# Stored data for newform 22.6.a.c, downloaded from the LMFDB on 04 June 2023. {"level_primes": [2, 11], "is_polredabs": true, "sato_tate_group": "5.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 1296477389105222849, "level_radical": 22, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 3, "analytic_conductor": 3.528444035885574, "inner_twist_count": 1, "field_disc_factorization": [], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "22.6.a.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "22.6.a.c", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": 0, "traces": [0, 1, 4, -29, 16, -31, -116, -230, 64, 598, -124, 121, -464, 112, -920, 899, 256, -1142, 2392, -612, -496, 6670, 484, -1941, -1856, -2164, 448, -10295, -3680, 1192, 3596, -1037, 1024, -3509, -4568, 7130, 9568, 8083, -2448, -3248, -1984, -10444, 26680, 58, 1936, -18538, -7764, 8656, -7424, 36093, -8656, 33118, 1792, -20318, -41180, -3751, -14720, 17748, 4768, -21351, 14384, 47044, -4148, -137540, 4096, -3472, -14036, 48093, -18272, 56289, 28520, -24967, 38272, -42288, 32332, 62756, -9792, -27830, -12992, -72410, -7936, 153241, -41776, -15806, 106720, 35402, 232, -34568, 7744, -114761, -74152, -25760, -31056, 30073, 34624, 18972, -29696, -5159, 144372, 72358, -34624, -61426, 132472, 185896, 7168, -206770, -81272, -23970, -164720, -56326, -15004, -234407, -58880, -261903, 70992, 60171, 19072, 66976, -85404, 262660, 57536, 14641, 188176, 302876, -16592, 163959, -550160, 87404, 16384, -1682, -13888, 265122, -56144, 140760, 192372, 319145, -73088, 245857, 225156, -363594, 114080, -251024, -99868, 13552, 153088, -36952, -169152, -1046697, 129328, -55750, 251024, 65642, -39168, -682916, -111320, 32147, -51968, -275367, -289640, 589222, -31744, 446430, 612964, 291940, -167104, 108779, -63224, -337344, 426880, -358749, 141608, -365976, 928, -116742, -138272, 497720, 30976, 619179, -459044, -19107, -296608, -16177, -103040, -1364276, -124224, -250573, 120292, -138182, 138496, 2367850, 75888, 685333, -118784, -309292, -20636, 100688, 577488, -120930, 289432, 915536, -138496, -1394697, -245704, -274160, 529888, 323764, 743584, -1160718, 28672, -74052, -827080, -134580, -325088, 724043, -95880, -1798, -658880, 238510, -225304, 1226352, -60016, -127904, -937628, 468839, -235520, -1294072, -1047612, 275022, 283968, -642281, 240684, 807070, 76288, -1504848, 267904, -268336, -341616, 2099890, 1050640, -304694, 230144, 1271808, 58564, -1942304, 752704, -1118883, 1211504, -68544, -66368, 458374, 655836, 629965, -2200640, -234861, 349616, -1026658, 65536, 544086, -6728, -1859090, -55552, 712816, 1060488, -1989334, -224576, 629858, 563040, 3328069, 769488, 1754458, 1276580, -1658240, -292352, 747040, 983428, -261844, 900624, -42634, -1454376, -620126, 456320, 319510, -1004096, -2027348, -399472, -550188, 54208, 2402120, 612352, -115693, -147808, 149611, -676608, 718844, -4186788, 661881, 517312, -1245695, -223000, -217392, 1004096, -13340, 262568, 1781354, -156672, -1458364, -2731664, -1981420, -445280, -5390984, 128588, -1510300, -207872, 2000919, -1101468, 4263740, -1158560, -259331, 2356888, 144232, -126976, 695130, 1785720, 698904, 2451856, -242368, 1167760, 1633454, -668416, -1990880, 435116, 51203, -252896, 4833634, -1349376, -1490883, 1707520, 266870, -1434996, 7595187, 566432, -125477, -1463904, -4435780, 3712, -1744959, -466968, 622800, -553088, 2436490, 1990880, -1153040, 123904, 1559571, 2476716, 773977, -1836176, -7617140, -76428, 1919608, -1186432, -2101555, -64708, -424589, -412160, 1310928, -5457104, 3612251, -496896, -6245512, -1002292, 4673140, 481168, 3939682, -552728, -4754811, 553984, 133504, 9471400, -2188289, 303552, -2534716, 2741332, 768387, -475136, 862730, -1237168, 34684, -82544, 324313, 402752, 2216622, 2309952, -7688538, -483720, 2244710, 1157728, 