# Stored data for newform 210.8.i.b, downloaded from the LMFDB on 25 April 2024. {"label": "210.8.i.b", "space_label": "210.8.i", "level": 210, "weight": 8, "hecke_orbit": 2, "hecke_orbit_code": 4504149517402322, "dim": 4, "is_polredabs": true, "trace_hash": 1069145041091420601, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [381647325353616, 104028113700, 47891421, -5325, 1]]], "qexp_display": "q+(-8+8\\beta _{1})q^{2}-3^{3}\\beta _{1}q^{3}-2^{6}\\beta _{1}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 13440, "analytic_conductor": 65.60085535166557, "hecke_ring_index": 3, "level_radical": 210, "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": [210, 3, [71, 127, 31], [3, 3, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [121, 151], "field_disc": 4503349449, "field_disc_factorization": [[3, 2], [22369, 2]], "field_poly": [31270464, 5592, 5593, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "4.050", "prec": 17}, {"__RealLiteral__": 0, "data": "1.243", "prec": 17}, {"__RealLiteral__": 0, "data": "64.093", "prec": 20}, {"__RealLiteral__": 0, "data": "30.299", "prec": 20}, {"__RealLiteral__": 0, "data": "1797.581", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "7.2.3.c3", "trace_display": [-16, -54, 250, -77], "traces": [0, 4, -16, -54, -128, 250, 864, -77, 2048, -1458, 2000, 5325, -3456, -13720, 1232, -13500, -8192, -21786, -11664, -44692, -32000, -2079, -85200, 46143, -27648, -31250, 54880, 78732, -4928, 481308, 54000, 341927, -65536, 143775, 348576, -19250, 186624, -258856, -357536, 185220, 128000, -641958, -16632, -1980190, 340800, 182250, 369144, -1722897, 442368, 1641157, 500000, -588222, 439040, -2994681, -314928, 1331250, -39424, 2413368, -1925232, 858450, 432000, 3920558, -5470832, 112266, 1048576, -857500, 1150200, 4109921, -1394304, -2491722, 77000, -12572220, -746496, -4115065, -2070848, -843750, 5720576, 16411353, -2963520, 1753115, 1024000, -1062882, 2567832, 31085664, 266112, -5446500, 7920760, -6497658, 2726400, 5883408, -2916000, -32148571, -5906304, 9232029, -13783176, 5586500, -1769472, -21519892, 13129256, -7763850, -2000000, -6505092, -4705776, -19058581, -7024640, 259875, 47914896, -6984288, -2519424, 4988237, -5325000, 13978224, 630784, 23066688, -9653472, -5767875, -15401856, 5000940, -13735200, -47343912, -6912000, -28452875, 31364464, 8666433, 21883328, -7812500, -449064, 4220936, -4194304, 26732565, -6860000, 23020263, -18403200, 3441284, -65758736, 4920750, -11154432, 31387896, 9966888, 168204806, 616000, 93036438, 50288880, -124763559, -5971968, 30081750, 65841040, -88622478, 33133568, -58414176, -6750000, 8705930, -22882304, 31763988, -128010624, 85481750, 11854080, -62110603, 14024920, -80856387, -16384000, -3553011, 17006112, -139550644, 20542656, -17971875, -124342656, 8926818, -1064448, 222060768, 21786000, -32580468, 63366080, -62989773, 103962528, -1203125, -43622400, 23178150, 47067264, -75797307, 11664000, -259755334, -4225760, -211710132, 23625216, 32357000, 73856232, 210807864, 220530816, -1515591, -89384000, 48298656, -14155776, -18131311, 86079568, 46305000, -210068096, -102231654, 31055400, 47818736, -16000000, 110967867, 104081472, -151599126, 75292416, -40122375, -152468648, 33638247, 28098560, 197271102, -4158000, 41835506, -191659584, 169724970, -55874304, -123761875, 40310784, -55184290, -79811792, -111106755, -42600000, 380331258, -55912896, 526392896, -2523136, 45562500, -92266752, 165426408, -77227776, -93289183, 92286000, -11070675, 246429696, 90389424, 40007520, 215362125, 54940800, -94668210, 365331120, -121908600, 27648000, -484245625, -227623000, -28697814, -501831424, -205144625, -138662928, -281962442, 175066624, -419656464, 31250000, 1089848934, -3592512, -8959590, -16883744, 73527750, -33554432, -240868716, -427721040, 19931912, 109760000, -175436766, 184162104, -534533916, 73612800, -748670250, 516111736, -317704032, 263034944, -389601450, 39366000, -167639032, 