# Stored data for newform 19.6.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "19.6.a.a", "space_label": "19.6.a", "level": 19, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663315, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 548660747956389839, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [6, 1]]], "qexp_display": "q-6q^{2}+4q^{3}+4q^{4}+54q^{5}-24q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 684, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 3.047292576446632, "hecke_ring_index": 1, "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": 1, "inner_twist_count": 1, "level_primes": [19], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "1.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "2.001", "prec": 17}, {"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "4.966", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[19, -1]], "trace_display": [-6, 4, 54, 248], "traces": [0, 1, -6, 4, 4, 54, -24, 248, 168, -227, -324, 204, 16, -370, -1488, 216, -1136, 1554, 1362, 361, 216, 992, -1224, -408, 672, -209, 2220, -1880, 992, 6174, -1296, -7840, 1440, 816, -9324, 13392, -908, -5146, -2166, -1480, 9072, -7830, -5952, -12532, 816, -12258, 2448, 2592, -4544, 44697, 1254, 6216, -1480, -20778, 11280, 11016, 41664, 1444, -37044, 18972, 864, -18418, 47040, -56296, 27712, -19980, -4896, -11548, 6216, -1632, -80352, -72984, -38136, 59114, 30876, -836, 1444, 50592, 8880, -44752, -61344, 47641, 46980, -27660, 3968, 83916, 75192, 24696, 34272, 20730, 73548, -91760, -1632, -31360, -15552, 19494, 5760, 14018, -268182, -46308, -836, 145782, -37296, 90152, -62160, 53568, 124668, 36108, -7520, 32654, -66096, -20584, -281728, -145806, -8664, -22032, 24696, 83990, -113832, 385392, 36288, -119435, 110508, -31320, -31360, -180036, 337776, -259936, -212352, -50128, 119880, -124092, 3264, 89528, 69288, -101520, 261072, 84330, 9792, -155476, 53568, 10368, 437904, -75480, 257872, 333396, -354684, 178788, -20584, -232794, 5016, 496184, 60648, -352758, -303552, -423360, -5920, 128078, 268512, -83112, 77760, -101184, -285846, -570652, -31320, 44064, 165960, -39864, 166656, -234393, -503496, -81947, -50128, 223086, -148176, -51832, -231744, 75888, -124380, 316980, -49032, 857270, 550560, -73672, -68544, -277884, 188160, 317016, 10368, -466240, -116964, 783600, 110848, 231074, -84108, -79920, 178788, 438966, 277848, -385000, -35112, -46192, -874692, 1531152, 24864, -422820, -540912, 92616, 420320, 73644, -321408, 438740, -83112, -291936, -216648, -676728, -315840, -1944320, -195924, 236456, 44064, -574980, 123504, -372352, 357120, 47443, 874836, 1011012, 5776, 571382, 132192, 202368, 1037232, -594678, -503940, 139968, 75888, -179008, -2312352, -380544, -245376, -1076782, 716610, 647404, -73672, 2413638, 187920, -133570, -1317120, -110640, 1080216, -113316, -225184, -83232, 1559616, 335664, 387328, 553218, 300768, -1276208, -79920, -1401498, 744552, 824088, 137088, -1122012, -537168, 82920, -46192, 1521582, 609120, -1083040, -1765344, -367040, -505980, -42636, -6528, 658598, 932856, 1779680, 2249856, 356346, -62208, 405116, -291936, 77976, 452880, -1941840, -326880, 995059, -2000376, 56072, 236456, -948570, -1072728, 1024488, -864528, -383520, 1396764, 150960, -3344, -3107936, -2977104, 583128, -410096, -994572, 2116548, -1162348, 202368, 360608, 2540160, -2557176, -248640, -1059430, -768468, -3039984, -179008, 2644254, 498672, 1259496, 1496448, 144432, 607104, 560994, 190564, 77330, 3423912, 130616, -1315440, 642816, -264384, 2390828, -110640, 1168142, 239184, -623592, -1126912, -1123822, 1406358, -583224, 335664, -1599360, 491682, 6916720, -2105376, -88128, -1338516, 