198, -135668666, 677212668, 791313300, -1344017466, -295775862, 107964897, 569202674, 868766643, 917428064, -309504078, 2316995814, -996256665, -1786886028, -902547240, -1367977020, -369627840, -2922304494, 37940184, 188183524, -385652358, 328579318, -2618530259, -2218031166, 813709674, 340052432, -2074373433, 1433306820, -526671000, -630728310, 268145240, 2344645280, -1535780790, -1720016580, -5115503016, 2660993202, -1535702535, -1032565222, 557142852, -825271552, -629578683, -2567013252, -1452926385, 3087553158, 3511210014, -1754029438, 53236430, -1067283030, 135563220, 4020963624, 3131925210, -833412696, -2747139408, -1835356152, 455321172, -2288789218, 2369391165, 234056516, 1936679491, 2151167520, -2908405053, -4299295148, 6489157506, 481301562, 1426382739, 1684224204, 177602085, 2140391612, 2760257520, 2965044318, -602806630, -817907772, -2902677930, 2448104832, 3331863207, 904731752, 790033338, -1441219620, 1502934900, -2852058280, 170268057, 864878118, -1036207665, -905015262, 3363627114, 3184625074, 7264680921, 334347684, -434391696, -4155843552, -3005590343, -2954658052, 2939954256, -3019940100, 1093489265, -209391552, -1982764971, -3030158380, -526244472, 271161228, 3482646507, -2612129682, 1363570058, -4620315384, 3363673050, 495518916, -2177249053, 2780038800, -3924488106, 3160257156, -5226355938, -3361378756, 3322921941, 728906988, 618235965, -4777201408, 5487851610, -3236195298, -7038286596, 391599954, 1182679974, -2682659986, 2147756559, 2037804720, -1571941530, 3227812362, -3253615774, -6166488800, -3213304128, -1592530216, 4597315695, -5592397710, -2479306770, -163971254, 5109923181, -2045344632, -11609426115, 330042840, -2148154020, 2220133684, 3518944272, -422145306, -1226039555, -6121760376, 2282486112, 3471364520, -1748446110, 4884412364, 2252452968, 8182806384, 724967904, -1911370284, 195625539, -2218308786, 3222548504, 8541801840, -988509366, 4910886722, 950980272, -4503856752, -1652534658, 6155164128, 4534699266, 8342008812, -3614585094, 6117855492, -6202507174, -4071608928, -922549500, 2436447250, 2557632141, -514027178, 10232078184, -295815324, -1244076652, 4854242214, -3170117394, 1184736888, -1578481092, 6368102496, -8738691210, -7160407354, -1771518228, 990815240, 13342366584, 9090406596, 1565747022, 1018514374, -2329855380, 10005408624, 256794101, -12798404184, -1290170160, 15968345184, -1995693237, -388648008, -2034386190, -23782860, -2509676700, -4663800982, 1486814517, -2152111168, -6709213449, 340468692, -1042763931, 6833592680, -19376417469, -3227826058, -9959593302, -1743859596, 4306734225, -336656804, -1870024068, 3586668000, -6017340856, -16211878242, 808764624, -1418696732, -8301580788, -866902428, -9838713528, 1770724860, 2698452888, -5164067124, 5136808734, 4764895898, 4340397330, -5453849040, 77781060, -1511939824, -4905911370, 2919591516, 3175430112, -7060048848, 8983039246, 1286912708, -12208895352, -1075418944, 8107388748, -7543727652, -6552632178, -3370108428, -1654314579, 7342483344, -9640412505, 11120279166, -1353361074, -2081432140, 9945616860, 917649936, -2104341898, 5911900176, 4487786910, -4939341174, 4421003088, -8601200884, 9272018979, -12255889248, -9464390235, 7966233896, 9191954052, 11164826060, 25381555514, -5095316760, 10276116354, 8913087560, -336495681, 110070318, -2517121368, 20710434648, 18191005098, -25597264906, 9331518636, 7172014680, 12649512582, 2292025374, 8655550794, -9807084004, -16508554752, 122712120, 1537211277, 9153999924, -785508103, 10357308136, -4513799565, -2485454676, -1609901626, -15513872028, 1561957128, 15958532402, -22787660970, -6695404990, 30019515075, -3456588180, 566336325, -16063311936, -21527580870, -8157364428, 19395910548, 12982939704, 15608656017, -4092158482, 10766641977, -5981724660, 1648279431, -1725128550, -3309974595, 22867044588, 1704702843, -21578765204, 