# Stored data for newform 784.2.x.b, downloaded from the LMFDB on 25 April 2024.
{"label": "784.2.x.b", "space_label": "784.2.x", "level": 784, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4505180208890640, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 2159020932298575842, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [64, 32, 8, 4, 1]], [5, [64, 32, 8, 4, 1]]], "qexp_display": "q+(1-\\zeta_{12}-\\zeta_{12}^{2})q^{2}+(-2\\zeta_{12}-2\\zeta_{12}^{2}+\\cdots)q^{3}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 112, "char_orbit_label": "x", "char_is_real": false, "Nk2": 3136, "analytic_conductor": 6.260271518468382, "hecke_ring_index": 1, "level_radical": 14, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.264", "prec": 17}, "analytic_rank_proved": true, "char_values": [784, 12, [687, 197, 689], [12, 3, 8]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 4, "level_primes": [2, 7], "conrey_indexes": [165, 373, 557, 765], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "3.719", "prec": 17}, {"__RealLiteral__": 0, "data": "0.750", "prec": 17}, {"__RealLiteral__": 0, "data": "66.309", "prec": 20}, {"__RealLiteral__": 0, "data": "39.159", "prec": 20}, {"__RealLiteral__": 0, "data": "2038.870", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c12", "trace_display": [2, -4, -4, 0], "traces": [0, 4, 2, -4, 0, -4, 0, 0, 8, 0, 8, 6, 8, 0, 0, 32, 8, -12, -10, -8, 16, 0, 24, 0, -16, 0, 0, -16, 0, -4, 16, 8, -8, 24, -24, 0, -40, -6, 0, 0, 0, 0, 0, -20, 12, -20, 4, -16, -32, 0, -12, -24, 0, -14, -16, 0, 0, 0, 0, 4, 0, 12, 16, 0, 0, 0, -24, 10, 0, 16, 0, 0, -20, 0, 12, -12, -32, 0, 0, 28, 16, 2, -4, 0, 0, 48, -20, 0, 0, 0, 0, 0, 16, 16, 16, -32, 0, 24, 0, -60, -12, 4, 0, 0, 0, 0, -56, -10, 16, 6, -24, 48, 0, -48, -32, 8, -4, 0, 16, 0, 64, 0, 0, 8, 0, 16, 0, 32, 16, 40, 0, 24, 0, 0, 0, 0, -24, 0, 16, 48, 0, 64, -16, 0, 0, 8, -40, 0, 24, 26, 24, 0, -32, 0, 0, -32, 0, 0, -28, -56, 64, 0, 4, 10, 8, 48, 0, 0, 0, 0, 48, 40, 20, 32, -16, 0, 48, 16, -12, -10, 40, -16, 0, 0, 8, 0, 0, 36, 0, 0, -64, -44, -32, 48, 12, 0, 0, -44, 0, 0, 12, 0, 16, 0, -96, -8, 0, -20, 0, -96, 0, -36, -28, 32, 20, 0, 0, 0, 0, -40, 48, 0, 24, -16, 0, 60, -24, 8, 64, 24, 0, 0, -16, 0, 0, -32, 8, -112, 0, -32, 64, -44, 14, -20, 48, 0, 32, 0, 16, 0, 0, -16, 0, 24, 16, -96, -32, -20, 80, 0, 0, -10, 0, 0, 48, 0, 0, -48, -20, -32, -32, 32, -96, 