# Stored data for newform 784.4.f.b, downloaded from the LMFDB on 16 April 2024. {"label": "784.4.f.b", "space_label": "784.4.f", "level": 784, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503943291863824, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 752155521379960876, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1, 1]]], "qexp_display": "q-q^{3}+3\\zeta_{6}q^{5}-26q^{9}-15\\zeta_{6}q^{11}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 28, "char_orbit_label": "f", "char_is_real": true, "Nk2": 12544, "analytic_conductor": 46.25749744450064, "hecke_ring_index": 2, "level_radical": 14, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [784, 2, [687, 197, 689], [1, 2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [783], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.889", "prec": 17}, {"__RealLiteral__": 0, "data": "0.160", "prec": 17}, {"__RealLiteral__": 0, "data": "14.706", "prec": 20}, {"__RealLiteral__": 0, "data": "1.849", "prec": 17}, {"__RealLiteral__": 0, "data": "145.273", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, -2, 0, 0], "traces": [0, 2, 0, -2, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 196, 0, 106, 0, 180, 0, -34, 0, 0, 0, 0, 0, 398, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1134, 0, 0, 0, 0, 0, -666, 0, 270, 0, -34, 0, -1602, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -196, 0, 0, 0, 0, 0, 1298, 0, 936, 0, -378, 0, -180, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2662, 0, 0, 0, 0, 0, 1582, 0, -398, 0, 1980, 0, -1458, 0, 0, 0, 0, 0, 1312, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5238, 0, 0, 0, 0, 0, -4122, 0, 2216, 0, 1134, 0, -3600, 0, 0, 0, 0, 0, 5526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 666, 0, 0, 0, 0, 0, -270, 0, 5400, 0, -5206, 0, -884, 0, 0, 0, 0, 0, 1602, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1890, 0, 0, 0, 0, 0, 2630, 0, -720, 0, 6516, 0, -3506, 0, 0, 0, 0, 0, -1944, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2628, 0, 0, 0, 0, 0, 5040, 0, -5792, 0, -5096, 0, 7398, 0, 0, 0, 0, 0, -11322, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4160, 0, 0, 0, 0, 0, -936, 0, -12240, 0, 7290, 0, 378, 0, 0, 0, 0, 0, -4680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11498, 0, 0, 0, 0, 0, -394, 0, 884, 0, -7236, 0, 7126, 0, 0, 0, 0, 0, 7180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19440, 0, 0, 0, 0, 0, -3726, 0, 14632, 0, 2662, 0, 5094, 0, 0, 0, 0, 0, 990, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1582, 0, 0, 0, 0, 0, -10348, 0, -2250, 0, -10388, 0, -1980, 0, 0, 0, 0, 0, 1458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5076, 0, 0, 0, 0, 0, -13140, 0, -1312, 0, -4194, 0, 24982, 0, 0, 0, 0, 0, -15554, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14562, 0, 0, 0, 0, 0, 23166, 0, -10206, 0, 5238, 0, -12402, 0, 0, 0, 0, 0, -15210, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4122, 0, 0, 0, 0, 0, -2216, 0, -25560, 0, 19604, 0, 29484, 0, 0, 0, 0, 0, 3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3010, 0, 0, 0, 0, 0, -1998, 0, -5526, 0, -36180, 0, 9720, 0, 0, 0, 0, 0, -23474, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16794, 0, 0, 0, 0, 0, 13140, 0, 3332, 0, 17316, 0, -31482, 0, 0, 0, 0, 0, 14472, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7020, 0, 0, 0, 0, 0, -5400, 0, -5616, 0, -17442, 0, 5206, 0, 0, 