# Stored data for newform 61.6.g.a, downloaded from the LMFDB on 23 May 2024. {"Nk2": 2196, "analytic_conductor": 9.783413008591818, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 61, "char_degree": 4, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 10, "char_parity": 1, "char_values": [61, 10, [2], [1]], "cm_discs": [], "conrey_index": 3, "dim": 104, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 412417523773, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 61, 7, 1, 10, 0]], "is_cm": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "61.6.g.a", "level": 61, "level_is_powerful": false, "level_is_prime": true, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [61], "level_radical": 61, "minimal_twist": "61.6.g.a", "prim_orbit_index": 7, "related_objects": [], "relative_dim": 26, "rm_discs": [], "sato_tate_group": "5.2.3.c10", "self_twist_discs": [], "self_twist_type": 0, "space_label": "61.6.g", "trace_display": [-5, 15, -122, 230], "traces": [104, -5, 15, 465, -122, 445, 230, -5, -2841, -595, 0, 1982, 2372, -4474, -1149, -8631, 950, 4340, -5597, -6627, 0, -8639, 9065, 17220, -7694, 14810, 4500, 19835, 0, -44585, 10905, 0, -19205, -15376, -43790, -25135, -5, 17555, 29401, 0, -21014, 62197, -31625, 146190, 153742, 13387, 27326, -82968, 14694, 0, 34090, 90072, -40270, -13760, 25140, -97860, 114893, -18003, -117435, -536650, -121867, -157388, -160825, 132509, -155852, 308443, 101665, 303780, 281945, 264985, 160970, 0, 127669, -133952, -139592, -641111, 128917, 1670, 187940, 785373, -453473, 0, -301209, 100475, -340045, -462669, 189245, -881635, -201970, 0, 93865, -622085, 0, -285265, -113308, 1215465, -342131, -616150, 714235, 473451, 0, -758027, -288975, -80550, 762760, 1237081, 314864, 2563108, 558242, 2569481, 0, 1500655, -65524, -2171355, 1093440, -1815740, -1131545, -366894, -1029343, -4487055, -1703394, 1083374, -2533322, -962415, 1379023, -728639, -390752, -373345, 2308580, -1323830, 1404381, 2624725, 0, 1309672, 67562, 4631884, -418168, 2494707, -344040, -2917715, 331219, -1455238, 0, -1151891, 665265, -1247130, 506092, 4075780, -1138748, 4528935, 0, -950355, -1584965, 0, 1121555, -3347730, 927175, -4180197, -3699835, -2199340, 1594417, 0, 1590866, 2009995, 889590, -2624680, 1052668, 873765, 875656, 3023856, 4008999, 0, 2479550, 3652532, -4536160, 1420900, -4356965, -2036404, -1719901, -13028869, -1777845, -3871188, -1399038, -8802722, 1809605, 703311, 1039317, -4053432, 3214820, 9563585, -3421205, 11181628, 2295130, 0, -1974954, -1157500, 1450570, 2874085, -865276, 5088995, -2227660, -3940272, 4028003, 0, -344448, 8268930, 2323485, -2321932, 3973390, -11535188, 5444120, 0, -1056950, -1022675, 0, -4641285, -5646791, 1084460, 333785, 5190265, -3926765, 9425425, 0, 7538927, 525151, 4081490, -3515570, 14719633, 1953784, -7656522, 3490646, 9048369, 0, 12082475, -1215905, -13348370, 2556735, -12086920, -3699244, -4299480, -8455255, 1286115, -15562730, -5343063, -11819298, -5292045, -1646361, 14986660, 146869, 811035, 10259655, -15298995, 5288726, -7864625, 0, -4708655, 7373008, -19770600, 8154728, -551006, 8169165, -7978095, -3565015, 13494977, 0, -12292545, 10906230, 8758910, -3389468, 60800830, -310838, 10270750, 0, 336765, -20642640, 0, 4977140, -6388122, 5001885, 557232, 8354055, -30757875, 8091524, 0, -2669367, 3926594, 182310, -19718020, 12156466, 13200262, -4249796, 19223758, -645513, 0, 13024020, -14444082, -26188220, 9410385, -9265675, -14118378, -2247435, -14041182, 3425390, -49280046, -1981638, -28369076, -2570555, 11341868, 