# Stored data for newform 980.4.i.n, downloaded from the LMFDB on 19 April 2024.
{"label": "980.4.i.n", "space_label": "980.4.i", "level": 980, "weight": 4, "hecke_orbit": 14, "hecke_orbit_code": 58547344978740180, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 824400913402678193, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [16, -4, 1]], [11, [3600, -60, 1]]], "qexp_display": "q+(4-4\\zeta_{6})q^{3}+5\\zeta_{6}q^{5}+11\\zeta_{6}q^{9}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 15680, "analytic_conductor": 57.821871805625804, "hecke_ring_index": 1, "level_radical": 70, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [980, 3, [491, 197, 101], [3, 3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5, 7], "conrey_indexes": [361, 961], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.050", "prec": 17}, {"__RealLiteral__": 0, "data": "1.980", "prec": 17}, {"__RealLiteral__": 0, "data": "0.151", "prec": 17}, {"__RealLiteral__": 0, "data": "12.013", "prec": 20}, {"__RealLiteral__": 0, "data": "0.413", "prec": 17}, {"__RealLiteral__": 0, "data": "111.118", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [0, 4, 5, 0], "traces": [0, 2, 0, 4, 0, 5, 0, 0, 0, 11, 0, 60, 0, -172, 0, 40, 0, 18, 0, 44, 0, 0, 0, -48, 0, -25, 0, 304, 0, -372, 0, 176, 0, -240, 0, 0, 0, -254, 0, -344, 0, -372, 0, -200, 0, -55, 0, 168, 0, 0, 0, -72, 0, 498, 0, 600, 0, 352, 0, -252, 0, -58, 0, 0, 0, -430, 0, 1036, 0, -384, 0, 336, 0, 506, 0, 100, 0, 0, 0, -272, 0, 311, 0, -1896, 0, 180, 0, -744, 0, -1014, 0, 0, 0, -704, 0, -220, 0, 1532, 0, 1320, 0, -1314, 0, -448, 0, 0, 0, -1548, 0, -278, 0, -2032, 0, -1116, 0, 240, 0, -946, 0, 0, 0, -2269, 0, -744, 0, -250, 0, 688, 0, -400, 0, 780, 0, 0, 0, 760, 0, -666, 0, -1768, 0, 1344, 0, -5160, 0, -930, 0, 0, 0, 114, 0, 40, 0, 396, 0, 1760, 0, -154, 0, -1992, 0, 0, 0, -2180, 0, 1200, 0, -7392, 0, 10398, 0, -484, 0, 1302, 0, 0, 0, 1008, 0, 4308, 0, -3100, 0, -464, 0, 1270, 0, -1080, 0, 0, 0, -48, 0, -1058, 0, -3440, 0, -7428, 0, -1768, 0, -4144, 0, 0, 0, -930, 0, 528, 0, 5280, 0, -8072, 0, 672, 0, -500, 0, 0, 0, -2024, 0, -1548, 0, -1360, 0, -550, 0, 2388, 0, -3874, 0, 0, 0, -3162, 0, -840, 0, -2176, 0, 10848, 0, -3886, 0, 2860, 0, 0, 0, -3784, 0, -3792, 0, 10200, 0, -5760, 0, 360, 0, 2178, 0, 0, 0, -2046, 0, 6144, 0, 4980, 0, -8112, 0, 822, 0, 8480, 0, 0, 0, 1500, 0, 1138, 0, 3872, 0, 11412, 0, -3028, 0, 880, 0, 0, 0, 4589, 0, 3064, 0, -6780, 0, -2520, 0, 9120, 0, 4128, 0, 0, 0, 5256, 0, 290, 0, 8312, 0, -3584, 0, 6552, 0, -1366, 0, 0, 0, -2598, 0, -11160, 0, -12384, 0, 1584, 0, 2150, 0, 1112, 0, 0, 0, 3292, 0, 2794, 0, 10360, 0, 12388, 0, -2232, 0, -10560, 0, 0, 0, -960, 0, 10020, 0, 6260, 0, -26144, 0, 4194, 0, 840, 0, 0, 0, 4104, 0, 4923, 0, -18152, 0, 5060, 0, 7496, 0, -2046, 0, 0, 0, 5842, 0, -500, 0, 31992, 0, -824, 0, 1376, 0, 2568, 0, 0, 0, -1100, 0, -13086, 0, -1728, 0, 6240, 0, 1360, 0, 10454, 0, 0, 0, 10830, 0, -15136, 0, 3110, 0, -30480, 0, -8566, 0, 2664, 0, 0, 0, -4740, 0, -3536, 0, -27768, 0, 8572, 0, -1848, 0, 450, 0, 0, 0, 20640, 0, -6336, 0, 17948, 0, -7440, 0, 2112, 0, -2968, 0, 0, 0, 12372, 0, 5070, 0, 912, 0, 22788, 0, -11160, 0, -160, 0, 0, 0, 358, 0, 2736, 0, 15060, 0, -27536, 0, 3520, 0, 13380, 0, 0, 0, 616, 0, -6000, 0, -2200, 0, 10956, 0, -6336, 0, 21844, 0, 0, 0, 3830, 0, 5008, 0, -17440, 0, 25800, 0, -3348, 0, 3300, 0, 0, 0, 8116, 0, -14784, 0, 9888, 0, -13140, 0, 20796, 0, -5466, 0, 0, 0, 6688, 0, 2240, 0, 20160, 