# Stored data for newform 450.6.c.j, downloaded from the LMFDB on 24 April 2024. {"label": "450.6.c.j", "space_label": "450.6.c", "level": 450, "weight": 6, "hecke_orbit": 10, "hecke_orbit_code": 40532534185951682, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1449566279906769787, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [30976, 0, 1]], [11, [-60, 1]]], "qexp_display": "q-2iq^{2}-2^{4}q^{4}+88iq^{7}+2^{5}iq^{8}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 16200, "analytic_conductor": 72.17271891584129, "hecke_ring_index": 2, "level_radical": 30, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [450, 2, [101, 127], [2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [199], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.973", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.367", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "168.755", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, -32, 0, 0, 0, 0, 0, 0, 120, 0, 0, 1408, 0, 512, 0, 0, -1912, 0, 0, 0, 0, 0, 0, 5264, 0, 0, 11148, 0, -7184, 0, 0, 3312, 0, 0, 0, 0, 0, 0, -38388, 0, 0, -1920, 0, 4800, 0, 0, -28338, 0, 0, 0, 0, 0, 0, -22528, 0, 0, 52680, 0, -62180, 0, 0, -8192, 0, 0, 0, 0, 0, 0, -12240, 0, 0, -67664, 0, 30592, 0, 0, -148816, 0, 0, 0, 0, 0, 0, -106528, 0, 0, -65484, 0, -231616, 0, 0, 157440, 0, 0, 0, 0, 0, 0, 44004, 0, 0, -84224, 0, -250128, 0, 0, 17060, 0, 0, 0, 0, 0, 0, -178368, 0, 0, -145728, 0, -314902, 0, 0, 114944, 0, 0, 0, 0, 0, 0, -302520, 0, 0, -134432, 0, -52992, 0, 0, -308392, 0, 0, 0, 0, 0, 0, 204464, 0, 0, 58908, 0, -407744, 0, 0, 84480, 0, 0, 0, 0, 0, 0, -211200, 0, 0, 614208, 0, -51744, 0, 0, -123342, 0, 0, 0, 0, 0, 0, 30720, 0, 0, -1386792, 0, 754348, 0, 0, -76800, 0, 0, 0, 0, 0, 0, 530688, 0, 0, 1328656, 0, 453408, 0, 0, -1304896, 0, 0, 0, 0, 0, 0, 634112, 0, 0, -114720, 0, -2294120, 0, 0, -1823904, 0, 0, 0, 0, 0, 0, -544824, 0, 0, 360448, 0, -1563504, 0, 0, -211660, 0, 0, 0, 0, 0, 0, -842880, 0, 0, 56928, 0, 1785124, 0, 0, 994880, 0, 0, 0, 0, 0, 0, 220248, 0, 0, 1384000, 0, 131072, 0, 0, 2977216, 0, 0, 0, 0, 0, 0, -1346048, 0, 0, -2229012, 0, 1135408, 0, 0, 1027632, 0, 0, 0, 0, 0, 0, -1375476, 0, 0, 195840, 0, 315840, 0, 0, 2496922, 0, 0, 0, 0, 0, 0, 1082624, 0, 0, -789600, 0, 4687232, 0, 0, -489472, 0, 0, 0, 0, 0, 0, 3004080, 0, 0, 1089136, 0, 2381056, 0, 0, 668880, 0, 0, 0, 0, 0, 0, 1368992, 0, 0, -6927360, 0, 2243944, 0, 0, 5409600, 0, 0, 0, 0, 0, 0, -431040, 0, 0, 1704448, 0, 1065264, 0, 0, -3673180, 0, 0, 0, 0, 0, 0, 1047744, 0, 0, 7481232, 0, -3124326, 0, 0, 3705856, 0, 0, 0, 0, 0, 0, 11005632, 0, 0, 198720, 0, -2519040, 0, 0, -6360232, 0, 0, 0, 0, 0, 0, -2362384, 0, 0, 6919548, 0, -496800, 0, 0, -1610352, 0, 0, 0, 0, 0, 0, -10882308, 0, 0, -704064, 0, 7848192, 0, 0, -3939892, 0, 0, 0, 0, 0, 0, 1347584, 0, 0, 278040, 0, 8654860, 0, 0, 4002048, 0, 0, 0, 0, 0, 0, 5598720, 0, 0, -5057536, 0, -272960, 0, 0, 893024, 0, 0, 0, 0, 0, 0, -5615680, 0, 0, -2412252, 0, -2303280, 0, 0, -9888864, 0, 0, 0, 0, 0, 0, 3489780, 0, 0, 2853888, 0, -3509424, 0, 0, 5915008, 0, 0, 0, 0, 0, 0, 2331648, 0, 0, 4689312, 0, 11130728, 0, 0, 5038432, 0, 0, 0, 0, 0, 0, 11890392, 0, 0, -5032384, 0, -1839104, 0, 0, -12956632, 0, 0, 0, 0, 0, 0, 288000, 0, 0, -3815412, 0, -8996416, 0, 0, -1126416, 0, 0, 0, 0, 0, 0, -16039476, 0, 0, 4840320, 0, -7510080, 0, 0, 12152686, 0, 0, 0, 0, 0, 0, 2150912, 0, 0, -1700280, 