# Stored data for newform 27.5.b.c, downloaded from the LMFDB on 23 April 2024.
{"label": "27.5.b.c", "space_label": "27.5.b", "level": 27, "weight": 5, "hecke_orbit": 3, "hecke_orbit_code": 9007268058103835, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 2302720930654432642, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [9, 0, 1]]], "qexp_display": "q+iq^{2}+7q^{4}+11iq^{5}-19q^{7}+23iq^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 675, "analytic_conductor": 2.790989003263797, "hecke_ring_index": 3, "level_radical": 3, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [27, 2, [2], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [26], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.870", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.247", "prec": 20}, {"__RealLiteral__": 0, "data": "0.983", "prec": 17}, {"__RealLiteral__": 0, "data": "138.519", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "4.2.3.c2", "trace_display": [0, 0, 0, -38], "traces": [0, 2, 0, 0, 14, 0, 0, -38, 0, 0, -198, 0, 0, 604, 0, 0, -190, 0, 0, -608, 0, 0, 738, 0, 0, -928, 0, 0, -266, 0, 0, 478, 0, 0, 2484, 0, 0, 1480, 0, 0, -4554, 0, 0, -1964, 0, 0, 1800, 0, 0, -4080, 0, 0, 4228, 0, 0, 8118, 0, 0, -4068, 0, 0, -632, 0, 0, -7954, 0, 0, 9244, 0, 0, 3762, 0, 0, -6062, 0, 0, -4256, 0, 0, -20900, 0, 0, 1368, 0, 0, 27324, 0, 0, 16974, 0, 0, -11476, 0, 0, 12996, 0, 0, -13034, 0, 0, -6496, 0, 0, -15308, 0, 0, -9558, 0, 0, 4648, 0, 0, 3610, 0, 0, 19800, 0, 0, -17532, 0, 0, -976, 0, 0, 3346, 0, 0, 49990, 0, 0, -59796, 0, 0, 11552, 0, 0, 57132, 0, 0, -23768, 0, 0, 10908, 0, 0, -44748, 0, 0, 10360, 0, 0, -5366, 0, 0, -14022, 0, 0, -64232, 0, 0, -54054, 0, 0, 45580, 0, 0, 75798, 0, 0, 125286, 0, 0, -13748, 0, 0, 17632, 0, 0, -42012, 0, 0, -99104, 0, 0, 41400, 0, 0, -101844, 0, 0, 60192, 0, 0, 70894, 0, 0, -28560, 0, 0, -62510, 0, 0, 35514, 0, 0, 15048, 0, 0, -57380, 0, 0, -30104, 0, 0, -3078, 0, 0, -9082, 0, 0, 56826, 0, 0, 100348, 0, 0, -29520, 0, 0, 68428, 0, 0, -93564, 0, 0, 142956, 0, 0, -47196, 0, 0, 82780, 0, 0, -4424, 0, 0, -183616, 0, 0, -31878, 0, 0, -73800, 0, 0, -134302, 0, 0, -28120, 0, 0, 170766, 0, 0, -105138, 0, 0, 64708, 0, 0, 147478, 0, 0, 14724, 0, 0, 23992, 0, 0, 86526, 0, 0, -2096, 0, 0, 222876, 0, 0, -175750, 0, 0, -42434, 0, 0, -192852, 0, 0, -131958, 0, 0, 37316, 0, 0, 57760, 0, 0, 308308, 0, 0, -47322, 0, 0, -51806, 0, 0, -146300, 0, 0, 166788, 0, 0, -34200, 0, 0, -280256, 0, 0, 31464, 0, 0, -329708, 0, 0, -216468, 0, 0, 297388, 0, 0, 191268, 0, 0, 168758, 0, 0, 118350, 0, 0, 255040, 0, 0, 201474, 0, 0, 119988, 0, 0, -293490, 0, 0, -75810, 0, 0, -80332, 0, 0, -302690, 0, 0, -146520, 0, 0, 475012, 0, 0, 298908, 0, 0, -523904, 0, 0, -272340, 0, 0, -154242, 0, 0, -91238, 0, 0, -248400, 0, 0, 214434, 0, 0, 434308, 0, 0, 88160, 0, 0, 144356, 0, 0, 77292, 0, 0, -398582, 0, 0, -107156, 0, 0, 833778, 0, 0, -224352, 0, 0, -60824, 0, 0, -219834, 0, 0, 12008, 0, 0, 194436, 0, 0, -427082, 0, 0, 32536, 0, 0, 133450, 0, 0, 750168, 0, 0, -462132, 0, 0, 151126, 0, 0, -56088, 0, 0, 115596, 0, 0, -181334, 0, 0, 138600, 0, 0, -647954, 0, 0, -224316, 0, 0, -175636, 0, 0, -403236, 0, 0, 282112, 0, 0, -370800, 0, 0, 446960, 0, 0, -6832, 0, 0, -69764, 0, 0, 403920, 0, 0, 561384, 0, 0, -45410, 0, 0, 929620, 0, 0, -496908, 0, 0, 390654, 0, 0, 349930, 0, 0, 115178, 0, 0, -117540, 0, 0, -532836, 0, 0, -1375308, 0, 0, -352868, 0, 0, 100152, 0, 0, 379682, 0, 0, 80864, 0, 0, -33858, 0, 0, 725436, 0, 0, -647672, 