2003868, 98784, 3608078, 310992, 695600, 293760, -1828254, -455328, -3941136, 82920, 1541568, -1901880, -2610120, -2059344, 130321, -5143620, -477740, -367040, 3192156, 442032, 391136, 463488, 1777410, 1667304, -5152944, -125440, 262070, -1902096, -720144, 435456, -2284380, 2797440, 824060, 77976, -1039744, -4701600, -3897792, -849408, 2731968, -1386444, 2844764, 56072, 1974006, 479520, -634032, 7509096, -496368, -2633796, -2416608, -185232, -2844034, 2310000, 358112, 237424, 5802354, 277152, 2900800, 583128, 2572614, -9186912, -1049784, 1044288, 5353370, 2536920, 337320, 360608, 4705056, -555696, -1493640, -532800, -621904, -441864, -1141980, 214272, -740794, -2632440, -588384, -3490704, -324786, 1751616, -4567664, 144432, -301920, 4060368, 1303536, 2135680, -7235566, 11665920, 1333584, 130616, -147288, -1418736, -415336, 1850688, -10146219, 3449880, 3932028, -82336, 1119420, 2234112, -931176, 6872576, -4766238, -284658, -1597320, -583224, 1984736, -6066072, -4955040, 242592, 2722154, -3428292, -2921520, -88128, 2466750, -1214208, -1637344, -7013664, -1693440, 3568068, 5945652, 335960, -2863904, -839808, 512312, 3187296, -2556528, 1074048, -75449, 1541568, 4716606, 2283264, -3855312, 311040, 1904020, 6460692, -404736, -477740, 756972, -3884424, -4548472, -3094224, -2282608, -14481828, 1668204, -125280, 9594396, 801420, -2500632, 8906240, -18100032, 663840, -956044, -720144, -159456, 679896, 5704104, -9457728, 7872228, 499392, -937572, -1039744, 6661086, -2013984, 14660272, 4471296, -678680, -3319308, 4868208, -200512, 528768, 7657248, 892344, -3356640, 5915466, 8408988, 5568716, -496368, -207328, -4944528, -12183360, -926976, -6269879, 6732072, -4306644, 358112, 2897100, -497520, 1949832, -1940064, 1267920, -9129492, 9118188, -406080, 744878, 6498240, 3429080, 2237760, 1763316, 2202240, -6024028, 337320, 4180886, 255816, 2228814, -274176, -11098496, -3951588, -1111536, -621904, -5297442, -10678080, 4636840, -15213312, 1268064, -2138076, -6333324, 41472, -7873524, -2430696, 11814968, -12261312, -3075078, -467856, 359036, -301920, 3134400, 11651040, 85272, -6290624, 6431042, -5970354, 924296, 1333584, -6859680, -336432, -4238712, 9931152, 4535460, 5691420, -7473300, 715152, -2830240, -6146928, 1755864, 5845856, -9414510, 2301120, 20811168, -931176, -1540000, -905760, -1223400, -140448, 4642682, 18647616, 2621396, 1984736, -6449490, -3498768, -2066464, 519840, 6124608, 5967432, -959040, -1411032, -16040842, 6974088, -1691280, 8499456, 8109834, -2163648, 6431468, -1693440, 767040, 15343056, 5141040, 1681280, -9068819, 6356580, 294576, 512312, -7996884, 18239904, 5742920, -7518336, 1754960, -15865524, -14036544, -332448, -16537890, -7556976, 16567368, -11467008, 6627810, -866592, -16711228, -404736, -2706912, -3365964, -599400, 8003688, 3870288, -463980, -7777280, -2282608, 11243262, -783696, -6700968, 8894880, -13418878, -3856896, 10089108, 176256, 22193558, -14344968, -2299920, -4646880, 4834512, -7008852, -2518992, -159456, -1489408, 3741552, -3757272, 1428480, 10078466, 6742932, 392920, -937572, -6393882, 3499344, 3476464, 14097888, 4044048, 9596160, -22539636, -327788, 4553820, -41500320, 2285528, 14236352, 7687860, 528768, -2240428, 892344, -11484384, -12023208, -8395704, 4148928, -12167820, -21648468, -2378712, -207328, 7241838, -4173600, -1857706, 5653248, 559872, 10969524, 36153936, 303552, -11047594, 23646816, 10158704, 3482640, 3198720, -9249408, -4075920, 1267920, -1522176, 15660720, -17640768, 13925088, 22357696, -781926, -4307128, 3429080, -1290366, 2866440, 10222376, -15415680, -8987147, -19152936, -19474728, -294688, -22706002, -2346816, 