# Stored data for newform 22.6.a.b, downloaded from the LMFDB on 03 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": 1485915793178152084, "level_radical": 22, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 2, "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.b", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "22.6.a.b", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": 0, "traces": [0, 1, -4, 1, 16, -51, -4, -166, -64, -242, 204, -121, 16, 692, 664, -51, 256, -738, 968, 1424, -816, -166, 484, -1779, -64, -524, -2768, -485, -2656, -2064, 204, 6245, -1024, -121, 2952, 8466, -3872, -14785, -5696, 692, 3264, 5304, 664, 17798, -1936, 12342, 7116, -17184, 256, 10749, 2096, -738, 11072, -30726, 1940, 6171, 10624, 1424, 8256, -34989, -816, -45940, -24980, 40172, 4096, -35292, 484, 25343, -11808, -1779, -33864, 13311, 15488, -53260, 59140, -524, 22784, 20086, -2768, 77234, -13056, 58321, -21216, 55014, -2656, 37638, -71192, -2064, 7744, 125415, -49368, -114872, -28464, 6245, 68736, -72624, -1024, -88807, -42996, 29282, -8384, 1482, 2952, -117496, -44288, 8466, 122904, -79362, -7760, 87842, -24684, -14785, -42496, -47247, -5696, 90729, -33024, -167464, 139956, 122508, 3264, 14641, 183760, 5304, 99920, 186099, -160688, -239416, -16384, 17798, 141168, -98142, -1936, -236384, -101372, 24735, 47232, 400137, 7116, 205766, 135456, -17184, -53244, -83732, -61952, 105264, 213040, 10749, -236560, 87726, 2096, -432778, -91136, 178596, -80344, -318495, 11072, -34075, -308936, -30726, 52224, 295314, -233284, 45020, 84864, 6171, -220056, 482556, 10624, 107571, -150552, -344608, 284768, -766254, 8256, 86984, -30976, -34989, -501660, 303399, 197472, -285181, 459488, -45940, 113856, 754035, -24980, 89298, -274944, 80510, 290496, 767067, 4096, 411668, 355228, -35292, 171984, -759258, -117128, -46600, 33536, 25343, -5928, 342624, -11808, -270504, 469984, 430518, 177152, -172304, -33864, -932428, -491616, 13311, 317448, -907698, 31040, -1036670, -351368, -53260, 98736, -510696, 59140, 169745, 169984, 126808, 188988, 198078, 22784, -849997, -362916, 20086, 132096, -401832, 669856, 876384, -559824, 77234, -490032, 855174, -13056, 1125464, -58564, 176176, -735040, -548199, -21216, 985408, -399680, 55014, -744396, -1197513, 642752, 215259, 957664, 37638, 65536, 37758, -71192, 2454310, -564672, 499488, 392568, -631254, 7744, 1567026, 945536, 125415, 405488, -1080342, -98940, -816100, -188928, -114872, -1600548, 63404, -28464, 1688198, -823064, -1511290, -541824, -879042, 68736, 1540268, 212976, -72624, 334928, -880464, 247808, -875213, -421056, -88807, -852160, 720840, -42996, 1784439, 946240, 58685, -350904, -1231068, -8384, -2954468, 1731112, 1482, 364544, 2342940, -714384, -1039048, 321376, -117496, 1273980, -1251348, -44288, -1443361, 136300, -2048772, 1235744, -2012079, 122904, 249744, -208896, -79362, -1181256, -1050912, 933136, -362608, -180080, 87842, -339456, 2852544, -24684, 2017337, 880224, 3577970, -1930224, -1292493, -42496, 264122, -430284, -47247, 602208, -755645, 1378432, 1005628, -1139072, 90729, 3065016, -1710492, -33024, 218822, -347936, -335620, 123904, 3681915, 139956, -678861, 2006640, 122508, -1213596, 1885284, -789888, -448323, 1140724, 14641, -1837952, 2716260, 183760, -3116659, -455424, -1283568, -3016140, 5100516, 99920, 1394414, -357192, 186099, 1099776, -1428288, -322040, -4260355, -1161984, -239416, -3068268, 201765, -16384, -1024386, -1646672, -4307116, -1420912, 1948821, 141168, 1312902, -687936, -98142, 