334758, 3662144, -4082040, -553984, -902022, -5578788, -116144, -982816, -4750471, -1096640, 978043, 2119552, -5004574, 1295056, -7129853, 2974336, 4910730, -4642872, 489986, 114688, 10544226, -296208, -3001236, -3308320, 4562238, -538320, 5176288, -1300352, 2471288, 2896172, -10820120, -383520, -393008, -7192, 4897826, -2635520, 6728757, 954040, 1071608, -901216, 1187892, 4905408, -3350336, -240064, 21583614, -511616, -7124343, -3750512, 3557591, 1875356, 1616750, -942080, -2709285, -5176288, -1263724, -4190448, -1903618, 1100088, 798560, 1135872, 2413612, -2569124, 11756890, 962736, -6560652, 3228280, -4724207, 305152, -932263, -6019392, -2284439, 1071616, -11061390, -1073344, 7985643, -1366464, 7018, 8399560, 1324368, 4202560, -12150164, -1218776, 951544, 920576, 905296, 5087232, -12946470, 234256, 159929, -7769216, 3514843, 3010816, -8466260, -4475532, -5787192, 4846016, -1361264, -274176, -2243098, -265472, 5742410, 1833496, 1029124, 2623344, 9782976, 2519860, -727370, -8802560, 1904206, -939444, 10403721, 1398464, -1946297, -4106632, 9726240, 262144, 6300540, 2176344, -5762776, -26912, 1047376, -7436360, 3385518, -222208, -10313283, 2851264, -6868396, 4241952, -14433880, -7957336, 1184254, -898304, -2668862, 2519432, -12767898, 2252160, -1169728, 13312276, 743070, 3077952, 554103, 7017832, 4367253, 5106320, 10054476, -6632960, 469133, -1169408, 1746106, 2988160, 9857248, 3933712, 28132312, -1047376, -729504, 3602496, 16654300, -170536, 7266617, -5817504, -14589166, -2480504, 6496, 1825280, 4007278, 1278040, -10241316, -4016384, 8118993, -8109392, -35245430, -1597888, -751816, -2200752, -7018540, 216832, -19874657, 9608480, 4200324, 2449408, -3363767, -462772, 8969468, -591232, 3635380, 598444, -2458478, -2706432, -2076256, 2875376, 14058548, -16747152, 634644, 2647524, 3506970, 2069248, -5394196, -4982780, -8142460, -892000, -26550544, -869568, -12020376, 4016384, 1646358, -53360, 28759614, 1050272, -453871, 7125416, 4884506, -626688, 7950640, -5833456, 969472, -10926656, 3490112, -7925680, -9389156, -1781120, 9120722, -21563936, 14663515, 514352, 19982595, -6041200, 26395030, -831488, 1679771, 8003676, 2147508, -4405872, -9230786, 17054960, -16387005, -4634240, 3902820, -1037324, -2709524, 9427552, 4042416, 576928, -14930266, -507904, -3268353, 2780520, 8328425, 7142880, 52142, 2795616, 2496941, 9807424, -2583471, -969472, -6916790, 4671040, -789105, 6533816, -8218782, -2673664, -25288224, -7963520, -8313926, 1740464, -4335171, 204812, 3709216, -1011584, -4363560, 19334536, -2313672, -5397504, -13596331, -5963532, 5692324, 6830080, 7293134, 1067480, 22278380, -5739984, 15581402, 30380748, 1186570, 2265728, -7975638, -501908, -2169304, -5855616, -7621567, -17743120, 18626149, 14848, -2275616, -6979836, -13219475, -1867872, -16642340, 2491200, 11271414, -2212352, 11927048, 9745960, 43640592, 7963520, -25939506, -4612160, -4946796, 495616, 7781744, 6238284, 14127980, 9906864, 3575311, 3095908, -43301180, -7344704, 2012817, -30468560, -420112, -305712, 8836126, 7678432, -1958141, -4745728, -42756080, -8406220, -36882432, -258832, -2579488, -1698356, 15535975, -1648640, 19089253, 5243712, -66236, -21828416, -14600204, 14449004, 32447607, -1987584, 5819253, -24982048, -20668246, -4009168, 1987776, 18692560, 11706452, 1924672, 1728250, 15758728, -9451988, -2210912, 5513100, -19019244, -12760715, 2215936, -18268985, 534016, -2034902, 37885600, -14086854, -8753156, 6810969, 1214208, 23382160, -10138864, 12954980, 10965328, 21170396, 3073548, -2391312, -1900544, -10957520, 3450920, -15778494, -4948672, 16933594, 138736, 2244068, -330176, 53913610, 1297252, 6391728, 1611008, -3021007, 8866488, -12271640, 9239808, 8536377, -30754152, -7516552, -1934880, 57690686, 8978840, 60237690, 4630912, 5268928, 1339032, -18265882, 14648576, 