0, -48, -18, -16, -2, 48, 0, 0, 0, 0, -12, 32, -64, 0, 0, -80, -38, -8, -24, -40, 40, 0, 0, 0, 0, -52, 0, 48, 0, 24, 16, 32, 48, -60, 32, 0, 0, -32, 0, 0, 0, 0, 0, 0, 30, 56, -12, 32, 80, 0, 96, 0, 0, 0, 0, 16, 0, 192, 30, 0, -30, 0, -80, 0, -32, 26, 48, -48, -24, 160, 0, 0, 0, 0, 26, -16, -64, 0, 0, 48, 36, -16, -32, -48, 0, 0, 0, -80, 0, -16, 56, 0, -80, 48, -32, 0, 20, -48, 0, 64, -10, -72, 0, -32, 0, 0, 68, 0, -32, 44, -32, -128, 0, 96, 50, 0, -38, 0, 0, 0, 0, -44, 56, -60, 0, -80, 0, 0, 8, 40, 0, 8, -8, 0, 0, -96, 0, 0, -48, 0, 0, -40, 0, 0, -96, -48, 40, 0, -100, 0, 0, 0, 0, 128, 0, 40, 0, -40, 0, -32, 8, 0, -32, -12, -16, 80, 0, 96, 0, 0, 34, 0, -24, -8, -208, 0, 136, 30, 12, 0, 24, 0, 0, 128, 0, -48, 48, -16, 112, 0, 56, -8, 64, -16, -32, 0, 0, -128, 0, 0, 0, 0, 48, 0, 140, -16, -16, -64, 0, -88, 0, 56, -24, 0, 0, 48, 0, 0, -44, 16, 12, 0, 120, 64, 0, 0, 30, 16, 0, -16, 0, 0, 0, 0, -52, 0, -24, -192, 0, -64, 64, 20, 0, 0, -96, 0, 0, 0, 0, 20, 52, 96, 0, -96, 48, -96, -38, 56, -40, 0, 0, -48, 0, 40, 0, 0, 0, -128, 58, -32, 32, -48, -48, 0, 76, -48, -60, 0, 0, 0, 0, -8, -48, -48, -30, 40, 0, 0, -288, 48, -44, 64, 48, -48, 0, 64, 0, 0, 42, 0, 176, 0, -24, -80, -52, 38, 96, 0, 0, 0, 0, 40, 0, 40, -32, 0, -64, -16, 88, 24, -44, -96, 0, -104, -80, 0, 0, 0, 0, 0, 100, 24, 28, -16, 40, 0, 0, 96, 0, 120, 30, 0, 0, 0, 0, 0, 36, 32, -16, -16, 0, 0, -62, 4, 96, 0, 72, 0, 0, 56, 0, 0, -32, 0, 0, -24, 80, 0, -88, 40, -104, 0, -160, 0, 0, 4, 0, 0, 0, 40, -50, 24, 96, 0, 200, 0, 68, 96, 60, -60, 0, 0, 0, 0, 4, 0, 16, -40, 144, 0, 104, -16, -24, -52, 16, 0, 0, 0, 0, 48, -10, 80, -96, 0, -192, -40, 0, 32, 24, 128, 0, 104, 0, 16, 0, 0, -64, 0, 52, 0, -48, -48, -128, 72, 0, 0, 62, 0, 0, -24, 0, 0, 0, 20, 32, 44, -16, -160, 0, 52, -88, 16, 6, 56, 0, 0, 0, 0, 60, -96, -4, -64, 0, 32, -60, -20, 10, -48, 0, 0, 0, 64, 0, 20, 0, -144, 0, 64, -80, 64, 32, 0, 48, 0, 132, 68, 0, -64, 0, 0, 0, 0, -120, 32, 0, -64, 120, 0, 80, 0, -60, 0, 0, 48, 0, -152, 16, 0, 48, 24, 32, 0, 0, 96, -24, 44, -96, 224, 0, -240, 0, 0, -112, -80, -32, 0, 192, -24, 60, -8, -60, 160, 0, 0, 0, 0, 0, -8, -120, 0, -128, -36, 40, 96, 80, 40, 0, -32, 14, 96, 0, 0, 0, 0, -52, 0, -4, 0, -8, 0, 0, -192, 0, 0, -32, 0, 0, 0, 0, -100, -96, -36, 52, 160, 0, -112, -48, 36, 12, 64, 16, 0, 0, 0, 0, 0, -8, -160, 0, 0, -12, 64, 128, 4, 152, 0, 168, 0, 0, 24, 0, -64, 0, 160, 42, 48, -80, 