20771055, -17520752, -1569015, 43220035, -11313120, 6140553, -7267570, 0, -13293866, -10561916, -20297050, 17154149, 4046652, 13727120, 20105095, -20025561, 1759873, 0, 3512061, 21865215, 16379905, 3027843, 16710605, -2251834, 26392060, 0, 4864365, -15228860, 0, -11215450, -23639620, 7233185, 6694740, 49053710, -26133355, 30501584, 0, 22013955, -2965228, 15425285, -10581455, 31757100, 5192093, -33863638, 8940982, 17179760, 0, 28094990, -8282552, -30968450, -15694695, -22731780, 3249771, -16950887, -28543793, 3033735, -26580496, -33806143, 16087970, -21991295, -13377394, 18291147, -1499068, -37486465, 31564590, -9566215, 22164065, -24466425, 0, -16649005, 12106052, -50403766, 5604167, 36070298, 34480010, -8583105, -11949148, 4526897, 0, 9247617, 24548390, 13987695, -1540418, 31229055, -11236711, 38659725, 0, 73757040, -12605270, 0, 11695125, 13338957, -19851315, 5915241, -18529550, -41490460, 28263205, 0, -3938642, 26599258, -22971010, -47886235, 25506991, 30696477, -5961984, -37896106, -16277562, 0, 59708330, -9612725, -27674745, -10723305, -6474630, -1437850, -30162161, -63770017, -21957565, 8241532, -2616834, 12629392, -15039135, 26983635, 812552, -29174242, -21957430, 64289815, -34094845, 19970936, 2728010, 0, 14560211, 35496464, -10560486, -50134743, 18897025, 42423655, 4782005, -25945661, -60564746, 0, 30264047, -104039065, 37960710, 33550768, -13653005, -32170324, 68357540, 0, 7320830, -23993310, 0, 61667795, -7018679, 37005595, 30239178, -36327705, 13815675, -22874457, 0, 85129041, -1738670, 66464235, -35168380, 37185422, 46281670, 34523466, -37451156, -37480786, 0, 81580070, 13482271, -123275435, -31002080, -12871870, -35452418, -57183360, -65636512, -54199360, 24071794, -61282241, 27072952, -20988485, -7062519, -46059786, -5648872, -134426800, 97551675, 10447960, -34506003, -119328685, 0, -7553328, 78519614, -47836906, -36256682, 171811507, -12357275, -1981740, 9502804, -73187366, 0, 131966914, -4178600, 41935285, 48581671, -28518225, 66344269, 148926155, 0, 88455370, -4763420, 0, 39841925, 151855151, 3043200, 78285386, -65396255, 58105705, 21073318, 0, 24178069, -75162070, -167969510, -122142080, -15232118, 103838087, 50903274, 23291318, -93538537, 0, 112505950, -115379084, -44677380, -53439560, 18644455, -722227, 5391512, -94289119, -51339595, 116327348, -33029329, 75975644, -78864010, -2521174, -2041764, -20855705, -121380515, 98058860, 10708895, -52259551, -59872195, 0, 8379435, -39308334, -121400702, -278442637, 75494675, 56872460, 137919130, -66381374, -77915094, 0, 72931113, -98521835, 84426870, 95184812, -91349755, 42618386, 131859270, 0, 140742430, 81555960, 0, 255832470, 66173614, -39240775, 177980395, 68398865, 14940990, -55313163, 0, 83945360, -73217005, -131644950, -61324900, 34349832, 104610566, -28706112, -66427126, -141610756, 0, 435251350, -70193694, -97068110, -209231005, 156909135, 4155065, -127338772, -52155964, -68662515, 47868558, -239956375, 127955788, -203266630, -33353609, 1215471, 99540200, -356622685, 26621875, 180463295, -24693990, -274583200, 0, 17994273, 87069726, -439154736, -125954013, 204689907, 26361095, 215947295, -5575013, -233286131, 0, 215976227, -97179955, 149020160, -28415556, -151028040, 45975548, 48698165, 0, 334828055, -44276145, 0, 37922840, 194134234, -122985975, 209639914, 57294400, 123470295, -5148759, 0, 71005938, -156064303, -5761035, -300126775, 37784539, 260438891, -102759606, -310762322, -193949632, 0, 191121190, -66899096, -133219505, -254543260, 183997740, 103032730, -46675923, -70750753, 50705660, 203616134, -113917637, 