# Stored data for newform 784.2.x.f, downloaded from the LMFDB on 19 April 2024.
{"label": "784.2.x.f", "space_label": "784.2.x", "level": 784, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22519578718372624, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 232705984899810296, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [4, -4, 2, -2, 1]], [5, [4, -4, 2, -2, 1]]], "qexp_display": "q+(1+\\zeta_{12}-\\zeta_{12}^{2})q^{2}+(\\zeta_{12}+\\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": "0.258", "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": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "3.975", "prec": 17}, {"__RealLiteral__": 0, "data": "0.559", "prec": 17}, {"__RealLiteral__": 0, "data": "79.107", "prec": 20}, {"__RealLiteral__": 0, "data": "29.623", "prec": 20}, {"__RealLiteral__": 0, "data": "2783.371", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c12", "trace_display": [2, 2, 2, 0], "traces": [0, 4, 2, 2, 0, 2, 8, 0, 8, 0, 0, -2, 4, -4, 0, 8, 8, 4, -2, -6, 8, 0, 0, 0, 0, 0, -4, -16, 0, 12, 4, 16, -8, 4, 8, 0, -8, -6, 12, 0, 8, 0, 0, 20, 4, -2, -12, -16, 16, 0, -12, -4, 4, 10, 0, 0, 0, 0, 12, 6, 0, 18, 32, 0, 0, -4, -4, 10, 0, -24, 0, 0, -4, 0, 0, -6, 24, 0, -8, 0, -8, -10, 0, -4, 0, 8, 0, 0, -8, 0, -8, 0, -48, -16, 16, 12, 16, -8, 0, -4, -12, -22, 8, 0, 0, 0, 0, 14, -16, -6, 4, -24, 0, -24, -12, -12, -12, 2, 0, 0, 16, 0, -36, 0, 0, -32, 0, 32, 16, 20, 4, -22, 0, 0, 40, 0, 8, 0, 0, -12, 0, -32, 20, 4, 0, 12, -16, 0, -24, -14, 0, 0, 0, 0, 0, 32, -8, -30, 0, -20, 0, 0, -20, 2, 0, -4, -4, 0, 0, 0, 0, -6, 20, 2, 24, 0, -16, -12, -8, 34, -4, -36, 0, 0, -24, 0, 32, 4, 0, 0, 24, 16, -16, -28, -4, -8, 0, -68, -4, 0, 12, 0, 0, 0, 16, 0, -12, 12, -8, 24, 0, -36, -20, -20, 0, 0, -64, 0, -24, -8, -8, -4, -12, 96, 0, 12, -12, -30, 24, -14, -48, 0, 0, 0, 0, 16, -12, 0, 0, 0, 16, 36, 18, -14, -72, 0, 0, 0, 32, 0, -32, 84, 0, -24, 16, 8, -32, 44, 40, 0, 0, -6, 44, 0, 8, 0, 0, -16, 20, -6, -16, 16, 32, 0, 32, -6, -24, -6, 0, 0, 0, 0, -32, 30, -40, -12, 8, 0, -16, 26, -12, -4, -16, 60, 0, 0, -24, 0, 0, 12, -24, 0, -40, 44, 24, -36, 4, -20, 0, -24, 0, 0, 8, 0, -120, 0, 0, 10, 20, -12, 16, 56, 0, -24, 0, -6, -4, 0, 0, 0, 0, -2, 4, 6, 4, 40, 0, 72, -22, -12, 8, 16, 0, 0, 80, 0, -4, -26, 24, 12, 0, 32, 0, 12, 12, 20, -32, 0, 136, 0, 0, 0, 0, 36, 0, -16, 36, -16, 0, 0, -24, 0, 64, 10, 0, 0, -32, 0, 0, -12, 0, 16, -16, 32, 0, 0, -56, 10, 0, 26, -8, 0, 0, 0, 0, 0, 4, 10, 56, 0, 0, 36, 20, -16, 44, -20, 0, 0, 0, 0, 0, 16, -48, 0, 24, -4, 16, -12, 12, 12, 0, -36, -36, 0, 40, 0, 0, 0, 56, -4, 20, -64, -32, 56, 0, 24, -12, -36, 0, 0, -16, 0, -16, 30, 0, -8, 48, -56, 0, 120, 6, 0, 0, -20, -120, 0, 48, 0, 0, -16, -24, 44, 0, -64, 24, 32, 8, 10, 8, 0, 0, 0, 24, 0, 0, -36, 0, 20, 0, 80, -16, 12, 72, 0, 72, -4, 28, 0, 0, 0, 0, -76, 0, 12, -12, -4, 128, 0, -8, -46, 32, -4, 0, 0, 0, 0, -24, 22, 0, -46, 16, 0, -64, 48, -44, -12, 0, 32, 0, 0, -8, 0, 0, -50, 88, 0, 24, -32, -16, 26, -20, 12, 0, 0, 0, 0, 0, 0, -24, 0, -64, 18, -16, -36, 16, -24, 0, -20, 32, 18, 12, 0, -96, 0, 0, -12, -12, 50, 16, -40, 0, 16, 40, -38, 32, -12, 0, 0, -80, 0, 24, -2, 0, 32, 0, 72, -16, -36, -26, 28, 0, 0, -16, 0, 16, 0, 0, -28, 0, -96, -12, -68, 24, -68, -32, 0, -56, 28, 0, 0, -24, 0, 0, -20, -40, 18, -44, 