0, -120, 0, -68, 0, 32, -68, 0, 96, 0, 0, -6, 0, -64, -104, 80, 0, 0, 68, -8, 0, -84, 0, 0, -96, 0, -48, 18, -16, -40, 0, 0, 0, 0, -52, 96, -96, 0, 192, 0, 32, 0, 0, 0, 0, -36, 28, 0, 0, -60, 128, 0, -64, -16, 0, 0, 0, 0, 0, 16, -64, 52, 0, -8, 32, 0, -120, -26, -112, 0, 48, 0, 0, 0, 0, -88, 0, -24, -32, 0, 0, 30, 0, -50, 0, -192, 0, 0, 28, 0, 48, 52, -80, 0, 8, 0, -48, 68, 40, -72, 0, 60, -44, 0, 0, 0, 0, 0, 0, -20, -120, 20, 32, -240, 0, -160, 0, 60, 0, 0, 64], "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, 7, 3, 1, 3, 0], [1, 1, 16, 5, 1, 4, 0], [1, 1, 112, 23, 1, 12, 0]], "char_orbit_index": 24, "prim_orbit_index": 23, "minimal_twist": "112.2.m.a", "char_is_minimal": false, "conrey_index": 165, "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, 0, 0], [1, 0, 0, 0], [1, -1, -1, 0], [0, -2, -2, 2], [0, -2, 0, 2], [-2, -2, 2, 0], [0, 0, 0, 4], [0, 0, 0, 0], [2, 0, 0, 2], [0, 5, 0, 0], [0, 0, 4, 0], [0, -3, 3, 3], [4, 4, -4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [4, 0, -4, 0], [0, 0, -6, 0], [0, 5, -5, -5], [-4, 4, 4, 0], [4, 0, 0, -4], [0, 0, 0, 0], [6, 0, 0, 0], [0, -2, 0, 0], [0, 0, -8, 0], [0, 3, 0, -3], [0, 0, 0, 0], [-4, 0, 0, -4], [0, 0, 0, 0], [-1, 0, 0, 1], [8, -8, -8, 0], [0, 0, 4, 0], [0, -4, -4, 4], [12, 0, -12, 0], [-6, 0, 0, 6], [0, 0, 0, 0], [-10, 0, 0, 0], [-3, -3, 3, 0], [0, 8, 0, -8], [0, 0, 0, 0], [0, -8, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-5, 0, 0, -5], [6, -6, -6, 0], [0, -10, -10, 10], [0, -2, 2, 2], [-8, 0, 8, 0], [-8, 0, 0, 8], [0, 0, 0, 0], [-3, 0, 0, -3], [-12, 12, 12, 0], [0, 0, 0, 0], [0, 7, -7, -7], [-8, 0, 8, 0], [0, 0, 0, -12], [0, 0, 0, 0], [0, 0, 0, -16], [0, 2, 0, 0], [0, -2, 2, 2], [0, -16, 0, 16], [6, -6, -6, 0], [4, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 8], [0, 0, 0, 0], [0, -12, -12, 12], [0, 5, 5, -5], [0, 12, 0, 0], [4, 0, 0, 4], [0, 0, 0, 0], [0, 0, 0, -8], [-10, 10, 10, 0], [0, 10, 0, -10], [0, 0, 6, 0], [-6, -6, 6, 0], [-8, 0, 0, -8], [0, 0, 0, 0], [0, 0, 0, 0], [14, 0, -14, 0], [0, -8, 8, 8], [0, 0, 1, 0], [-2, -2, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [12, 0, 0, 12], [-10, 0, 10, 0], [0, 4, 0, -4], [0, -12, 0, 12], [0, 6, 0, 0], [0, 0, 0, 20], [0, 0, 0, 0], [4, 0, 0, 0], [8, -8, -8, 0], [0, 8, 8, -8], [0, 0, -16, 0], [0, 16, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [-15, 0, 0, 15], [-6, 0, 6, 0]]}