# Stored data for newform 27.6.c.a, downloaded from the LMFDB on 23 April 2024. {"label": "27.6.c.a", "space_label": "27.6.c", "level": 27, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 137539616795, "dim": 8, "is_polredabs": true, "trace_hash": 1403514109957690378, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [], "qexp_display": "q+(-1+\\beta _{1}-\\beta _{2}-\\beta _{3})q^{2}+(-13\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "c", "char_is_real": false, "Nk2": 972, "analytic_conductor": 4.330363134950477, "hecke_ring_index": 26244, "level_radical": 3, "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": [27, 3, [2], [1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [10, 19], "field_disc": 23765829750441, "field_disc_factorization": [[3, 4], [541669, 2]], "field_poly": [7056, 0, 3363, 0, 568, 0, 40, 0, 1], "hecke_ring_index_factorization": [[2, 2], [3, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.616", "prec": 17}, {"__RealLiteral__": 0, "data": "1.547", "prec": 17}, {"__RealLiteral__": 0, "data": "231.259", "prec": 24}, {"__RealLiteral__": 0, "data": "122.746", "prec": 24}, {"__RealLiteral__": 0, "data": "12819.053", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "5.2.3.c3", "trace_display": [-3, 0, -78, 28], "traces": [0, 8, -3, 0, -49, -78, 0, 28, 750, 0, 60, -444, 0, -182, -1392, 0, -289, 4356, 0, 952, -6684, 0, 1011, -8844, 0, -1654, 24888, 0, -1604, -12018, 0, 1132, -8703, 0, 10125, 16224, 0, -15176, 11145, 0, -8736, -1248, 0, -6092, -49530, 0, 45960, 60, 0, 9090, 57057, 0, -32510, -20952, 0, -36120, 61170, 0, 8328, -2076, 0, 48142, -241764, 0, -20926, 13146, 0, -7148, 123129, 0, -654, 71856, 0, 122452, 160320, 0, -49571, -39534, 0, -59516, -124512, 0, -233598, -117696, 0, 28836, 15915, 0, 104523, 451728, 0, 111392, -134034, 0, 169464, -294888, 0, 33976, -57654, 0, 175118, -355422, 0, -231644, -184062, 0, -273456, 710424, 0, -443864, 39798, 0, 2590, -129462, 0, 83640, 184380, 0, 639798, -272952, 0, 396680, 258942, 0, 246472, 29076, 0, 162736, 340161, 0, -732930, -413304, 0, -393244, -336210, 0, -1388502, 130920, 0, -7508, 365532, 0, 539460, -202200, 0, 927348, 218829, 0, 1127404, 355854, 0, 199540, -1086222, 0, 727008, 241728, 0, -825266, 869142, 0, -1156032, -1230780, 0, -2226944, 436593, 0, 165954, 200964, 0, 567234, -1526904, 0, 1594510, 816846, 0, 894208, 205197, 0, 387018, -8928, 0, 2072608, 156426, 0, -1855914, 1033620, 0, -1271052, 1113108, 0, -3879888, -358212, 0, 282472, -1837851, 0, 1968615, -956808, 0, 685312, -672765, 0, 1422858, -514824, 0, 429618, 4211616, 0, 3255364, -57858, 0, -1538336, -1293948, 0, -3417957, 2343624, 0, -4017412, -2644980, 0, 313764, 991728, 0, 2124388, 3313692, 0, 2167296, -129612, 0, 1292146, -2368926, 0, 43098, -3615588, 0, 3745392, -2466141, 0, -1881306, -1412628, 0, -1935800, 675780, 0, -7741640, 2576916, 0, 1350320, -359508, 0, 3374670, 1846872, 0, 966876, -1296114, 0, 2646239, 2853300, 0, 678800, 1705128, 0, 4993116, -1007796, 0, -2587140, -262686, 0, -3803789, -4665384, 0, -5188736, 2151261, 0, -1358061, 844476, 0, 992386, 3566046, 0, 2423904, 4091082, 