# Stored data for newform 784.2.x.e, downloaded from the LMFDB on 19 April 2024.
{"label": "784.2.x.e", "space_label": "784.2.x", "level": 784, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18015979091002128, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 254551056601567647, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [0, 1]], [5, [64, -32, 8, -4, 1]]], "qexp_display": "q+(1-\\zeta_{12}-\\zeta_{12}^{2})q^{2}+(-2\\zeta_{12}+2\\zeta_{12}^{3})q^{4}+\\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": "0.261", "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": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "3.764", "prec": 17}, {"__RealLiteral__": 0, "data": "0.619", "prec": 17}, {"__RealLiteral__": 0, "data": "63.338", "prec": 20}, {"__RealLiteral__": 0, "data": "45.332", "prec": 20}, {"__RealLiteral__": 0, "data": "1888.330", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c12", "trace_display": [2, 0, 4, 0], "traces": [0, 4, 2, 0, 0, 4, 0, 0, 8, 0, -8, -2, 0, 0, 0, 0, 8, -4, 6, 4, -16, 0, -8, 0, 0, 0, 0, 0, 0, 28, 0, -16, -8, 0, -8, 0, 24, 10, 0, 0, 0, 0, 0, -4, -4, -12, -12, -24, 0, 0, -12, 0, 0, 2, 0, 0, 0, 0, 0, 16, 0, 12, -32, 0, 0, 0, 0, -6, 0, 0, 0, 0, 12, 0, -20, 0, 16, 0, 0, -20, -16, 18, -20, 40, 0, -16, -4, 0, 0, 0, 0, 0, -48, 0, 24, -16, 0, 8, 0, -12, -12, 12, 0, 0, 0, 0, 8, -10, 0, 6, -8, 0, 0, 16, 0, 24, 28, 0, 64, 0, 0, 0, 0, 0, 0, -16, 0, 32, 16, 0, 0, -28, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 56, -24, 0, -40, -6, 0, 0, 16, 0, 0, -64, 0, -24, 20, 0, -64, 0, 36, -30, 40, 0, 0, 0, 0, 0, -16, 12, 4, 0, 0, 0, -16, 0, 28, 6, 24, 16, 0, 0, -24, 0, 0, -4, 0, 0, -32, 36, 0, 32, 4, 0, 0, 20, 0, 0, 12, 0, 48, 0, 0, 40, -8, -36, 0, -16, 0, -36, 4, 0, 20, 0, 0, 0, 0, 0, 16, 0, 0, -16, 0, -36, 8, -4, 0, 16, 0, 0, 112, 0, 0, 48, 32, 0, 0, 0, 0, 44, -18, 0, 48, 0, 0, 0, -32, 0, 0, 56, 0, 24, 16, 0, -32, -4, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 12, -16, 0, -16, -32, 0, -48, 6, 0, 30, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 48, 26, -56, 0, -24, -56, 0, 0, 0, 0, 12, 0, 0, 0, -40, 0, -16, -48, 12, -72, 0, 0, -64, 0, 0, 0, 0, 0, 0, 14, 0, -28, -32, 0, 0, -16, 0, 0, 0, 0, 80, 0, 0, -42, 40, -30, -24, -48, 0, 32, 26, 0, 16, -16, 48, 0, 0, 0, 0, -30, 0, -48, 0, 0, -16, -12, 0, 0, 112, 0, 0, 0, -48, 0, 16, 0, 0, 48, 0, -64, 0, -60, -80, 0, 0, 22, 8, 0, -48, 0, 0, 52, 0, 0, -36, 8, 0, 0, 64, -6, 0, -6, 0, 0, 0, 0, 20, 40, -12, -24, -96, 0, 0, -24, 0, 0, 24, 72, 0, 0, 0, 0, 0, 0, -32, 0, -72, 80, 0, 0, -8, -48, 0, -36, 0, 0, 0, 0, 0, 0, 40, 0, 8, 16, 0, 24, 0, 0, -12, -24, 0, 0, 32, 0, 0, 2, 0, -56, -8, 0, 0, -120, -18, -20, 0, 0, 0, 0, 0, 0, -32, 0, -48, -64, 0, 56, 56, 0, -32, 36, 0, 0, 192, 0, 0, 0, 0, -24, 0, 12, 0, -40, 0, 0, 88, 0, -72, 8, 0, 0, 48, 0, 0, -76, 0, -28, 0, -24, -128, 0, 0, 46, -16, 0, 56, 0, 0, 0, 0, 0, 0, -16, 0, 0, -64, 0, 4, 16, 0, 48, 0, 0, 0, 0, 84, 48, -112, 0, 64, -32, 0, 26, 8, 96, 0, 0, 0, 0, -24, 0, 0, 0, 0, -22, 16, 0, -16, 48, 0, 92, -48, 36, 0, 0, 0, 0, 120, 0, -8, 34, 48, 0, 0, 0, 0, 40, 0, 16, 32, 0, 0, 0, 0, 18, 0, 0, 0, 72, 48, -4, -26, 0, 0, 0, 0, 