309002242, -48656255, 16528347, -692103, 35804465, -149481760, 327656945, 101333060, -258089409, -270757595, 0, -46954281, 231885594, -353675246, -177547988, 202953566, 108170250, 139710350, -282302611, -101975205, 0, 232794300, -62376880, 321570310, 326581339, -126676660, 131387025, 201882570, 0, 194022295, 154518405, 0, 175517015, 275250516, -166009075, 181470724, 73948530, 27278025, 160958885, 0, 91913797, -91076442, -207386315, -259395935, 94246247, 132680258, 13484460, -196016742, -711970091, 0, 256780715, -84085316, -173192965, -229094730, 185191510, -16437751, -135462794, -258780849, -14207700, 4771222, -262518274, 136743552, -185663885, -38712204, 87718372, -31364782, -797614985, 144355830, -134259140, -199265128, -450282460, 0, -163557239, 196509520, -473337332, -135463445, 375169682, 192476590, 273884555, -143614044, -224880735, 0, 283684626, -119747170, 566252125, 185352394, -47438685, 221454110, 654361435, 0, 486105025, -29698905, 0, 371174120, 354914234, 73608535, 614051745, 54661110, 5679685, 118499839, 0, 145324686, -71930453, -17870110, -530597805, 21117573, 175836490, -36944036, -613507182, -332036917, 0, 369905450, -310408913, -218651510, -478153700, 6888965, 82075399, -73962239, -309252559, 61764995, 417800460, -165453204, 401300128, -163704280, 39425580, 14894114, -156851876, -287749030, 427540515, 75429020, -122261756, -492808060, 0, -140410622, 407509480, -552706190, -233942589, 181980257, 521279935, 68239085, -413248051, -243869698, 0, 170149536, -46042355, 160169395, 163800344, -102795960, 259287482, 307578330, 0, 406152745, -332220700, 0, 256484125, 241591960, -51877725, 308072376, 50912765, -250999505, 227690417, 0, 240571834, -66301905, -145465320, -589488945, 68170119, 372960463, -509211744, -177670150, -419718798, 0, 940639315, -101748044, -668241865, -212401405, 294105555, 44225432, -423620314, -178318038, -240966800, 37805480, -253691620, 494566406, -219954950, -19516881, 201229654, -151107342, -1045538780, 418929120, -74679670, 34224242, -1330819410, 0, -189221922, 146951994, -733590678, -275000894, 704445964, 158960930, 615539210, -255660846, -261549393, 0, 646348895, -40696900, 550431950, 395135075, 173410085, -13375738, 1036581535, 0, 761908435, 115942125, 0, 126949670, 529359466, -151894800, 413664747, 206906805, -299967135, 195869367, 0, 141451102, -304464996, -29382345, -716275790, 265321320, 818862974, -179742614, -47538082, -446996161, 0, 670144955, -531974565, -462100665, -593591125, 122649510, 38291476, -218865912, -965976722, 65770500, -27791320, -408306310, 225201420, -427495765, -18608382, 105403313, -248018146, -719867410, 755634375, -261686375, 20304606, -415465230, 0, -199534477, 162671594, -353195470, -381469956, 599304155, 474258740, 188462660, -359353955, -271024988, 0, 332465895, -181737375, 655194070, 425494756, 154181355, 200841226, 522367540, 0, 638251785, -203278980, 0, 672837295, 281833176, -14109650, 489064794, 219330280, 15754095, 338575174, 0, 344798416, -290867990, -329136085, -342634210, 701939759, 337101373, -232662870, -508455632, -415091896, 0, 1611942975, -155744106, -941173750, -335514495, -208216915, -119317208, -739524150, -632854347, -444463485, -177369620, -593674956, 18597142, -109667000, 60835873, 277420104, -281634603, -873607105, 736257380, 47964620, 11228997, -550984655, 0, -113368916, 258988976, -1554512890, -332695270, 872320625, 405581200, 186041690, -233314546, -525034157, 0, 550080120, -216477770, 660275200], "weight": 6, "weight_parity": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}