# Stored data for newform 27.5.b.b, downloaded from the LMFDB on 25 April 2025.
{"Nk2": 675, "analytic_conductor": 2.790989003263797, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 3, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": -1, "char_values": [27, 2, [2], [1]], "cm_discs": [], "conrey_index": 26, "dim": 2, "field_disc": -24, "field_disc_factorization": [[-1, 1], [2, 3], [3, 1]], "field_poly": [6, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [54, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503668430733339, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "27.5.b.b", "level": 27, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3], "level_radical": 3, "minimal_twist": "27.5.b.b", "nf_label": "2.0.24.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta q^{2}-38q^{4}+2\\beta q^{5}+17q^{7}-22\\beta q^{8}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "4.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "27.5.b", "trace_display": [0, 0, 0, 34], "trace_hash": 2027827495511827146, "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "1.901", "prec": 17}, {"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "15.204", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "152.370", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 2, 0, 0, -76, 0, 0, 34, 0, 0, -216, 0, 0, 190, 0, 0, 1160, 0, 0, 418, 0, 0, -2376, 0, 0, 818, 0, 0, -1292, 0, 0, 1900, 0, 0, -4536, 0, 0, -2354, 0, 0, 4752, 0, 0, 2860, 0, 0, 12744, 0, 0, -4224, 0, 0, -7220, 0, 0, -4752, 0, 0, 4752, 0, 0, -2882, 0, 0, -6064, 0, 0, 6994, 0, 0, -3672, 0, 0, -18050, 0, 0, -15884, 0, 0, 10546, 0, 0, 31536, 0, 0, -9072, 0, 0, 52272, 0, 0, 3230, 0, 0, -23112, 0, 0, -5618, 0, 0, -31084, 0, 0, 32770, 0, 0, -42768, 0, 0, 3892, 0, 0, 19720, 0, 0, 25488, 0, 0, -31320, 0, 0, -22990, 0, 0, -72200, 0, 0, 13756, 0, 0, -20520, 0, 0, 7106, 0, 0, 99792, 0, 0, 20098, 0, 0, 28512, 0, 0, 9504, 0, 0, 89452, 0, 0, -26030, 0, 0, -40392, 0, 0, -37484, 0, 0, -49248, 0, 0, -26942, 0, 0, 90288, 0, 0, -39072, 0, 0, -108680, 0, 0, 13906, 0, 0, 163944, 0, 0, 114142, 0, 0, -280368, 0, 0, -99792, 0, 0, -45144, 0, 0, -118898, 0, 0, 160512, 0, 0, -34430, 0, 0, 91584, 0, 0, 63072, 0, 0, 110200, 0, 0, 40546, 0, 0, 106920, 0, 0, 32300, 0, 0, 180576, 0, 0, -95924, 0, 0, -225720, 0, 0, 49060, 0, 0, -104544, 0, 0, -46224, 0, 0, -77112, 0, 0, 77614, 0, 0, 109516, 0, 0, 39710, 0, 0, -223344, 0, 0, 280368, 0, 0, -163552, 0, 0, -40018, 0, 0, -90288, 0, 0, -85536, 0, 0, -265772, 0, 0, -147038, 0, 0, -28296, 0, 0, 279700, 0, 0, 80784, 0, 0, 105868, 0, 0, -225720, 0, 0, -23470, 0, 0, 685900, 0, 0, -62640, 0, 0, 377568, 0, 0, 48620, 0, 0, 242440, 0, 0, -270356, 0, 0, -205200, 0, 0, -125714, 0, 0, -400748, 0, 0, 104544, 0, 0, 216648, 0, 0, 77710, 0, 0, -693792, 0, 0, 163330, 0, 0, 629640, 0, 0, -291410, 0, 0, 344736, 0, 0, -153442, 0, 0, -194832, 0, 0, 81070, 0, 0, -541728, 0, 0, 57024, 0, 0, -313632, 0, 0, -173280, 0, 0, -122740, 0, 0, -239438, 0, 0, 254232, 0, 0, 2638, 0, 0, 508464, 0, 0, -329774, 0, 0, 605448, 0, 0, -80784, 0, 0, 213484, 0, 0, 535248, 0, 0, 288360, 0, 0, 42484, 0, 0, 474440, 0, 0, 180500, 0, 0, 80784, 0, 0, -605330, 0, 0, -1245260, 0, 0, 180576, 0, 0, -496584, 0, 0, 390958, 0, 0, 940896, 0, 0, -48994, 0, 0, -308880, 0, 0, -346028, 0, 0, -147896, 0, 0, 230668, 0, 0, -430920, 0, 0, 327888, 0, 0, -103088, 0, 0, 693792, 0, 0, 19008, 0, 0, -511148, 0, 0, -968544, 0, 0, 311698, 0, 0, -1511136, 0, 0, 118898, 0, 0, 689040, 0, 0, 170962, 0, 0, -1073952, 0, 0, -223630, 0, 0, 873620, 0, 0, 218002, 0, 0, 456192, 0, 0, 199584, 0, 