0, 10416, 0, 10074, 0, -13828, 0, 0, 0, -3168, 0, 9863, 0, -5544, 0, 31992, 0, 7740, 0, -17232, 0, 0, 0, 15226, 0, -6200, 0, -2780, 0, -26456, 0, 638, 0, -8184, 0, 0, 0, -5080, 0, 8490, 0, 17200, 0, -8640, 0, -10284, 0, -2790, 0, 0, 0, -1770, 0, -6068, 0, -384, 0, 2400, 0, 21506, 0, 4232, 0, 0, 0, -29880, 0, 4730, 0, -24216, 0, 15488, 0, -14856, 0, 15474, 0, 0, 0, 7072, 0, 2520, 0, 25580, 0, 22792, 0, 11345, 0, 11576, 0, 0, 0, -14448, 0, -20126, 0, -7440, 0, -55884, 0, -22540, 0, -7296, 0, 0, 0, -625, 0, 10560, 0, -9144, 0, -10256, 0, -16144, 0, 1720, 0, 0, 0, 1848, 0, 12798, 0, 42296, 0, -4000, 0, 16464, 0, 15120, 0, 0, 0, 24234, 0, -3900, 0, 11132, 0, -45672, 0, 26318, 0, 6192, 0, 0, 0, 8928, 0, -2720, 0, -6960, 0, 57604, 0, -3800, 0, 2526, 0, 0, 0, -9552, 0, 23076, 0, -6660, 0, -30992, 0, -42828, 0, 7868, 0, 0, 0, -4420, 0, -3348, 0, -25296, 0, 43020, 0, 11176, 0, 3360, 0, 0, 0, -30014, 0, 2992, 0, -16896, 0, -51600, 0, 21696, 0, -816, 0, 0, 0, 15544, 0, 4650, 0, 19904, 0, 39674, 0, -1800, 0, -33946, 0, 0, 0, -62160, 0, -23420, 0, -30272, 0, -29184, 0, -570, 0, -10428, 0, 0, 0, -9056, 0, 20400, 0, 400, 0, -35108, 0, -11520, 0, -36438, 0, 0, 0, 990, 0, 21672, 0, 18044, 0, 17424, 0, 1470, 0, 4400, 0, 0, 0, -8184, 0, 10080, 0, -56544, 0, -1540, 0, 5252, 0, -24576, 0, 0, 0, 4988, 0, 9960, 0, -24588, 0, 6048, 0, 11154, 0, -30360, 0, 0, 0, -3288, 0, -15546, 0, -38728, 0, 67840, 0, 10900, 0, -4400, 0, 0, 0, 7314, 0, -11984, 0, 12000, 0, 27000, 0, -44602, 0, -4552, 0, 0, 0, -18480, 0, 26752, 0, -70896, 0, 20414, 0, 22824, 0, 25995, 0, 0, 0, 12112, 0, -12192, 0, -25180, 0, -4840, 0, 24906, 0, 23204, 0, 0, 0, -19848, 0, -6510, 0, 36712, 0, -32640, 0, -89096, 0, 8426, 0, 0, 0, -27542, 0, -13560, 0, 41436, 0, 50344, 0, -5040, 0, -12864, 0, 0, 0, -18660, 0, -7392, 0, 43080, 0, 33024, 0, -32736, 0, -8964, 0, 0, 0, -7750, 0, 23092, 0, -28908, 0, -28416, 0, -56880, 0, -1160, 0, 0, 0, 26584, 0, 16624, 0, -28896, 0, 12700, 0, 4928, 0, 162, 0, 0, 0, -26208, 0, 5400, 0, 59468, 0, -10928, 0, 17142, 0, 8928, 0, 0, 0, -26436, 0, -43516, 0, -20784, 0, 55764, 0, 240, 0, 44640, 0, 0, 0, -1185, 0, 17028, 0, -10580, 0, 25312, 0, 3168, 0, 2916, 0, 0, 0, -8600, 0, 6894, 0, -121680, 0, -6116, 0, -45264, 0, -18570, 0, 0, 0, 4800, 0, -52016, 0, 26336, 0, -17680, 0, -13858, 0, -38608, 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, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "20.4.a.a", "char_is_minimal": false, "conrey_index": 361, "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, 0], [4, -4], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [0, 11], [0, 0], [60, -60], [0, 0], [-86, 0], [0, 0], [20, 0], [0, 0], [18, -18], [0, 0], [0, 44], [0, 0], [0, 0], [0, 0], [0, -48], [0, 0], [-25, 25], [0, 0], [152, 0], [0, 0], [-186, 0], [0, 0], [176, -176], [0, 0], [0, -240], [0, 0], [0, 0], [0, 0], [0, -254], [0, 0], [-344, 344], [0, 0], [-186, 0], [0, 0], [-100, 0], [0, 0], [-55, 55], [0, 0], [0, 168], [0, 0], [0, 0], [0, 0], [0, -72], [0, 0], [498, -498], [0, 0], [300, 0], [0, 0], [176, 0], [0, 0], [-252, 252], [0, 0], [0, -58], [0, 0], [0, 0], [0, 0], [0, -430], [0, 0], [1036, -1036], [0, 0], [-192, 0], [0, 0], [168, 0], [0, 0], [506, -506], [0, 0], [0, 100], [0, 0], [0, 0], [0, 0], [0, -272], [0, 0], [311, -311], [0, 0], [-948, 0], [0, 0], [90, 0], [0, 0], [-744, 744], [0, 0], [0, -1014], [0, 0], [0, 0], [0, 0], [0, -704], [0, 0], [-220, 220], [0, 0], [766, 0], [0, 0], [660, 0], [0, 0]]}