3937885, -16328160, -9885152, -2215936, -68627078, -3608088, -5116848, -22315152, -13839330, -464576, -50879282, -3931264, -17360900, -19001884, 27085002, -4386560, 48088960, 3912172, -9050140, 8478208, -35496, -20018296, -15404480, 5180224, 35938390, -28519412, -505509, 11897344, 7593476, 19642920, -29995488, -18571488, 29694153, 1959944, 1236386, 458752, -41218206, 42176904, 10457664, -1184832, 10675915, -12004944, -14137137, -13233280, -19090285, 18248952, -9265790, -2153280, 11121219, 20705152, -3367430, -5201408, 58793092, 9885152, -15689103, 11584688, -4685394, -43280480, 11345256, -1534080, -41284552, -1572032, -3548051, -28768, -69661480, 19591304, -30760536, -10542080, 3619002, 26915028, 3355097, 3816160, -8761610, 4286432, 5386416, -3604864, -3085082, 4751568, -37710570, 19621632, 30553528, -13401344, -20846476, -960256, 42101773, 86334456, 57164, -2046464, -19194549, -28497372, -11610630, -15002048, -20102920, 14230364, 18542161, 7501424, -5297472, 6467000, 592317, -3768320, 6304368, -10837140, -1236104, -20705152, 23203156, -5054896, 386860, -16761792, 501487, -7614472, 20985492, 4400352, -36732748, 3194240, 47412500, 4543488, -1912526, 9654448, 42292556, -10276496, -60978060, 47027560, 40432586, 3850944, 57461180, -26242608, -2796304, 12913120, -17491612, -18896828, 111165808, 1220608, 33075690, -3729052, -22088916, -24077568, 43798700, -9137756, 4283642, 4286464, -31513244, -44245560, -58026651, -4293376, -9541470, 31942572, 20271804, -5465856, -73403350, 28072, 22420753, 33598240, -4736256, 5297472, 7520599, 16810240, 16898478, -48600656, -21245323, -4875104, -4182728, 3806176, -56547110, 3682304, -27553782, 3621184, -14334060, 20348928, 9588052, -51785880, -30694648, 937024, -20268216, 639716, 33566411, -31076864, 83626620, 14059372, 7028672, 12043264, 24789677, -33865040, -13886081, -17902128, -33682948, -23148768, 5226059, 19384064, 3748830, -5445056, 57735520, -1096704, -112578, -8972392, 24082600, -1061888, -1484887, 22969640, -28381616, 7333984, -13260598, 4116496, -83214485, 10493376], "hecke_ring_index_factorization": [], "nf_label": "1.1.1.1", "field_poly": [0, 1], "atkin_lehner_string": "--", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, -1], [11, -1]], "char_values": [22, 1, [13], [1]], "Nk2": 792, "field_poly_root_of_unity": 0, "analytic_rank": 1, "char_orbit_label": "a", "weight": 6, "trace_display": [4, -29, -31, -230], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+4q^{2}-29q^{3}+2^{4}q^{4}-31q^{5}-116q^{6}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[3, [29, 1]]], "space_label": "22.6.a", "level": 22, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 1, "hecke_orbit_code": 9007199355404310, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.970", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.915", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.786", "prec": 17}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0], [1], [4], [-29], [16], [-31], [-116], [-230], [64], [598], [-124], [121], [-464], [112], [-920], [899], [256], [-1142], [2392], [-612], [-496], [6670], [484], [-1941], [-1856], [-2164], [448], [-10295], [-3680], [1192], [3596], [-1037], [1024], [-3509], [-4568], [7130], [9568], [8083], [-2448], [-3248], [-1984], [-10444], [26680], [58], [1936], [-18538], [-7764], [8656], [-7424], [36093], [-8656], [33118], [1792], [-20318], [-41180], [-3751], [-14720], [17748], [4768], [-21351], [14384], [47044], [-4148], [-137540], [4096], [-3472], [-14036], [48093], [-18272], [56289], [28520], [-24967], [38272], [-42288], [32332], [62756], [-9792], [-27830], [-12992], [-72410], [-7936], [153241], [-41776], [-15806], [106720], [35402], [232], [-34568], [7744], [-114761], [-74152], [-25760], [-31056], [30073], [34624], [18972], [-29696], [-5159], [144372], [72358], [-34624]]}