# Stored data for newform 16.6.a.b, downloaded from the LMFDB on 24 April 2024.
{"label": "16.6.a.b", "space_label": "16.6.a", "level": 16, "weight": 6, "hecke_orbit": 2, "hecke_orbit_code": 4503599728033808, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 830374051440028741, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-12, 1]]], "qexp_display": "q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 576, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 2.56614111700769, "hecke_ring_index": 1, "level_radical": 2, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [16, 1, [15, 5], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "0.990", "prec": 17}, {"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "1.957", "prec": 17}, {"__RealLiteral__": 0, "data": "0.068", "prec": 17}, {"__RealLiteral__": 0, "data": "4.828", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, -1]], "trace_display": [0, 12, 54, 88], "traces": [0, 1, 0, 12, 0, 54, 0, 88, 0, -99, 0, -540, 0, -418, 0, 648, 0, 594, 0, -836, 0, 1056, 0, 4104, 0, -209, 0, -4104, 0, -594, 0, -4256, 0, -6480, 0, 4752, 0, -298, 0, -5016, 0, 17226, 0, 12100, 0, -5346, 0, 1296, 0, -9063, 0, 7128, 0, 19494, 0, -29160, 0, -10032, 0, 7668, 0, -34738, 0, -8712, 0, -22572, 0, -21812, 0, 49248, 0, 46872, 0, 67562, 0, -2508, 0, -47520, 0, 76912, 0, -25191, 0, -67716, 0, 32076, 0, -7128, 0, 29754, 0, -36784, 0, -51072, 0, -45144, 0, -122398, 0, 53460, 0, 11286, 0, 27256, 0, 57024, 0, -122364, 0, 99902, 0, -3576, 0, -29646, 0, 221616, 0, 41382, 0, 52272, 0, 130549, 0, 206712, 0, -180036, 0, -336512, 0, 145200, 0, -100980, 0, -73568, 0, -221616, 0, -317142, 0, 148324, 0, 15552, 0, 225720, 0, -32076, 0, -108756, 0, 196614, 0, -74360, 0, -58806, 0, -229824, 0, 120878, 0, 233928, 0, 361152, 0, 111340, 0, -349920, 0, 491832, 0, -196569, 0, 82764, 0, 707454, 0, -18392, 0, 92016, 0, -493668, 0, -559450, 0, -416856, 0, -16092, 0, -320760, 0, -361152, 0, 724032, 0, 7106, 0, -270864, 0, -530442, 0, -56168, 0, -261744, 0, -52272, 0, 930204, 0, -406296, 0, 451440, 0, 339196, 0, 562464, 0, 653400, 0, -374528, 0, 810744, 0, -248292, 0, -779360, 0, 20691, 0, 744876, 0, -272746, 0, -570240, 0, -153846, 0, 69984, 0, 922944, 0, -1154736, 0, 657074, 0, 694980, 0, -489402, 0, 349448, 0, -812592, 0, -1341900, 0, -2216160, 0, 384912, 0, 132354, 0, -26224, 0, 58806, 0, -943272, 0, 1052676, 0, 357048, 0, 967518, 0, 518320, 0, -441408, 0, 112860, 0, 2222726, 0, 421344, 0, -196614, 0, 1552276, 0, -541728, 0, 1515888, 0, -1067021, 0, -1468776, 0, -1072170, 0, 414072, 0, 2216160, 0, -1715472, 0, 1064800, 0, 135432, 0, -1875852, 0, -1585892, 0, 327072, 0, 730728, 0, 584858, 0, -470448, 0, -2482866, 0, 320760, 0, -1468368, 0, -496584, 0, 87362, 0, 1198824, 0, 114048, 0, -377948, 0, 29502, 0, -1177848, 0, 639122, 0, -355752, 0, 2298240, 0, -2276560, 0, 2659392, 0, 2904660, 0, -3991570, 0, 1715472, 0, 1429218, 0, 2531088, 0, 627264, 0, -1161864, 0, -1777203, 0, 1566588, 0, 3648348, 0, 1089232, 0, -1705374, 0, 1715472, 0, 3505766, 0, -2160432, 0, 248292, 0, -4043852, 0, -4038144, 0, -5187456, 0, -2566080, 0, -1197900, 0, -950346, 0, 2437776, 0, -1211760, 0, 4153248, 0, -520738, 0, -882816, 0, 764370, 0, 1779008, 0, -1360314, 0, 160920, 0, 2640506, 0, -3805704, 0, 674784, 0, -3656664, 0, 1779888, 0, 4980204, 0, -237994, 0, -128304, 0, -124146, 0, -3056944, 0, 2708640, 0, 3882384, 0, -66958, 0, -384912, 0, -3430944, 0, 6501352, 0, 897237, 0, 4607604, 0, 1606716, 0, 2359368, 0, 3776706, 0, -9302040, 0, -892320, 0, -1986336, 0, -3180694, 0, -2437776, 0, 6685470, 0, 4351216, 0, -2757888, 0, -7079940, 0, -1919456, 0, 1450536, 0, -6534000, 0, 174724, 0, -1929906, 0, -3221856, 0, 124564, 0, 4333824, 0, -6609492, 0, -2297096, 0, 1336080, 0, -2821500, 0, -352836, 0, 2886840, 0, 4124736, 0, 4136284, 0, 5901984, 0, -8332632, 0, 609444, 0, -2358828, 0, 4341006, 0, 5945456, 0, 3430944, 0, 1471824, 0, -699840, 0, 8489448, 