0, 0, 0, 1802, 0, 0, 0, 0, 0, 0, 0, 0, 0, -37582, 0, 0, 0, 0, 0, -15032, 0, 41652, 0, 25920, 0, -17226, 0, 0, 0, 0, 0, 25094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3060, 0, 0, 0, 0, 0, 7038, 0, 35040, 0, -1890, 0, -17154, 0, 0, 0, 0, 0, 21726, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2630, 0, 0, 0, 0, 0, -18720, 0, -19368, 0, -578, 0, -6516, 0, 0, 0, 0, 0, 3506, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24590, 0, 0, 0, 0, 0, 2110, 0, 1944, 0, 2988, 0, 11198, 0, 0, 0, 0, 0, 12458, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18540, 0, 0, 0, 0, 0, 44046, 0, -20072, 0, 2628, 0, -55386, 0, 0, 0, 0, 0, 2574, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5040, 0, 0, 0, 0, 0, 5792, 0, 18630, 0, 29036, 0, 10388, 0, 0, 0, 0, 0, -7398, 0, 0, 0, 0, 0, 0, 0, 0, 0, -39814, 0, 0, 0, 0, 0, -13608, 0, 11322, 0, 24588, 0, 6766, 0, 0, 0, 0, 0, -16322, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27990, 0, 0, 0, 0, 0, 17640, 0, -2464, 0, -30886, 0, -18396, 0, 0, 0, 0, 0, 11250, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24336, 0, 0, 0, 0, 0, 12240, 0, -8586, 0, -34124, 0, -7290, 0, 0, 0, 0, 0, 9828, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3332, 0, 0, 0, 0, 0, -25380, 0, 9540, 0, 9126, 0, -54130, 0, 0, 0, 0, 0, 49680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20970, 0, 0, 0, 0, 0, -44658, 0, 86504, 0, -11498, 0, -25218, 0, 0, 0, 0, 0, 59382, 0, 0, 0, 0, 0, 0, 0, 0, 0, 394, 0, 0, 0, 0, 0, -1802, 0, -19296, 0, -32578, 0, 7236, 0, 0, 0, 0, 0, -7126, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2030, 0, 0, 0, 0, 0, 14418, 0, -7180, 0, 62010, 0, 30000, 0, 0, 0, 0, 0, -31082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12258, 0, 0, 0, 0, 0, -19278, 0, -26514, 0, -19440, 0, -3060, 0, 0, 0, 0, 0, -9144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3726, 0, 0, 0, 0, 0, -14632, 0, -67680, 0, 39004, 0, 69212, 0, 0, 0, 0, 0, -5094, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52488, 0, 0, 0, 0, 0, 55920, 0, -990, 0, 13932, 0, 11718, 0, 0, 0, 0, 0, -59004, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44298, 0, 0, 0, 0, 0, 53478, 0, 9990, 0, -41132, 0, 10494, 0, 0, 0, 0, 0, -70956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21094, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 28, 4, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 4, "minimal_twist": "112.4.p.b", "char_is_minimal": true, "conrey_index": 783, "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], [-1, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [-26, 0], [0, 0], [0, -15], [0, 0], [0, -40], [0, 0], [0, -3], [0, 0], [0, 21], [0, 0], [17, 0], [0, 0], [0, 0], [0, 0], [0, 81], [0, 0], [98, 0], [0, 0], [53, 0], [0, 0], [90, 0], [0, 0], [-17, 0], [0, 0], [0, 15], [0, 0], [0, 0], [0, 0], [199, 0], [0, 0], [0, 40], [0, 0], [0, 108], [0, 0], [0, 146], [0, 0], [0, -78], [0, 0], [-567, 0], [0, 0], [0, 0], [0, 0], [0, -21], [0, 0], [-333, 0], [0, 0], [135, 0], [0, 0], [-17, 0], [0, 0], [-801, 0], [0, 0], [0, 207], [0, 0], [0, 0], [0, 0], [360, 0], [0, 0], [0, 125], [0, 0], [0, -81], [0, 0], [0, -282], [0, 0], [0, 233], [0, 0], [-98, 0], [0, 0], [0, 0], [0, 0], [0, 689], [0, 0], [649, 0], [0, 0], [468, 0], [0, 0], [-189, 0], [0, 0], [-90, 0], [0, 0], [0, 111], [0, 0], [0, 0], [0, 0], [17, 0], [0, 0], [0, 51], [0, 0], [0, -804], [0, 0], [0, 390], [0, 0]]}