3037032, -3938934, 468512, -1468258, 186400, -236384, -134144, 2246178, -101372, 4321540, 23712, -2974371, -1370496, 1788985, 47232, -3614878, 1082016, 400137, -1879936, 5808174, -1722072, -2805714, -708608, 205766, 689216, -3812388, 135456, 1973462, 3729712, 4158528, 1966464, 386712, -53244, 7626040, -1269792, -83732, 3630792, -2083590, -124160, -72691, 4146680, 105264, 1405472, -2533296, 213040, 594392, -394944, -2601258, 2042784, 4566507, -236560, -6396165, -678980, 87726, -679936, -5443821, -507232, -641784, -755952, -432778, -792312, 5858472, -91136, 6703124, 3399988, 357930, 1451664, -1259940, -80344, -5023081, -528384, -318495, 1607328, -2356605, -2679424, -4206938, -3505536, -34075, 2239296, -2153558, -308936, -746176, 1960128, 7435692, -3420696, -6722580, 52224, -10231220, -4501856, 295314, 234256, 4529157, -704704, 1960013, 2940160, 45020, 2192796, -579624, 84864, 1523232, -3941632, -1493382, 1598720, -2209626, -220056, 1369052, 2977584, 482556, 4790052, 1833426, -2571008, -75582, -861036, 107571, -3830656, -1712661, -150552, 8841160, -262144, -690640, -151032, 5992296, 284768, 2079264, -9817240, -766254, 2258688, -789435, -1997952, 627392, -1570272, 86984, 2525016, -4608810, -30976, -3271502, -6268104, 8467338, -3782144, 3670368, -501660, 4047462, -1621952, 303399, 4321368, -1300629, 395760, 3208952, 3264400, -285181, 755712, -4479942, 459488, 3426584, 6402192, 11117480, -253616, -2939136, 113856, -12820844, -6752792, 754035, 3292256, 10519830, 6045160, 12316216, 2167296, 89298, 3516168, 5472876, -274944, 2409597, -6161072, -9681286, -851904, -11778672, 290496, -8356276, -1339712, 767067, 3521856, 932196, -991232, -13775839, 3500852, 411668, 1684224, -9132324, 355228, 3717846, 3408640, 8540664, -2883360, -12709308, 171984, 8892880, -7137756, -759258, -3784960, 1008252, -234740, -6247908, 1403616, -46600, 4924272, 10510032, 33536, -199390, 11817872, -6133006, -6924448, -746691, -5928, 16190, -1458176, 342624, -9371760, -11891328, 2857536, -11525344, 4156192, -270504, -1285504, 16997394, 469984, -18487471, -5095920, 862815, 5005392, -20818890, 177152, -7853549, 5773444, -172304, -545200, 10911330, 8195088, -4542811, -4942976, -932428, 8048316, 12210216, -491616, 7438308, -998976, -3221262, 835584, 18428631, 317448, 9666035, 4725024, -907698, 4203648, -4514301, -3732544, 4233669, 1450432, -1036670, 720320, -5372349, -351368, 5005242, 1357824, 12888920, -11410176, 9879558, 98736, 10805201, -8069348, -510696, -3520896, 12055584, -14311880, 3671856, 7720896, 169745, 5169972, 5558740, 169984, 11327486, -1056488, 254140, 1721136, -12059490, 188988, 14741962, -2408832, 198078, 3022580, -5141664, -5513728, -20406987, -4022512, -849997, 4556288, -21262392, -362916, 13124255, -12260064, -4860812, 6841968, -10494066, 132096, -3914352, -875288, -401832, 1391744, 3659562, 1342480, -21053840, -495616, 876384, -14727660, -246012, -559824, 10225211, 2715444, -18690628, -8026560, -11109855, -490032, 4270332, 4854384, 855174, -7541136, 24168285, 3159552, 19504336, 1793292, 1125464, -4562896, 1081536, -58564, 16824641, 7351808, -13995827, -10865040, -13134924, -735040, -5041684, 12466636, -548199, 1821696, -3066503, 5134272, -6263746, 12064560, 985408, -20402064, 3639756, -399680, -4474026, -5577656, -13313388, 1428768, 13174092, -744396, -18736957, -4399104, -1197513, 5713152, 22071678, 1288160, 489242, 17041420, 215259, 4647936, 14696940, 957664, -14581772, 12273072, -9108396, -807060, -24212388, 65536, 24207236, 4097544, 