0, -23980100, 0, 0, 847872, 0, 0, 0, 0, 0, 0, -10657488, 0, 0, -9706064, 0, 4934272, 0, 0, 17523856, 0, 0, 0, 0, 0, 0, 6647264, 0, 0, -10926444, 0, -20464760, 0, 0, -27025152, 0, 0, 0, 0, 0, 0, 2276736, 0, 0, -3271424, 0, -10501008, 0, 0, 6867904, 0, 0, 0, 0, 0, 0, -942528, 0, 0, -18599568, 0, -22923404, 0, 0, 6523904, 0, 0, 0, 0, 0, 0, -25898880, 0, 0, 13521760, 0, -1351680, 0, 0, 10137752, 0, 0, 0, 0, 0, 0, -6486736, 0, 0, 7003224, 0, 31183744, 0, 0, -7228464, 0, 0, 0, 0, 0, 0, -21940260, 0, 0, 3379200, 0, -3166272, 0, 0, 3160800, 0, 0, 0, 0, 0, 0, -9827328, 0, 0, 14836056, 0, 1535308, 0, 0, 827904, 0, 0, 0, 0, 0, 0, -3730800, 0, 0, -22017392, 0, 1973472, 0, 0, -58460864, 0, 0, 0, 0, 0, 0, 3714304, 0, 0, 41146056, 0, -11752712, 0, 0, -15339936, 0, 0, 0, 0, 0, 0, -7201548, 0, 0, -491520, 0, -4976112, 0, 0, -18450316, 0, 0, 0, 0, 0, 0, 22188672, 0, 0, -52784640, 0, -27900928, 0, 0, -12069568, 0, 0, 0, 0, 0, 0, 11025648, 0, 0, 129856, 0, 1228800, 0, 0, 33141704, 0, 0, 0, 0, 0, 0, -2348848, 0, 0, 80251776, 0, 33588880, 0, 0, 29341536, 0, 0, 0, 0, 0, 0, 4295724, 0, 0, -8491008, 0, -23838720, 0, 0, 26211836, 0, 0, 0, 0, 0, 0, -21258496, 0, 0, 36698928, 0, -734400, 0, 0, -7254528, 0, 0, 0, 0, 0, 0, 68794176, 0, 0, -31233296, 0, 20878336, 0, 0, -16295040, 0, 0, 0, 0, 0, 0, -18908288, 0, 0, -52155468, 0, 38004232, 0, 0, -4059840, 0, 0, 0, 0, 0, 0, 62034564, 0, 0, -10145792, 0, 37086720, 0, 0, -4123516, 0, 0, 0, 0, 0, 0, 1835520, 0, 0, 60780048, 0, 21116654, 0, 0, 36705920, 0, 0, 0, 0, 0, 0, 10149600, 0, 0, -43774720, 0, 29182464, 0, 0, 67132568, 0, 0, 0, 0, 0, 0, 47219312, 0, 0, -8928960, 0, 22114064, 0, 0, -4588800, 0, 0, 0, 0, 0, 0, -61062372, 0, 0, 8717184, 0, 27962016, 0, 0, -60896000, 0, 0, 0, 0, 0, 0, -5767168, 0, 0, -40043616, 0, 25888248, 0, 0, 25016064, 0, 0, 0, 0, 0, 0, -2380704, 0, 0, 1868368, 0, 3386560, 0, 0, 94399232, 0, 0, 0, 0, 0, 0, 23342912, 0, 0, 2671908, 0, 27091128, 0, 0, 42486048, 0, 0, 0, 0, 0, 0, 53839284, 0, 0, 13486080, 0, -6391680, 0, 0, -33634328, 0, 0, 0, 0, 0, 0, -910848, 0, 0, -45215808, 0, -31453374, 0, 0, -28561984, 0, 0, 0, 0, 0, 0, -33463368, 0, 0, 78522496, 0, -15918080, 0, 0, -3929040, 0, 0, 0, 0, 0, 0, 18461088, 0, 0, 15979200, 0, 19169968, 0, 0, -8616960, 0, 0, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "6.6.a.a", "char_is_minimal": false, "conrey_index": 199, "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, -2], [0, 0], [-16, 0], [0, 0], [0, 0], [0, 88], [0, 32], [0, 0], [0, 0], [60, 0], [0, 0], [0, 329], [704, 0], [0, 0], [256, 0], [0, 207], [0, 0], [-956, 0], [0, 0], [0, 0], [0, -120], [0, 300], [0, 0], [0, 0], [2632, 0], [0, 0], [0, -1408], [5574, 0], [0, 0], [-3592, 0], [0, -512], [0, 0], [1656, 0], [0, 0], [0, 0], [0, -4229], [0, 1912], [0, 0], [0, 0], [-19194, 0], [0, 0], [0, -6658], [-960, 0], [0, 0], [2400, 0], [0, 9840], [0, 0], [-14169, 0], [0, 0], [0, 0], [0, -5264], [0, -15633], [0, 0], [0, 0], [-11264, 0], [0, 0], [0, -11148], [26340, 0], [0, 0], [-31090, 0], [0, 7184], [0, 0], [-4096, 0], [0, 0], [0, 0], [0, -8402], [0, -3312], [0, 0], [0, 0], [-6120, 0], [0, 0], [0, 12779], [-33832, 0], [0, 0], [15296, 0], [0, 5280], [0, 0], [-74408, 0], [0, 0], [0, 0], [0, 38388], [0, -3234], [0, 0], [0, 0], [-53264, 0], [0, 0], [0, 1920], [-32742, 0], [0, 0], [-115808, 0], [0, -4800], [0, 0], [78720, 0], [0, 0], [0, 0], [0, 83041], [0, 28338], [0, 0], [0, 0]]}