13680827696, -20059137930, -957478635, -19727761446, -9731964192, 10369631390, -17738454024, -730926498, -3996090360, 5133437984, -37089104733, -10641559848, -10332809982, -3867529458, 18765006732, -11519883630, 8885763036, -3867256156, 3914032284, -10925322690, 6380069517, -13993757788, -21748278240, -14119868210, -25725971652, 2253201852, 17446601934, 12989441560, 12817068156, 9115486698, -3637017936, 7808080680, -1052239190, -24902900622, 8308276155, 15018212540, 20323744940, -6106042038, 1250375940, -21082639990, 10403601498, -1224273270, 9069138954, -1589888658, -20298170295, 36823407948, -19560843810, 2053356072, -22838055691, 2011701228, -7071176655, -1855085140, 22780856586, 2403352260, 177571359, 14646188460, 5911093533, -32722009420, 647343144, -18259779616, -8372703960, 8505288324, 382575177, 19175918688, 4993104096, 17223248580, 17093729115, 28463353890, 3423538776, 7699654492, -423412929, -18015906856, 20413062614, 54330311904, 5172895701, -25155240322, 16766283645, -3669440732, 6243239988, 7717630926, -1936154746, 23932525016, -18547028748, 3728154960, -17715713013, 36813747768, -21743399376, -25275524374, -4134446040, -1854015136, 4697262207, 5499350220, -10528538040, 24398762670, -16123835421, -13707650472, 31709885310, -341877276, -8759369160, -9437192296, -13523784168, 23445667488, -349058421, 27710267892, -4505544817, 16226856206, 48137216445, -9520620012, 1583523612, 12587366472, -22993250238, 5004413038, -15576126261, -4220131842, -13068720702, 149134128, -1324985309, 28575709040, 6919642296, -14215319388, -56542028638, -16932175116, -3108444408, -28004201956, -23785887474, -557597420, 20918997270, -5683120476, 11771039940, -33778197540, -54512903313, -17474404728, -2804890974, 17562444108, -10718084916, -10552133122, 16935765840, -12686224428, -30136457304, 32675959380, -25094646180, 19941078436, -32939847360, 6335473140, 8310355571, 293450352, 4995457713, -74426629410, 31619862135, 3478933344, -19773220248, 23107047666, 7586067857, 6014078964, 4491962208, -5628965736, -19138462830, 17851332384, -15005202156, -25320077902, -40431720831, 6314490440, 36192877812, 17422339560, 299355081, 256896986, 65676352860, -41312738924, -68133354480, -20355980034, 13087201347, 1257497210, 9635120874, 1335591840, -19369648485, 4892415870, 53098505082, 25448436368, -19468265976, -6327216040, -6357097285, 50625454752, 2683249560, 10434137868, 266636766, -16699913932, 44610657120, 20199025656, 6637284180, 32586648022, 36596714877, -7384361232, 24312560099, 33687375642, 51697808496, 22816202012, 20589664971, -11058159652, -13233246849, -33562036188, -5036134170, -37398292240, 9538521570, 1006174146, 2423825721, 46434900492, -9693994842, -23907640606, 22721489592, -31526585328, 18137958282, 16820831916, 1667572245, 29208093084, 13660590690, 26055744448, 54270539032, -31724493672, -12967690140, -12147430544, -5333188455, 40638920456, 13095676071, -13096959558, 2528550119, 11622261332, -23813617860, 36254717520, 20980851912, -85416236154, -28860897564, -19689683122, 34039633629, 12434009580, 14315998986, -24550196148, 6735114810, -57900464432, -1540114128, -55808940678, -56840490514, 2302360530, 22079968200, -2627023860, -71815369113, -23691963762, 72753537150, -30944750604, 48051493522, -9327747744, -37424368656, -30282328472, 68282582094, 15058668516, -7865822646, 323267162, -78853064649, -4251390348, -20661300684, -28285516608, 9371060737, -17915053248, 49594107015, -22460656260, -111564743170, 28407791202, 15001298685, -53060223592, 37868747724, 39221456192, 46659983292, 25778090172, 2221199394, -79521453760, -49187380212, -46194754708, 55887276915, -72944054874, -7469729280, -463394040, 27538583370, 3443411652, -83271970350, -14022936594, 49623954066, -32139315028, -53729879049, -1627752226, 49309047576, -74452925988, 17659023822, 103078833624, -84735215781, 57932580660, -26335643400, 