# Stored data for newform 784.2.x.i, downloaded from the LMFDB on 24 April 2024. {"label": "784.2.x.i", "space_label": "784.2.x", "level": 784, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36030377600484112, "dim": 8, "is_polredabs": true, "nf_label": "8.0.49787136.1", "trace_hash": 501172896219366178, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [0, 1]], [5, [0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(-1-\\beta _{2}+\\beta _{4}+\\beta _{6})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": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.692", "prec": 17}, "analytic_rank_proved": true, "char_values": [784, 12, [687, 197, 689], [12, 3, 8]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 8, "level_primes": [2, 7], "conrey_indexes": [165, 373, 557, 765], "field_disc": 49787136, "field_disc_factorization": [[2, 8], [3, 4], [7, 4]], "field_poly": [16, 0, 12, 0, 5, 0, 3, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.349", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "602.671", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "92422.847", "prec": 30}], "related_objects": [], "self_twist_discs": [-7], "cm_discs": [-7], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.1.d12", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, -6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -48, 26, 0, 0, 0, 0, 0, 20, 0, 0, 20, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, -36, 0, 0, -8, 0, 0, 0, 0, 30, 0, -22, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 2, 0, -34, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 76, 40, 0, -36, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -20, -44, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, -92, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 30, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 58, 0, -34, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 120, -112, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 128, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 62, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 40, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, 68, 0, 0, 0, 0, 0, 0, 2, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, -128, 0, 0, 0, 0, 54, 0, -62, 0, 0, 0, 0, 72, 0, 36, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 92, 0, 0, -8, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 48, 0, 0, 140, 0, 0, 0, -224, -72, 0, -76, 0, 0, 0, 0, 54, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, -104, 82, 0, -78, 0, 0, 0, -148, 0, 0, 128, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, -28, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, -128, 0, 0, 20, 0, 0, 0, 0, 0, 0, -62, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -176, -112, 0, -50, 0, 0, 0, 148, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 48, 28, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 84, 0, -6, 0, 0, 0, -280, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 204, -100, 0, 0, 0, 0, 0, 176, 0, 0, -50, 0, 0, 0, -204, -112, 0, 0, 0, 0, 0, -240, 112, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 188, 0, 0, 0, 0, 0, 0, 8, 0, 0, 34, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, -76, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -136, 0, -104, 0, 0, 0, 0, 0, 0, -106, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -216, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -78, 0, 0, 0, -20, 0, 0, 128, 0, 0, 0, 0, 0, 0, -106, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -110, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58, 0, 106, 0, 0, 0, -188, 0, 0, 112, 0, 0, 0, 0, -114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, -62, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, -48, 0, 0, -78, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, 224, 0, 0, 120, 0, 0, 0, 128, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, -84, 0, 50, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 40, 0, 0, 0, 0, 0, 0, 54, 0, -96, 0, 0, 0, 0, 124, 0, -120, 0, 0, 0, 0, 110, 0, 0, 0, 0, 0, 0, 0, 0, -184, 0, 0, 0, 216, 30, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, -34, 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, 2, -1, 2, -7], [1, 1, 7, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 16, 5, 1, 4, 0], [1, 1, 112, 12, -1, 4, 0], [1, 1, 112, 23, 1, 12, 0], [1, 1, 112, 24, -1, 12, 0]], "char_orbit_index": 24, "prim_orbit_index": 23, "minimal_twist": "784.2.m.f", "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 2, 0, 1], [0, 0, 0, -3, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -2, -1, -3, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -3, 0, -3, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 3, 0, 3, 0, 4, 1, -3], [0, 0, 4, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 0, -4, 0, -1, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 6, 0, -3], [0, 4, 4, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 2, 0, 2, 0, -5, 2, -2], [0, 5, 1, 2, 7, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, -4, -3, -7, 0, 4, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 8, -5, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, 0, 0, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 6, 1, 5, 0, -6, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -16, 0, 0], [0, 0, 3, 0, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -5, 9, 3, 0, 5, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -12, 0, -6, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, -9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, -7, 4, -3, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, -3, -5, 7, 0, 3, 7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-10, 0, 0, 0, 0, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 6, 0, 6, 0, -3, -6, -6], [0, 5, 0, 10, 0, 10, 0, 0]]}