0, -6741846, 0, 7721956, 0, -220704, 0, -2528064, 0, 10406473, 0, -759132, 0, -7200468, 0, -6607656, 0, -5924016, 0, 4894020, 0, -682066, 0, -6713400, 0, 5394708, 0, -2157716, 0, 3439062, 0, 496584, 0, 6768256, 0, -193104, 0, -2675970, 0, -5057800, 0, -3849120, 0, 3553308, 0, -1600884, 0, -2216808, 0, -12922470, 0, 6083572, 0, 8688384, 0, -857736, 0, -15824062, 0, 85272, 0, -5959008, 0, -10526760, 0, 2234628, 0, -4602204, 0, 3558016, 0, -6365304, 0, 8611218, 0, 2822688, 0, -674016, 0, 7982280, 0, 10174010, 0, 2159388, 0, 7049646, 0, 9958432, 0, -627264, 0, -541728, 0, 4195862, 0, 11162448, 0, 9125514, 0, -6457340, 0, -16842816, 0, 2618352, 0, -9068819, 0, 5417280, 0, -177012, 0, 14051368, 0, 4070352, 0, -18171648, 0, 3788334, 0, -4640328, 0, 8471682, 0, -488564, 0, 7840800, 0, -2481192, 0, -4140720, 0, -4494336, 0, -5291298, 0, -5452920, 0, -6688638, 0, -4724676, 0, -6174202, 0, -2979504, 0, -3972672, 0, -2437776, 0, -9352320, 0, 18758520, 0, -9409246, 0, 857736, 0, 15008598, 0, -10771024, 0, 8938512, 0, 12970692, 0, -17125668, 0, -3272952, 0, -8148492, 0, -22655588, 0, 4704480, 0, 8009496, 0, 10232244, 0, -1846152, 0, 19016910, 0, 249128, 0, 839808, 0, 993168, 0, 15131126, 0, -7614288, 0, -17466624, 0, 12188880, 0, -13856832, 0, 15032304, 0, 2398528, 0, 7884888, 0, 124146, 0, 7412296, 0, 14461173, 0, 7187400, 0, -2779282, 0, -5872824, 0, 11778480, 0, 12104620, 0, 4193376, 0, -4469256, 0, 10617156, 0, 6703884, 0, -10768032, 0, -28846256, 0, -16102800, 0, -4015440, 0, 9608678, 0, -26593920, 0, 4545882, 0, 8791376, 0, -3175524, 0, -3205224, 0, -21592318, 0, 1588248, 0, -14840010, 0, 889504, 0, -314688, 0, -14400936, 0, -25310880, 0, 2437776, 0, 6527412, 0, 24878524, 0, -11319264, 0, -2608848, 0, 14520484, 0, 12632112, 0, 31607982, 0, 769824, 0, -2945646, 0, -36483480, 0, 19502208, 0, 11610216, 0, -3100086, 0, -1871804, 0, 6219840, 0, 6012360, 0, -10115600, 0, 3641616, 0, -20018394, 0, -15311768, 0, 1354320, 0, -9593100, 0, 25220942, 0, 26672712, 0, -5383422, 0, 26558928, 0, 17466624, 0, 17762328, 0, -20158313, 0, -2359368, 0, -10614726, 0, 11488312, 0, 18627312, 0, -1222992, 0, -486970, 0, 4469256, 0, -1926342, 0, -22353836, 0, 18190656, 0, -18583776, 0, 38202516, 0, -12804252, 0, -41532480, 0, 9117416, 0, 12117402, 0, -15843168, 0, -29104834, 0, -12866040, 0, -3146958, 0, -15999524, 0, 4968864, 0, 34587432, 0, -29613056, 0, 13603140, 0, -1083456, 0, -26658072, 0, -20585664, 0, 2528064, 0, 11579436, 0, 12777600, 0, -30210300, 0, -17439644, 0, -1117314, 0, 2595888, 0, 36566640, 0, -22510224, 0, -8886240, 0, 17641096, 0, -19030704, 0, -19592496, 0, 62282, 0, -2698344, 0, 39678498, 0, 7576668, 0, 8768736, 0, -17321040, 0, 39341258, 0, 7018296, 0, 46250622, 0, 70695504, 0, -19502208, 0, 37902492, 0, -28240916, 0, -29794392, 0, -26646246, 0, 39097728, 0, 3849120, 0, -27908496, 0, -10515615, 0, 12114036, 0, 383724, 0, -40979048, 0, -5959008, 0, 27203364, 0, 13052512, 0, 1048344, 0, 25355538, 0, -16067160, 0, -9890298, 0, -11913912, 0, -28643868, 0, 1368576, 0, 49658400, 0, -29193056, 0, -4535376, 0, -3033072, 0, -17300074, 0, 1222992, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "4.6.a.a", "char_is_minimal": false, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [0], [12], [0], [54], [0], [88], [0], [-99], [0], [-540], [0], [-418], [0], [648], [0], [594], [0], [-836], [0], [1056], [0], [4104], [0], [-209], [0], [-4104], [0], [-594], [0], [-4256], [0], [-6480], [0], [4752], [0], [-298], [0], [-5016], [0], [17226], [0], [12100], [0], [-5346], [0], [1296], [0], [-9063], [0], [7128], [0], [19494], [0], [-29160], [0], [-10032], [0], [7668], [0], [-34738], [0], [-8712], [0], [-22572], [0], [-21812], [0], [49248], [0], [46872], [0], [67562], [0], [-2508], [0], [-47520], [0], [76912], [0], [-25191], [0], [-67716], [0], [32076], [0], [-7128], [0], [29754], [0], [-36784], [0], [-51072], [0], [-45144], [0], [-122398], [0], [53460], [0]]}