64, 96, 0, -72, 16, -8, 50, -20, 0, 0, 0, 0, -34, 32, -48, 120, 0, 0, -2, -32, 12, -60, -24, 0, 0, 0, 0, -20, 16, 0, 0, -24, -20, -32, 36, 28, -84, 0, 40, -24, 0, -20, 0, 0, 0, -8, -38, -12, 44, 0, 16, 0, -68, 8, 18, 0, 0, 0, 0, 24, -36, -8, 48, 20, -72, 0, 56, 36, 24, 44, -6, -48, 0, 32, 0, 0, -10, 12, 32, 0, -56, 40, -20, -24, 18, -8, 0, 0, 0, -24, 0, 12, 16, 0, 124, 16, -36, -16, -32, 24, 0, 0, -54, -40, 0, -16, 0, 0, 8, 68, 0, 52, 0, -16, 0, 4, -36, -36, 18, 0, 0, 0, 0, -16, 20, -72, 42, -32, 0, -96, 20, 0, -46, -24, -24, 0, 0, 0, 0, 0, 2, 16, 0, -64, -64, 64, 84, -12, -40, 0, 92, 0, 0, 24, 0, 64, 0, 0, 4, -32, -12, 32, -200, 0, 88, 0, 10, -20, 0, -16, 0, 0, 0, 8, -20, 24, -96, 0, -120, -44, -30, -68, 12, 0, 0, 0, 0, -20, 20, 56, -100, 0, -64, -24, 8, -36, -8, 80, 0, -64, 0, -88, 0, 0, -156, 0, 32, -12, -4, 16, -60, -64, 0, 0, -22, 0, 0, -24, 0, 0, 132, 0, -46, 4, 12, 32, 0, -24, 4, 0, -64, 12, 0, 0, 0, 0, -40, 36, -22, 32, 0, 80, -60, -12, 36, 40, -20, 0, 0, 56, 0, 8, 6, 80, 0, -128, -48, 0, -4, 28, 52, 0, 0, 24, 0, 0, 0, 0, 0, -32, 10, -28, 60, 0, 8, 0, -84, -8, 12, 0, 0, -48, 0, -32, -10, 0, -48, -28, 136, 0, 48, 60, 48, 0, -20, 0, 0, -48, 0, 0, 54, -60, -44, 0, -32, 0, 4, 64, 36, -56, 0, 0, 0, 0, 0, 44, 40, 0, 36, -32, 12, -48, -60, 64, 0, 32, 60, -20, 0, 8, 0, 0, -64, -32, 58, -60, 0, 48, 0, 40, 10, 0, -8, 0, 0, 0, 0, 20, -16, 0, 12, 160, 0, 0, -66, -12, -14, 0, -56, 0, 0, 36, 0, 0, 38, 56, 0, -8, 12, -72, 4, 4, -16, 0, 12, 0, 0, 0, 0, 48, 0, -48, 60, 4, -64, 64, -8, 0, 56, -8, 74, 92, 0, 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, 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": "16.2.e.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, 1, 1, -1], [0, 2, 0, -2], [1, 1, -1, 0], [2, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, -2], [0, -1, 0, 0], [0, 2, 0, -2], [0, 1, -1, -1], [2, 2, -2, 0], [-1, 0, 0, 1], [0, 0, 0, 0], [2, 0, 0, 0], [4, 0, -4, 0], [0, 0, 2, 0], [0, -1, -1, 1], [-3, 3, 3, 0], [2, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, -2], [0, -6, 0, 0], [0, 4, 0, -4], [0, -3, 0, 3], [-2, 0, 2, 0], [-4, 0, 0, -4], [0, 0, 0, 0], [3, 0, 0, -3], [2, 2, -2, 0], [0, 0, 8, 0], [0, 4, -4, -4], [2, 0, -2, 0], [2, 0, 0, 2], [0, 0, 0, 0], [-2, 0, 0, 0], [-3, -3, 3, 0], [0, 0, 6, 0], [0, -2, 0, 2], [4, 0, -4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [5, 0, 0, 5], [2, -2, -2, 0], [0, -1, -1, 1], [0, -6, -6, 6], [-8, 0, 8, 0], [4, 0, 0, -4], [0, 0, 0, 0], [-3, 0, 0, 3], [-2, 2, 2, 0], [0, -2, 2, 2], [0, -5, 5, 5], [0, -8, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 6], [6, 0, -6, 0], [0, -3, 3, 3], [0, 4, 0, -4], [9, -9, -9, 0], [8, 0, 0, 8], [0, 0, 0, 0], [0, 0, 0, -8], [-2, 0, 2, 0], [0, 2, -2, -2], [0, 5, 5, -5], [0, 4, 0, 0], [-6, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, -10], [-2, -2, 2, 0], [0, -4, 0, 4], [0, -6, 0, 6], [-3, -3, 3, 0], [6, 0, 0, 6], [0, 0, 0, 0], [-2, 0, 0, 2], [0, 0, 0, 0], [0, 4, -4, -4], [0, 0, -5, 0], [0, 0, 0, 0], [-1, 0, 0, 1], [0, 0, 0, 0], [2, 0, 0, 2], [0, 10, 0, 0], [0, 6, 0, -6], [0, 0, -4, 0], [0, -4, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-12, 0, 0, 0], [-8, 8, 8, 0], [0, -8, 8, 8], [0, 0, 6, 0], [8, 0, -8, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 1], [-6, 0, 6, 0]]}