0, 24, 0, -56, -40, 0, -64, 64, 0, -40, -12, 0, 0, 24, 0, 0, 0, 0, 0, 0, 36, -40, 36, 0, 56, 0, 0, -96, 0, -24, -18, 0, 0, 0, 0, 0, -24, 64, 0, 80, 0, 0, -62, -28, 0, 48, -40, 0, 0, -40, 0, 0, 32, 0, 0, -56, 0, 0, -24, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, -120, -50, 0, 112, 0, -72, 0, -12, 0, 52, 84, 0, 160, 0, 0, 84, 48, 0, -24, -48, 0, 136, 16, 0, -52, -40, 0, 0, 0, 0, 32, 22, 24, 96, 0, 0, -8, 0, 0, 52, 0, 0, -120, 0, 0, 0, 0, 0, 0, -76, 0, -40, 16, 0, -24, 0, 0, 14, 0, 0, 56, 0, 0, 0, -12, 0, 12, 40, -96, 0, -44, 0, -16, -42, 0, 0, 0, 0, 0, 4, 0, -20, -128, 0, -96, -12, 60, -14, -80, 0, 0, 0, 0, 0, -44, -60, 16, 0, 0, -64, 96, 0, 0, 80, 0, -60, 52, 0, -32, 0, 0, 0, 0, -24, -8, 0, 0, 40, 0, 0, 0, -12, 0, 0, 16, 0, -24, -40, 0, 0, -24, 0, 0, -192, 0, 36, -20, 0, 160, 0, -48, 0, 0, 0, -96, 128, 0, 96, -24, 84, 24, 12, 0, 0, 0, 0, 0, 0, 72, 96, 0, 0, -20, 120, 0, -8, -56, 0, 160, -2, 0, 0, -16, 0, 0, -20, 0, 4, -80, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, -36, 0, -36, -52, -144, 0, 16, 0, 12, 60, 0, -96, 0, 0, 0, 0, 0, -4, 32, 0, 32, -28, 0, 0, 12, 0, 0, 40, 0, 0, 24, 0, -96, 0, 0, -6, -32, 0, 0, 72, 0, -100, 0, 0, -4, 0, 0, 0, 0, 18, 0, 48, 0, 48, 0, 0, -60, -112, 0, 4, 0, 0, 32, 0, 0, -30, 8, 72, 0, -192, 0, -40, 44, 0, -64, 0, 0, 0, 96, 0, 0, 0, 0, 60, 28, -24, 0, -100, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 96, 52, 0, 120, 128, 0, 8, -66, 0, 0, -24, 0, 0, 0, 0, -72, 0, 0, -80, 0, 0, -66, 0, 30, 0, 128, 0, 0, -36, 0, -16, -8, 0, 0, -88, 0, -48, -76, 0, -56, 0, -36, -76, 0, 0, 0, 0, 0, 0, 12, 24, -44, -64, 0, 0, 192, 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.b", "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, 0, 0, 0], [0, -2, 0, 2], [2, 2, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 2], [0, -3, 0, 0], [0, 0, -4, 0], [0, 1, -1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4, 0, -4, 0], [0, 0, -2, 0], [0, -3, 3, 3], [2, -2, -2, 0], [-4, 0, 0, 4], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [0, 3, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [7, 0, 0, -7], [0, 0, 0, 0], [0, 0, -8, 0], [0, -4, -4, 4], [0, 0, 0, 0], [-2, 0, 0, 2], [0, 0, 0, 0], [6, 0, 0, 0], [5, 5, -5, 0], [0, -4, 0, 4], [0, 0, 0, 0], [0, 8, 0, 0], [0, 0, 0, -10], [0, 0, 0, 0], [-1, 0, 0, -1], [-2, 2, 2, 0], [0, -6, -6, 6], [0, 6, -6, -6], [-12, 0, 12, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 1, 1], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, -14, 0, 0], [0, -8, 8, 8], [0, 0, 0, 0], [6, -6, -6, 0], [-8, 0, 0, 8], [0, 0, 0, 0], [0, 0, 0, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, -3, 3], [0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, -6, -6, 0], [0, 6, 0, -6], [0, 0, -10, 0], [0, 0, 0, 0], [4, 0, 0, 4], [0, 0, 0, 0], [0, 0, 0, 0], [-10, 0, 10, 0], [0, 8, -8, -8], [0, 0, 9, 0], [-10, -10, 10, 0], [10, 0, 0, -10], [0, 0, 0, 0], [-4, 0, 0, -4], [-2, 0, 2, 0], [0, 0, 0, 0], [0, 4, 0, -4], [0, -14, 0, 0], [0, 0, 0, 12], [0, 0, 0, 0], [-12, 0, 0, 0], [0, 0, 0, 0], [0, 12, 12, -12], [0, 0, -8, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 0, 3], [-6, 0, 6, 0]]}