0, 831472, -572796, 0, 1071636, -3167256, 0, 2836556, 2237274, 0, -3106511, 2496702, 0, -2160492, -8628024, 0, -2266536, -2254296, 0, 926894, 5083356, 0, 3633937, -11690868, 0, 3917752, 605262, 0, 4534878, -594924, 0, -526976, 1137180, 0, -2488448, 7323486, 0, -2027796, 3083808, 0, -2448690, 5037192, 0, -7663016, 1642188, 0, 485823, 722226, 0, -3093200, -5858112, 0, 4203636, -5681316, 0, 998548, -1440891, 0, 2015928, -544020, 0, 4318712, -3149481, 0, -641076, -1423428, 0, 2840230, 27804, 0, 1762074, -2079300, 0, 524232, -4767210, 0, 251748, 21375216, 0, -1257636, 2926902, 0, 136688, -1173252, 0, 2223460, 10745292, 0, -11891544, -7243776, 0, -2898326, -5104485, 0, 113622, -2803524, 0, 4572088, 147120, 0, -4563636, -13068996, 0, -2723334, -4410186, 0, 3208570, -2187498, 0, 293544, 7660773, 0, -4173768, 15732384, 0, -231464, -5784918, 0, 6130661, 3263016, 0, 7524944, 14355096, 0, 10029588, -4377048, 0, 5961976, 4117986, 0, -5926034, 1654260, 0, -6245688, 2164626, 0, -3284121, -13407936, 0, 852238, -37381236, 0, -6571368, 2519622, 0, 2657144, -4868937, 0, 3458154, 22565520, 0, 6575596, -419970, 0, -7518680, 9369996, 0, -9161828, -11478240, 0, -10179756, -6761460, 0, -12493116, 9204744, 0, -3088466, -2266668, 0, 3063048, 14285010, 0, 14738475, -1603356, 0, 8057872, -882960, 0, 36930504, 2950854, 0, 4120252, 4061670, 0, 7539723, -15480216, 0, -11296324, 15064542, 0, -9224187, 4028664, 0, -4840556, -11325780, 0, -35497488, -8623308, 0, 11103836, 14417121, 0, 9919778, -29402220, 0, -3674576, 11296680, 0, -4185108, -1417740, 0, -12658680, 11995116, 0, -20595176, 16483896, 0, -15423284, 11693436, 0, -1547667, 18901008, 0, 16462068, 8398404, 0, 20497078, 3247842, 0, 17832728, -44071170, 0, 62607822, -1520832, 0, 3815814, -3815724, 0, -9516576, -10439964, 0, -26794640, -31615764, 0, -16239840, 631440, 0, -6815662, 2511000, 0, -25052692, 7452978, 0, 6610248, -14376963, 0, 3080268, 21153816, 0, 18287656, 1375212, 0, -11287917, 231828, 0, -12945716, 27501846, 0, -7667502, -11834592, 0, -10377394, -17139048, 0, -11180981, -10806768, 0, -2440792, -6867696, 0, 29053200, -11301108, 0, 23837106, 55517340, 0, 34782696, -11287920, 0, 16758628, 9690942, 0, -2769180, 1920288, 0, -11774108, -24552210, 0, -15348828, 562206, 0, 4160808, 61474938, 0, -50064528, 16440252, 0, 3928424, -11914398, 0, 17498212, -14769648, 0, 14967504, -5237322, 0, -28510638, -21125148, 0, -30031100, -4841976, 0, -10608572, 12337284, 0, -23284172, -31503969, 0, -3982938, -27120624, 0, 17856808, -27107601, 0, 18583302, 34702140, 0, 24694732, 4531704, 0, 65991840, -998640, 0, 12495296, -24042867, 0, 6584848, 48154464, 0, -6907520, 26209644, 0, 20640432, 32660448, 0, 1964232, 8078400, 0, -69352896, -18488784, 0, -9700652, -13541880, 0, -7537293, -9640944, 0, -25441608, -13089174, 0, 754228, 22128798, 0, -38383908, -20847858, 0, -4949364, 20248584, 0, -13083194, 5323710, 0, 3072660, -53833632, 0, 26198592, -15358128, 0, 21382014, -11030100, 0, 29093302, 364602, 0, 51855462, 39441786, 0, 12850364, 26677728, 0, 2402574, -49206888, 0, 9424572, 14796690, 0, 2954401, -13716972, 0, -132128, -29664588, 