178470912, 882273357, -502206336, 83203125, 79735104, 72943151, -672819224, -498529566, -9856000, -603923058, -372145752, -395962999, 402311040, 150835500, 1996216944, 507708012, 95551488, 144885310, 240654000, 290518542, -263364160, 729581190, 354489912, 214612500, -132534272, 104811975, -467313408, 96400575, 108000000, -837728353, -139294880, -175637484, -183058432, -490069750, -127055952, 3545878550, -26241600, 1029163374, -341927000, -398789028, 94832640, 129679727, 993769648, 7016625, -224398720, -680960400, -646851096, 173072592, 65536000, 377151552, -295822296, -275335572, -68024448, 107187500, -1116405152, 134682399, -328682496, 132663069, 287550000, -700572088, -994741248, -188706024, -35707272, 1027480250, -8515584, -1912778986, -888243072, -311400288, 174288000, -685807062, 521287488, -379563800, -1013857280, -155732625, -503918184, -451078062, -415850112, 1308419612, -9625000, -270050760, 174489600, 654834468, 185425200, -785763750, -753076224, 45293094, 1212756912, -1127191542, 93312000, -100380132, 1039021336, 1536455250, 2091314624, -1028766250, 846840528, -1693007476, 189001728, 233993691, -517712000, -500724273, -1181699712, -2136322759, 1686462912, 105468750, -882123264, 219788292, 24249456, 132081908, 357536000, -56982636, 386389248, 955543833, 226492416, 2000166000, 290100976, 721779255, 688636544, 307521870, -185220000, -274476168, 840272384, -1243094202, 408926616, -219139375, 248443200, 468671261, -765099776, -1834791777, 256000000, 2859061341, 887742936, -723662459, -416325888, -265720500, 148242864, -2128530246, -301169664, -2797175119, -320979000, 847473192, 2439498368, 7080694572, -538211952, 1942854000, 224788480, -2270764881, -789084408, -331066878, 16632000, 2595100886, -167342024, -1255991913, -1533276672, -340406250, -2715599520, -301882966, 893988864, -3368616093, -990095000, 1606889934, -161243136, 4876648130, 652101352, -1624414500, 319247168, 1551526263, -888854040, -2463124876, 681600000, 1196403453, -6085300128, -230930460, -447303168, -735426000, -2105571584, 3154365504, -20185088, -3004735566, -182250000, 772973037, -738134016, 235060110, -2646822528, 66027500, 1235644416, 34615355, -746313464, -428813838, -369144000, 7776146388, 3544852248, -4715659900, -985718784, -1154003625, 723115392, 354354270, -640120320, 1244056772, -3445794000, -1676986281, 439526400, -5513910972, 378672840, 1396625000, 107361408, 4366244898, 487634400, -2670420942, 221184000, 1637998126, 7747930000, 1094331546, 3641968000, -1344993250, -229582512, 3265958117, 2007325696, 7535734776, 3282314000, -14178211344, 554651712, -1279438236, -2255699536, -485240625, -2801065984, -5717690328, 6714503424, -1228261819, 250000000, -120512043, -4359395736, -3646407948, 57480192, -1626273000, 35838360, -2997820368, -135069952, 6295350180, -1176444000, 6295216634, 536870912, -879672636, -1926949728, 2382322625, 1710884160, -6428609406, -992919704, 3401447742, -439040000, -6153234783, -1403494128, -1670713933, -2946593664, 64968750, 8552542656, 3080182290, 588902400, 5440564657, 2994681000, -1251620100, -4349136064, -4308402558, 1270816128, 873036000, 2104279552, -2046527289, 6233623200, 8739161025, -629856000, 8357305553, -1341112256, 3506697009, -713883648, 1247059250, -6944091336, -6006999808, 2008825344, 2858086782, 665625000, -7288995858, -1275761664, -134989855, -1167090416, 873639000, -5382553792, 9521177571, 1994118264, 18303183838, 39424000, -11383624656, 2415692232, 35728500, -2977166016, 1441668000, 6335407984, -40920957, -6436976640, 2688306861, 1206684000, -4347304963, -7984867776, -2608127424, -197723064, -1441968750, -382205952, -6417830983, 1159082480, -489545397, -3850464000, -2808098328, -4648296672, 9239747913, -2106913280, -625117500, -2918324760, 32646331416, 2835919296, -17117046362, -858450000, 1380127329, -1060274176, -7743229992, -1676991600, -5708298750, 7477014528, 1291105872, 771204600, -4733622174, -432000000, -8458293910, -609898520, -5992264818, 