37758, 6586688, 13526010, 17228464, -3272380, 5683648, 2454310, -7795284, 7552896, -564672, -1610631, -5251608, 1001040, 2751744, 1737825, 392568, 14209424, -12148128, -631254, 15755736, 7843002, -1874048, -31790480, 5873032, 1567026, -745600, -7933335, 945536, 12681792, 536576, -30350430, -8984712, 6444460, 405488, -15061014, -17286160, -1080342, -94848, -10468512, 11897484, 11914742, 5481984, -816100, -7155940, -2296020, -188928, 25344352, 14459512, 27799024, -4328064, -1861122, -1600548, 23015285, 7519744, 63404, -23232696, -16835148, 6888288, -23529859, 11222856, 1688198, 2834432, -7932762, -823064, -24610356, -2756864, -3028825, 15249552, 29154921, -541824, -16251053, -7893848, -879042, -14918848, -5486121, -16634112, -2430406, -7865856, 1540268, -1546848, 26302515, 212976, -9490522, -30504160, 17575008, 5079168, -1815528, 334928, -10781209, -14523168, -880464, 8334360, -28335456, 496640, 39078954, 290764, -875213, -16586720, -9345314, -421056, 17537356, -5621888, 21491294, 10133184, -30892434, -852160, -26891884, -2377568, 720840, 1579776, -19213227, 10405032, 11593100, -8171136, 1784439, -18266028, 13185678, 946240, 39743056, 25584660, -7056841, 2715920, -24470016, -350904, -15473349, 2719744, -1231068, 21775284, -12889680, 2028928, 22675788, 2567136, -2954468, 3023808, 14544231, 1731112, 2981948, 3169248, -358644, -23433888, 29657868, 364544, -6656694, -26812496, 2342940, -13599952, 16291572, -1431720, 31805678, -5806656, -1039048, 5039760, 9211212, 321376, 7747340, 20092324, 28434032, 2113536, -23344446, 1273980, 15306576, -6429312, -1251348, 9426420, -4554198, 10717696, 20737208, 16827752, -1443361, 14022144, 26919282, 136300, -9435816, -8957184, -4106010, 8614232, 10189563, 1235744, -36855920, 2984704, -2012079, -7840512, 10392354, -29742768, -39120417, 13682784, 249744, 26890320, -66422742, -208896, 10370874, 40924880, 19205604, 18007424, -20995068, -1181256, -8188768, -937024, -1050912, -18116628, -17327439, 2818816, -34157156, -7840052, -362608, -11760640, -438963, -180080, -15175215, -8771184, -21257764, 2318496, -27912387, -339456, 38722158, -6092928, 2852544, 15766528, -31662642, 5973528, -42684640, -6394880, 2017337, 8838504, 2376600, 880224, -22104418, -5476208, 7170725, -11910336], "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, 1, -51, -166], "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}+q^{3}+2^{4}q^{4}-51q^{5}-4q^{6}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[3, [-1, 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": 4503599728033814, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.965", "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], [1], [16], [-51], [-4], [-166], [-64], [-242], [204], [-121], [16], [692], [664], [-51], [256], [-738], [968], [1424], [-816], [-166], [484], [-1779], [-64], [-524], [-2768], [-485], [-2656], [-2064], [204], [6245], [-1024], [-121], [2952], [8466], [-3872], [-14785], [-5696], [692], [3264], [5304], [664], [17798], [-1936], [12342], [7116], [-17184], [256], [10749], [2096], [-738], [11072], [-30726], [1940], [6171], [10624], [1424], [8256], [-34989], [-816], [-45940], [-24980], [40172], [4096], [-35292], [484], [25343], [-11808], [-1779], [-33864], [13311], [15488], [-53260], [59140], [-524], [22784], [20086], [-2768], [77234], [-13056], [58321], [-21216], [55014], [-2656], [37638], [-71192], [-2064], [7744], [125415], [-49368], [-114872], [-28464], [6245], [68736], [-72624], [-1024], [-88807], [-42996], [29282], [-8384]]}