0, -58054854, 26836620, 0, -8214534, 26859126, 0, -9792158, -26475552, 0, -5684224, -15284307, 0, -45444903, 48183096, 0, -4109210, -27616032, 0, 29225772, -2128422, 0, 5452608, 20536668, 0, -4311954, -22959360, 0, 29042828, 46265652, 0, -13705118, -6521628, 0, 10089892, -2887080, 0, 4080792, 17131356, 0, 34635490, -37794642, 0, 14947254, -48341472, 0, -31920536, 37360248, 0, 8894124, 13313964, 0, 11511390, 76718928, 0, -11221254, -20497428, 0, -22576412, 27346074, 0, -33996126, 5091792, 0, -78741920, -12389199, 0, -21754848, -19713966, 0, -21694336, 14975628, 0, 75621660, -22597788, 0, -777026, 3845502, 0, -5979485, 83603376, 0, 95522416, -45066819, 0, 13485972, 4820028, 0, 8151840, -95465844, 0, -2872998, -11904222, 0, 36811960, -48001716, 0, 85291266, 40162200, 0, -27929836, -49078824, 0, 49668274, -62557494, 0, 6382152, 15706026, 0, -69551670, 18424884, 0, -44886918, 18600810, 0, -77184192, 121606596, 0, -122889080, 18273000, 0, -25138704, -20440344, 0, -15163522, 92682894, 0, -4204104, -37414506, 0, -4832156, -34448034, 0, 14775528, -102460320, 0, 107621440, -1621242, 0, 5293582, -48208446, 0, 2257248, 17456610, 0, 27315636, -69306708, 0, 31804898, 61520754, 0, 64967920, 56164032, 0, 55232656, -9022644, 0, 34913835, 27571776, 0, -17994302, 2806260, 0, 95970582, -43400550, 0, -48759068, -34606596, 0, -91166958, 24789024, 0, -145880508, 51202119, 0, -34763260, -24070506, 0, 11843612, 31173216, 0, 12977940, 34671288, 0, -2028530, -14194374, 0, 15482832, 166348656, 0, 108547000, 71723034, 0, -59759655, -5956404, 0, -30095080, -117073944, 0, -175011284, -47928660, 0, 76379112, 39783954, 0, 100771209, -16837584, 0, -19556640, -3852063, 0, 39066474, -17428332, 0, 59552452, -101777322, 0, -29021052, -4684548, 0, -37752522, -22717815, 0, -57871802, 2469084, 0, -60943952, -12609648, 0, -37903884, 28144440, 0, -16596392, -176550900, 0, 120474540, 14516106, 0, 28467324, 115625511, 0, -62452215, 20667744, 0, 227294512, 21088932, 0, -18647580, -52362654, 0, -4893756, 72302394, 0, -37033194, 116210724, 0, 3611192, 69507435, 0, 87586758, 27455940, 0, 1238064, 21419850, 0, 128662356, 23480076, 0, 8082090, -207512184, 0, -93288638, -70624362, 0, -111421748, 73220286, 0, -166749090, -207179856, 0, -198242884, 86345670, 0, 11195656, -38240016, 0, -14898816, -149331888, 0, 80922138, 940452, 0, -22222188, -1062666, 0, 59288954, 17702916, 0, 65923072, 39503196, 0, -4894344, 130697448, 0, 40961206, 149208906, 0, -55285248], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "9.6.c.a", "char_is_minimal": false, "conrey_index": 10, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -13, 2, 0, 1, 0, 0, 0], [-1, -19, -1, 0, 1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [7, -7, -8, -8, 0, 2, 3, 0], [95, 0, 0, 8, -5, 5, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [18, 0, 0, 55, 1, -1, 0, 6], [-107, 107, 5, 5, 0, 7, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, -65, 71, 0, 1, 0, 3, -3], [-2, -342, -13, 0, -7, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-109, 109, -120, -120, 0, -3, -12, 0], [531, 0, 0, -57, 35, -35, 0, -19], [0, 0, 0, 