557179520, 3556609375, -1405099872, 1430366906, 2928934912, 3592856736, 7841116000, 3163719591, -1016447616, -7324927849, -14183514200, 2166608250, 8402612736, -24310921644, -4116653496, -8941898662, -2735416000, 908232669, 6380624448, -453022416, -1517322240, -488281250, 1037437816, -2663159877, -3975078592, 7791960948, 56133000, 18296051852, 897594880, -564779331, -5447683200, 263808500, 10349617536, -3133392073, -2769161472, 4582574190, 524288000, -1502131803, -1508606208, 12077260334, 2593971072, 6683141250, 1101342288, 1770068073, -544195584, -25442168508, -1715000000, -710866233, 17862482432, 16305283041, 1077459192, -2877532875, 1314729984, 5999764770, 2812081608, -4273317312, -1150200000, 6663342689, -5604576704, 10268943966, 15915859968, -8064245875, 3019296384, 6670586916, -285658176, -7106304096, -4109921000, 13644313104, 136249344, 9022931282, 7651115944, -615093750, -7105944576, 1261845207, 4982404608, -19260239446, -2788608000, 4466513016, -5486456496, 5318523402, -2085149952, 7846974000, 1518255200, 5037615882, 4055429120, 12804575331, -1245861000, -28078513429, 8062690944, -11664968112, 7217248992, 10512800375, -3326800896, -1174021632, -5233678448, -4881028896, 154000000, -7013000352, 1080203040, -4251538082, 1395916800, 5814777375, -10477351488, -24413395104, -2966803200, 8658087998, -6286110000, 1278020835, 3012304896, 16851585096, -10226284992, -31190889750, -4851027648, 1645766100, -9017532336, -13438848900, -1492992000, 1467510737, 1606082112, -13074631875, 8312170688, -3760218750, -6145821000, -2512988332, -16460068352, 1549681956, 4115065000, 19043090934, 6774724224, 6261980102, 27088119616, -5538904875, -3024027648, -14510374764, 1871949528, -28568431480, 2070848000, 15225971868, 2161070688, -13588634910, 4726798848, 7301772000, -17090582072, -11330724528, -26983406592, 537790176, -1687500000, 17591264795, -7056986112, -14712960609, -879153168, 2176482500, -96997824, 30811375784, -528327632, 120954465, 2860288000, 14947102419, 911722176, 48138153182, -6182227968, 1985249250, 7644350664, -49257574266, -905969664, 34031956940, 410025000, 13006910664, -1160403904, 7422036495, 5774234040, 5342609375, -11018184704, 2812942377, -4920349920, 13824443895, -1481760000, -36318657582, 1097904672, 9473585364, 6722179072, -15527650750, 4972376808, -6022203658, 3271412928, -14432415732, 3506230000, -37374760626, -3975091200, -6214855694, 3749370088, 10107048375, 3060399104, 37623984120, 743317344, 29655732744, -1024000000, 4289004432, 22872490728, -10248478386, -14203886976, 4622223375, 11578599344, -10519239150, -3330607104, -42536542155, 1062882000, 773596538, 8516401152, 9052507728, 8514120984, 17443830500, -2409357312, 10363288729, 44754801904, -385072380, 5135664000, 21014316042, 6779785536, 10304247584, -9757993472, -4492968750, -56116751376, 11308118520, 2152847808, 1709039639, 15542832000, 1969465077, -3596615680, -35754246402, 36332238096, 557926125, -6312675264, 6730149141, 1324267512, 5031048900, 133056000, -2870455436, -10380403544, 8152961283, -1338736192, 13878798000, 20095870608, 2190871375, 24532426752, -10691000973, -2723250000, 5075311149, 10862398080, -28312982968, -7597443392, -8145117000, -3575955456, 128379120, -26948928744, 37035915896, 15841520000, -13040800983, -25710238944, -16059882213, -1289945088, 7873721625, -19506592520, -7823806740, -1685016256, -67755909192, 6497658000, -21232449233, 2553977344, 7844000634, -24824420208, 150390625, 14221664640, 26126284745, -19704999008, -9849346065, -2726400000, 8759513454, -19142455248, -115646403766, 24341200512, -2897268750, -1847443680, -15311910540, 7156850688, 62268062003, 11766816000, 2829923325, -16844572672, -44110873953, -12617462016, -18949326750, 322961408, -5205631050, 12018942264, 43115391966, -1458000000, -36255105504, -12367568592, 24677073036, 11810144256, -16234708375, 1880480880, 11974424531, 10587290112, 9484424136, -32676791000, 