0, 1102000, 0, 0, 86428, 0, 0, 1569456, 0, 0, 183168, 0, 0, -522728, 0, 0, -306850, 0, 0, 257040, 0, 0, -508464, 0, 0, 451440, 0, 0, 77890, 0, 0, -1331424, 0, 0, -944110, 0, 0, -270028, 0, 0, 213840, 0, 0, 1786536, 0, 0, 110542, 0, 0, -1034208, 0, 0, 594898, 0, 0, -971784, 0, 0, 179282, 0, 0, -763724, 0, 0, 271700, 0, 0, 1772496, 0, 0, -451440, 0, 0, -627264, 0, 0, -824030, 0, 0, 536112, 0, 0, -216194, 0, 0, -361152, 0, 0, -940896, 0, 0, -1309176, 0, 0, 397100, 0, 0, -1365320, 0, 0, -154224, 0, 0, 1210680, 0, 0, 396340, 0, 0, 989140, 0, 0, -864350, 0, 0, 311256, 0, 0, 215662, 0, 0, 888624, 0, 0, 127186, 0, 0, 2354616, 0, 0, 64562, 0, 0, 1424392, 0, 0, 1061554, 0, 0, -721008, 0, 0, -401280, 0, 0, -133056, 0, 0, -988532, 0, 0, -948024, 0, 0, -689040, 0, 0, 1023796, 0, 0, -180576, 0, 0, -392904, 0, 0, 1609390, 0, 0, -1986336, 0, 0, -560736, 0, 0, -755352, 0, 0, 617614, 0, 0, 1484736, 0, 0, -95506, 0, 0, -2257200, 0, 0, -56592, 0, 0, 1658800, 0, 0, 1519180, 0, 0, -1556064, 0, 0, 1324512, 0, 0, -528428, 0, 0, -491986, 0, 0, -123552, 0, 0, 366910, 0, 0, -3606768, 0, 0, -451440, 0, 0, -283176, 0, 0, 557090, 0, 0, -4337396, 0, 0, -893684, 0, 0, 1949400, 0, 0, 408628, 0, 0, 2905632, 0, 0, 281740, 0, 0, -727056, 0, 0, 755136, 0, 0, 3792096, 0, 0, -631646, 0, 0, 451440, 0, 0, -873122, 0, 0, 993168, 0, 0, 66164, 0, 0, -433728, 0, 0, 1395550, 0, 0, 4518124, 0, 0, 777100, 0, 0, -2482920, 0, 0, 627264, 0, 0, -2449920, 0, 0, -1531646, 0, 0, -1138968, 0, 0, -273790, 0, 0, 1308340, 0, 0, -970704, 0, 0, 1608768, 0, 0, 433296, 0, 0, -2014848, 0, 0, -2392628, 0, 0, 2796552, 0, 0, 597740, 0, 0, -2396736, 0, 0, 1146178, 0, 0, -532440, 0, 0, -1180562, 0, 0, -576080, 0, 0, 1259280, 0, 0, 4403592, 0, 0, 1205474, 0, 0, -1540748, 0, 0, -390830, 0, 0, -1855224, 0, 0, -2143586, 0, 0, -2352240, 0, 0, -2397230, 0, 0, -534600, 0, 0, -389664, 0, 0, -1227400, 0, 0, 664430, 0, 0, 2663496, 0, 0, -1278530, 0, 0, -2756160, 0, 0, 1423858, 0, 0, 139536, 0, 0, 233852, 0, 0, 3645112, 0, 0, -627264, 0, 0, 2429352, 0, 0, -1796256, 0, 0, 4965840, 0, 0, 1525282, 0, 0, -348840, 0, 0, 1986336, 0, 0, -1864280, 0, 0, 1230124, 0, 0, 3447576, 0, 0, -962786, 0, 0, 1083456, 0, 0, -882816, 0, 0, -776952, 0, 0, -352850, 0, 0, 1756512, 0, 0, -3721248, 0, 0, -3397680, 0, 0, -1714750, 0, 0, 1696464, 0, 0, 1210896, 0, 0, -1280880, 0, 0, -42042, 0, 0, -2949332, 0, 0, 3198034, 0, 0, 606744, 0, 0, 341666, 0, 0, -1671560, 0, 0, 3606768, 0, 0, -2811240, 0, 0, 576720, 0, 0, -1508980, 0, 0, 1500754, 0, 0, 484704, 0, 0, -417836, 0, 0, 4913568], "weight": 5, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 1], [0, 0], [-38, 0], [0, 2], [0, 0], [17, 0], [0, -22], [0, 0], [-108, 0], [0, 22], [0, 0], [95, 0], [0, 17], [0, 0], [580, 0], [0, 42], [0, 0], [209, 0], [0, -76], [0, 0], [-1188, 0], [0, -118], [0, 0], [409, 0], [0, 95], [0, 0], [-646, 0], [0, -44], [0, 0], [950, 0], [0, 228], [0, 0], [-2268, 0], [0, 34], [0, 0], [-1177, 0], [0, 209], [0, 0], [2376, 0], [0, -292], [0, 0], [1430, 0], [0, -836], [0, 0], [6372, 0], [0, 214], [0, 0], [-2112, 0], [0, 409], [0, 0], [-3610, 0], [0, 396], [0, 0], [-2376, 0], [0, -374], [0, 0], [2376, 0], [0, 290], [0, 0], [-1441, 0], [0, 950], [0, 0], [-3032, 0], [0, 190], [0, 0], [3497, 0], [0, -1596], [0, 0], [-1836, 0], [0, -264], [0, 0], [-9025, 0], [0, -1177], [0, 0], [-7942, 0], [0, 374], [0, 0], [5273, 0], [0, 1160], [0, 0], [15768, 0], [0, -836], [0, 0], [-4536, 0], [0, 1430], [0, 0], [26136, 0], [0, -1518], [0, 0], [1615, 0], [0, 4484], [0, 0], [-11556, 0], [0, 418], [0, 0], [-2809, 0], [0, -2112], [0, 0], [-15542, 0]]}