0, 0, 0, 0, 0], [119, 0, 0, -81, -3, 3, 0, -39], [-1692, 1692, -14, -14, 0, -38, -16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-24, 285, -49, 0, -32, 0, -24, 24], [49, -2265, 104, 0, 14, 0, 49, -49], [0, 0, 0, 0, 0, 0, 0, 0], [-346, 346, 355, 355, 0, -55, -15, 0], [3164, 0, 0, 125, -83, 83, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-250, 0, 0, -78, -24, 24, 0, 72], [-2947, 2947, 107, 107, 0, 21, 51, 0], [0, 0, 0, 0, 0, 0, 0, 0], [69, 409, -682, 0, 40, 0, 69, -69], [-140, -2083, -96, 0, 5, 0, -140, 140], [0, 0, 0, 0, 0, 0, 0, 0], [2685, -2685, 192, 192, 0, 219, 102, 0], [1966, 0, 0, 40, 66, -66, 0, 111], [0, 0, 0, 0, 0, 0, 0, 0], [-2140, 0, 0, -810, 150, -150, 0, 6], [2653, -2653, -542, -542, 0, 189, -90, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-72, -2376, 704, 0, 208, 0, -72, 72], [54, -173, -646, 0, -18, 0, 54, -54], [0, 0, 0, 0, 0, 0, 0, 0], [-1517, 1517, 205, 205, 0, -181, 0, 0], [-6353, 0, 0, -686, -7, 7, 0, -16], [0, 0, 0, 0, 0, 0, 0, 0], [6372, 0, 0, 2131, -293, 293, 0, -42], [297, -297, 1100, 1100, 0, -190, 109, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 2364, 77, 0, -425, 0, -9, 9], [190, 13909, 1186, 0, -145, 0, 190, -190], [0, 0, 0, 0, 0, 0, 0, 0], [-9110, 9110, -3114, -3114, 0, -336, -240, 0], [-2052, 0, 0, 1458, -30, 30, 0, -390], [0, 0, 0, 0, 0, 0, 0, 0], [-4482, 0, 0, -182, 76, -76, 0, -195], [15202, -15202, 104, 104, 0, -434, -16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [18, 1422, 2927, 0, -323, 0, 18, -18], [14, -1033, 1637, 0, 391, 0, 14, -14], [0, 0, 0, 0, 0, 0, 0, 0], [12271, -12271, 919, 919, 0, 545, -261, 0], [-30550, 0, 0, -919, 355, -355, 0, 22], [0, 0, 0, 0, 0, 0, 0, 0], [-2735, 0, 0, -48, 597, -597, 0, -84], [2015, -2015, -4411, -4411, 0, 63, -369, 0], [0, 0, 0, 0, 0, 0, 0, 0], [24, -1679, -1459, 0, 979, 0, 24, -24], [-64, 32149, -5304, 0, -35, 0, -64, 64], [0, 0, 0, 0, 0, 0, 0, 0], [252, -252, 865, 865, 0, -175, 486, 0], [7956, 0, 0, -3288, -616, 616, 0, 716], [0, 0, 0, 0, 0, 0, 0, 0], [14699, 0, 0, -1701, -1017, 1017, 0, 873], [42388, -42388, 6766, 6766, 0, 1242, 612, 0], [0, 0, 0, 0, 0, 0, 0, 0], [312, -11255, -5324, 0, 149, 0, 312, -312], [-969, -9689, 1955, 0, -795, 0, -969, 969], [0, 0, 0, 0, 0, 0, 0, 0], [-12761, 12761, 5494, 5494, 0, 392, 1293, 0], [-13648, 0, 0, 8696, 104, -104, 0, 464], [0, 0, 0, 0, 0, 0, 0, 0], [-29637, 0, 0, -1571, 538, -538, 0, -180], [-28999, 28999, 1016, 1016, 0, 846, -81, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-942, 8862, -4434, 0, -294, 0, -942, 942], [724, 2073, 5837, 0, 338, 0, 724, -724], [0, 0, 0, 0, 0, 0, 0, 0], [26919, -26919, 5120, 5120, 0, -311, -828, 0], [56034, 0, 0, -3696, -536, 536, 0, -716], [0, 0, 0, 0, 0, 0, 0, 0], [13702, 0, 0, -1132, 146, -146, 0, -195], [-37202, 37202, -12962, -12962, 0, -2436, 312, 0], [0, 0, 0, 0, 0, 0, 0, 0], [978, 40926, 4661, 0, -857, 0, 978, -978], [412, -70940, -12476, 0, 524, 0, 412, -412], [0, 0, 0, 0, 0, 0, 0, 0], [4549, -4549, -11342, -11342, 0, -154, -2142, 0], [-9873, 0, 0, -12804, 1225, -1225, 0, -1682], [0, 0, 0, 0, 0, 0, 0, 0], [20683, 0, 0, -7268, 439, -439, 0, -1440]]}