9654552, -587520, -2355792, -10664460, 13981700, -1111536, -534280, 30917664, 21238344, -5268480, -12570876, -1572420, 6278820, 1268064, 8954784, 4320864, 1080080, -2944512, -453264, 13706280, 26793936, -1864960, -6160858, -4944360, -332928, 3274992, -6964710, 6238464, 8098192, 3134400, -19048932, 23386752, -7019640, 1549312, 10834946, -16391808, 2212872, 924296, 26279814, -17068584, 1638560, 2355024, -5104832, -11844036, -2826630, -319680, -14888736, 3804192, -11607120, -50775792, 6916212, 2978208, -15438988, 1755864, 3296352, 14499648, -36159888, -7779744, 6814660, 17064204, -4488048, -1540000, 11925534, -2148672, 4027968, -300960, -4705710, -34814124, 12059256, -184768, -5463936, -17404800, 6086328, 24491376, 34937802, -15435684, -5936020, 6124608, -4332160, 6298704, -30815208, -7061376, -4524052, -32120220, 20829520, -1691280, 20835846, -2023920, -23726584, 15145536, -170544, -28230336, -11161284, 370464, -8580706, 8961840, 2634392, -10253440, 69459138, 3731424, -2152656, 294576, 14739200, 6851880, 10929288, 8999424, 17607127, 4444764, 1425384, 1754960, -12657222, 3530304, -29619880, 23603808, 1620464, 1948716, 2099568, -1167744, 38496326, 27405984, -4425138, 6066144, -6860454, 1811520, -6588676, -2706912, -7767360, -7821216, -16686144, -2707200, 12046644, 43413396, 3980236, -7777280, -9129408, -8001504, 4272760, 5485872, -3182086, 883728, -44648928, 945824, 33425486, 2492016, -3794280, -12514176, -2043342, 60877314, 42570452, -2299920, 4097952, -23592168, -14705832, -3458112, -64464128, -6716520, 9718764, -1489408, 935712, 5587056, 17116920, -52663296, 603840, 28597428, -48404160, 189772, -32289012, 9583920, -12431744, -24495408, 46292580, -11908416, -38973172, 4044048, -33092514, 29730240, 34753200, -1640384, -5642640, -16332924, -3978288, 2285528, -30774816, 17529120, -18125080, -3701376, -4649392, -14800500, 27004080, 809472, 1075514, 9824064, -20464504, 8890560, -4550622, 10160640, 16135617, -2378712, -10228704, -35673912, 17118864, 14110320, 5078090, 17183424, -4237720, 559872, 14079534, -3073872, 3194640, -21552192, -25176960, 15339168, 20967348, -716032, -21872180, 452694, 10577016, 64745856, -1797510, -28299636, 42314400, -1522176, 5037984, 23131872, 20913840, 5985792, 32836449, -11424120, -8196516, -4307128, 12477996, 2428416, -23080744, -20065080, 2243976, -4541832, -55269588, 2589616, -38558048, 27290832, 309320, 20922848, -30611022, 13695648, 4228920, 9654552, -7412458, -10009224, 15546648, -5261760, 23704164, -57566376, 2571264, -534280, 5113056, 15003792, -7445536, -11289600, 9563312, 108600192, -20790000, -442560, -27192586, 5736264, 9674480, -30246048], "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": "19.6.a.a", "char_is_minimal": true, "conrey_index": 1, "id": 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], [1], [-6], [4], [4], [54], [-24], [248], [168], [-227], [-324], [204], [16], [-370], [-1488], [216], [-1136], [1554], [1362], [361], [216], [992], [-1224], [-408], [672], [-209], [2220], [-1880], [992], [6174], [-1296], [-7840], [1440], [816], [-9324], [13392], [-908], [-5146], [-2166], [-1480], [9072], [-7830], [-5952], [-12532], [816], [-12258], [2448], [2592], [-4544], [44697], [1254], [6216], [-1480], [-20778], [11280], [11016], [41664], [1444], [-37044], [18972], [864], [-18418], [47040], [-56296], [27712], [-19980], [-4896], [-11548], [6216], [-1632], [-80352], [-72984], [-38136], [59114], [30876], [-836], [1444], [50592], [8880], [-44752], [-61344], [47641], [46980], [-27660], [3968], [83916], [75192], [24696], [34272], [20730], [73548], [-91760], [-1632], [-31360], [-15552], [19494], [5760], [14018], [-268182], [-46308], [-836]]}