56906496504, -4942577664, 34122349656, 276922840, -13231883250, 11941015424, -1772560251, 6861021408, -15884256085, -2953152000, -47869360425, -31104585552, 121450273428, -27650294784, 8089250000, 18862639600, -13893705549, -7885750272, 4607578269, 18464058000, 31573229429, -11569846272, -10767303756, 2834834160, -26350983000, 2560481280, 66966442394, -7420742840, -7002705258, 13783176000, 66530291964, -13415890248, -11297505231, -7032422400, -378897750, 88222575552, 27990406830, 3029382720, -28295004947, -5586500000, 36771861600, -24240082944, 54564293544, -17464979592, -6037332000, 3901075200, 4672959984, 42726735072, 1211252490, -3538944000, -4378923087, 13103985008, -5091545952, -30991720000, -4532827750, -767450376, -111643155826, -14567872000, 3717030222, -10759946000, 38170843029, 3673320192, -14946671215, -52255329872, 2894062500, 16058605568, 27203705226, -30142939104, -22253644476, -13129256000, -7272849546, 56712845376, -70768558431, 4437213696, -6389478375, 20471011776, -13072678290, 36091192576, -15961321710, -3881925000, -35860592569, 11204263936, 37830892752, -3872243760, 11954684000, -26858013696, -44205238351, -9826094552, -5095062648, -4000000000], "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": 9, "prim_orbit_index": 3, "minimal_twist": "210.8.i.b", "char_is_minimal": true, "conrey_index": 121, "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], [1, 0, 0, 0], [-8, 8, 0, 0], [0, -27, 0, 0], [0, -64, 0, 0], [125, -125, 0, 0], [216, 0, 0, 0], [7, -42, -7, -7], [512, 0, 0, 0], [-729, 729, 0, 0], [0, 1000, 0, 0], [0, 2651, 23, -23], [-1728, 1728, 0, 0], [-3499, 46, 46, 92], [280, 0, 56, 0], [-3375, 0, 0, 0], [-4096, 4096, 0, 0], [0, -10860, -66, 66], [0, -5832, 0, 0], [-22205, 22299, -188, -94], [-8000, 0, 0, 0], [-1134, 1134, 0, 189], [-21576, 184, 184, 368], [22989, -23044, 110, 55], [0, -13824, 0, 0], [0, -15625, 0, 0], [27992, -27624, -736, -368], [19683, 0, 0, 0], [-2688, 2688, 0, 448], [120024, 202, 202, 404], [27000, -27000, 0, 0], [0, 171012, -97, 97], [0, -32768, 0, 0], [72819, -72198, -1242, -621], [87936, -528, -528, -1056], [-4375, 0, -875, 0], [46656, 0, 0, 0], [-129671, 129509, 324, 162], [0, -179144, 752, -752], [0, 91989, 1242, -1242], [64000, -64000, 0, 0], [-159435, -703, -703, -1406], [1512, -9072, -1512, -1512], [-496912, 1243, 1243, 2486], [172608, -171136, -2944, -1472], [0, 91125, 0, 0], [0, 184792, -440, 440], [-860559, 861152, -1186, -593], [110592, 0, 0, 0], [820309, -820309, 0, 539], [125000, 0, 0, 0], [-296784, 295002, 3564, 1782], [0, 218048, 2944, -2944], [0, -1497067, -547, 547], [-157464, 157464, 0, 0], [337125, -2875, -2875, -5750], [3584, -21504, -3584, -3584], [599535, 2538, 2538, 5076], [-960192, 961808, -3232, -1616], [0, 424224, 10002, -10002], [0, 216000, 0, 0], [1957936, -1959498, 3124, 1562], [-1366544, -776, -776, -1552], [25515, 0, 5103, 0], [262144, 0, 0, 0], [-437375, 431625, 11500, 5750], [0, 572616, 4968, -4968], [0, 2054190, 1541, -1541], [-703488, 699264, 8448, 4224], [-620703, -1485, -1485, -2970], [42000, -42000, 0, -7000], [-3155742, 8458, 8458, 16916], [-373248, 373248, 0, 0], [0, -2062112, 9159, -9159], [0, -1034776, -1296, 1296], [-421875, 421875, 0, 0], [1421120, 6016, 6016, 12032], [2814210, 2588789, -1771, -19523], [-755784, 9936, 9936, 19872], [851584, -868233, 33298, 16649], [0, 512000, 0, 0], [0, -531441, 0, 0], [1275480, -1281104, 11248, 5624], [7766712, 3136, 3136, 6272], [60480, 0, 12096, 0], [-1374000, 8250, 8250, 16500], [3975296, -3965352, -19888, -9944], [0, -3251556, 5454, -5454], [0, 1357312, 11776, -11776], [2924346, -2935918, 23144, 11572], [-729000, 0, 0, 0], [-10828237, 5545288, 25781, 22239], [-1471296, -3520, -3520, -7040], [4612086, -4614705, 5238, 2619], [0, -6893960, 4744, -4744], [0, 2799125, -11750, 11750], [-884736, 884736, 0, 0], [-5421856, 27922, 27922, 55844], [4312, 6562472, -4312, -4312], [-1966113, 16767, 16767, 33534], [-1000000, 1000000, 0, 0]]}