59639223924, -21556231534, 44483568592, 5590174167, -74578502640, -46546647075, -10202108952, 51660876654, 38755854738, 111398739747, 22770982188, 54110931300, 30389461410, 19016306220, 48414760788, -50495739858, -31900261392, 5376664592, -84004874256, 27506390049, 30874321496, 6545647485, 7183554162, 12214447128, 70236618720, -61660936544, -10258811426, -2315222694, 38759337440, 36909014474, 64565934324, 62318141784, 1329128928, -53485437096, 25252333808, -2491572708, 17322123384, 5731702560, 107739077292, -26681017977, 67803530700, 11920166933, -37347712452, -47739400272, 10025122112, -59199690888, 27304616102, 56201873778, -50311049358, -9184772490, 74129197190, 42276069000, 66762216272, 42077453112], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "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": "19.8.a.a", "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, 0], [1, 0, 0, 0], [-2, 1, 0, 0], [-4, -1, -1, 0], [8, -10, 4, -1], [-59, -11, 3, 6], [-156, -18, -6, -3], [-311, -20, -4, -26], [-892, 50, -36, 27], [-1201, 77, 23, 6], [-1598, 83, -14, 17], [-2121, 177, 87, 30], [-1564, -10, 32, -3], [-1054, -99, 123, -240], [-586, -187, -192, 30], [-690, 60, 90, 150], [4588, -858, -276, -93], [-1175, 778, -510, 528], [12942, -1323, 378, 9], [6859, 0, 0, 0], [20236, -1196, -12, -924], [9100, 1183, 619, -474], [28590, -1683, 1002, 141], [-7042, 4217, -429, 1428], [22980, 1530, 780, 525], [-5722, 887, -1931, -2062], [7376, 2924, -1110, 831], [-17926, 569, 2495, -174], [8352, -814, -500, 2717], [-63172, 953, -2907, -3510], [3180, 510, 1020, 150], [-79472, -7694, -2428, 4306], [-11508, -834, 252, -3609], [-92226, -6330, -372, -162], [57046, -19675, 4204, -3346], [-140419, -2431, 6363, 1746], [-35236, 21968, -7444, 2058], [-69986, -18722, 9572, 334], [-13718, 6859, 0, 0], [-66206, -1085, 1453, -5112], [61256, 20764, -6712, -104], [-207854, 17284, -6306, 13830], [186204, 14202, 4074, 1767], [2927, -15777, -12495, -2526], [15756, 41160, -15300, 1710], [41613, 17277, -7941, -10422], [471320, -53072, 21722, -7361], [88385, -30067, 33855, -14082], [349652, 28130, 5684, 1449], [-16918, 29344, -15400, 14056], [190456, -51176, -8562, -6549], [260712, 7365, -1551, 10284], [420748, -29426, -2944, 22525], [3542, -61405, 6159, 7314], [201240, 32760, 6570, 9585], [261861, 33129, -23757, -29154], [-228164, 22366, 31188, -7743], [-27436, -6859, -6859, 0], [369716, -127730, -16042, -9071], [-767012, 122233, 10575, 9522], [172920, 13560, -6840, -15780], [82493, -30189, -13935, -27546], [-1192720, -79948, -18408, -6324], [-24521, -17087, -14729, 41502], [-449732, 117750, 18060, 17355], [-1127764, -49516, 48468, -2964], [-653292, -49446, -26712, 5004], [-33310, 100737, 74733, 38388], [-2225504, 214042, -18396, -27747], [-391902, -68841, -27687, 18624], [58802, 15523, 9986, 26137], [-542294, -70856, -85524, -53328], [951984, -209520, 32832, -54954], [-37495, 204564, 23496, -38004], [-2045068, 289706, -54408, 56676], [1541030, 110945, 28115, -40170], [54872, -68590, 27436, -6859], [-893121, -91371, -36297, 94302], [342408, -15336, -21882, 12009], [4023872, -24108, 39378, -54354], [-180416, -99224, 70752, 70764], [603053, -292348, -63676, -25968], [1665604, -512518, 111844, -56338], [2086224, -173070, 40110, 46272], [361804, 7258, -7208, 60999], [1093417, 199973, -99089, 50402], [-2336698, -140695, -98202, -31677], [2621958, 233283, 101565, -67848], [1149888, -438120, 12624, -122118], [803576, 204626, 1716, -108870], [2568546, -250461, 11538, -38619], [5714162, 75005, -230993, 176582], [-5910004, 848726, -143376, -35463], [3312760, 318976, 150508, 120792], [-2217334, 1101895, -108886, 179569], [-404681, -75449, 20577, 41154], [167364, 50922, 29844, -74043], [-969756, 482594, 216394, -188896], [2571084, -618582, 142800, -105000], [6353907, -146937, -42663, -48906], [-6284772, 311062, -856, 287413]]}