0, 0, 678132, 0, 0, -446780, 0, 0, -342432, 0, 0, 397100, 0, 0, -166376, 0, 0, -593128, 0, 0, 306756, 0, 0, -324720, 0, 0, 250884, 0, 0, 161452, 0, 0, -25992, 0, 0, 522364, 0, 0, -313236, 0, 0, 391878, 0, 0, 385092, 0, 0, -145312, 0, 0, -140600, 0, 0, -519156, 0, 0, 543600, 0, 0, 804346, 0, 0, -37562, 0, 0, -757340, 0, 0, 62568, 0, 0, 575140, 0, 0, -322506, 0, 0, 446524, 0, 0, 564480, 0, 0, -930658, 0, 0, -449624, 0, 0, 86746, 0, 0, -581058, 0, 0, -1232160, 0, 0, -77418, 0, 0, -1092176, 0, 0, -755136, 0, 0, 718812, 0, 0, 319060, 0, 0, 1878426, 0, 0, -246924, 0, 0, 461440, 0, 0, 1743354, 0, 0, 406800, 0, 0, -915156, 0, 0, -938738, 0, 0, 877002, 0, 0, 247646, 0, 0, 176382, 0, 0, 161964, 0, 0, 186580, 0, 0, -533000, 0, 0, -646038, 0, 0, -188784, 0, 0, 123424, 0, 0, -449920, 0, 0, -852624, 0, 0, -210368, 0, 0, -966276, 0, 0, 2451636, 0, 0, -116532, 0, 0, 290852, 0, 0, -693728, 0, 0, 252178, 0, 0, 600138, 0, 0, 195472, 0, 0, 491400, 0, 0, -1714316, 0, 0, 181602, 0, 0, -1451538, 0, 0, -712908, 0, 0, 122446, 0, 0, -1228536, 0, 0, 1565140, 0, 0, 1384416, 0, 0, -88312, 0, 0, -522972, 0, 0, -170090, 0, 0, 496258, 0, 0, -221792, 0, 0, 1436058, 0, 0, -447228, 0, 0, 387600, 0, 0, 2137096, 0, 0, 2069100, 0, 0, -190864, 0, 0, -437570, 0, 0, -1793448, 0, 0, -1537200, 0, 0, -376200, 0, 0, 816822, 0, 0, -1922720, 0, 0, 546120, 0, 0, 597056, 0, 0, 105336, 0, 0, -987110, 0, 0, 333108, 0, 0, 1154452, 0, 0, -2402108, 0, 0, -2381148, 0, 0, 1507644, 0, 0, 495194, 0, 0, -210728, 0, 0, 18544, 0, 0, -1152576, 0, 0, 162412, 0, 0, -70794, 0, 0, 1006696, 0, 0, 970380, 0, 0, 1301850, 0, 0, -63574, 0, 0, 2791688, 0, 0, -547200, 0, 0, 1400068, 0, 0, -771210, 0, 0, 685408, 0, 0, -1645020, 0, 0, -949810, 0, 0, 702436, 0, 0, -3228390, 0, 0, -1402704, 0, 0, 1319004, 0, 0, -678960, 0, 0, 3139000, 0, 0, 1136124, 0, 0, -3107718, 0, 0, 478996, 0, 0, 2074306, 0, 0, 1211742, 0, 0, -686720, 0, 0, -1110564, 0, 0, 1240320, 0, 0, 461646, 0, 0, -1758902, 0, 0, 1000692, 0, 0, -136800, 0, 0, -724716, 0, 0, -1830724, 0, 0, -1085508, 0, 0, -2995740, 0, 0, 1159308, 0, 0, -1732800, 0, 0, 579460, 0, 0, -732374, 0, 0, 1290366, 0, 0, 451592, 0, 0, 60040, 0, 0, 1722492, 0, 0, 1302282, 0, 0, 2358774, 0, 0, -1285312, 0, 0, 1963750, 0, 0, -207252, 0, 0, 483892, 0, 0, -733194], "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, 3, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "27.5.b.c", "char_is_minimal": true, "conrey_index": 26, "id": 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], [1, 0], [0, 1], [0, 0], [7, 0], [0, 11], [0, 0], [-19, 0], [0, 23], [0, 0], [-99, 0], [0, -41], [0, 0], [302, 0], [0, -19], [0, 0], [-95, 0], [0, -138], [0, 0], [-304, 0], [0, 77], [0, 0], [369, 0], [0, -100], [0, 0], [-464, 0], [0, 302], [0, 0], [-133, 0], [0, 226], [0, 0], [239, 0], [0, 273], [0, 0], [1242, 0], [0, -209], [0, 0], [740, 0], [0, -304], [0, 0], [-2277, 0], [0, -76], [0, 0], [-982, 0], [0, -287], [0, 0], [900, 0], [0, -722], [0, 0], [-2040, 0], [0, -464], [0, 0], [2114, 0], [0, 531], [0, 0], [4059, 0], [0, -437], [0, 0], [-2034, 0], [0, 974], [0, 0], [-316, 0], [0, 239], [0, 0], [-3977, 0], [0, 3322], [0, 0], [4622, 0], [0, -966], [0, 0], [1881, 0], [0, -606], [0, 0], [-3031, 0], [0, 740], [0, 0], [-2128, 0], [0, 779], [0, 0], [-10450, 0], [0, -1045], [0, 0], [684, 0], [0, -4211], [0, 0], [13662, 0], [0, -982], [0, 0], [8487, 0], [0, 2334], [0, 0], [-5738, 0], [0, -700], [0, 0], [6498, 0], [0, -3344], [0, 0], [-6517, 0], [0, -2040], [0, 0], [-3248, 0]]}