# Stored data for newform 1170.2.e.g, downloaded from the LMFDB on 25 April 2024. {"label": "1170.2.e.g", "space_label": "1170.2.e", "level": 1170, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021872675685522, "dim": 6, "is_polredabs": true, "nf_label": "6.0.350464.1", "trace_hash": 1597768334733300281, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [16, 0, 32, 0, 16, 0, 1]], [11, [2, 1]]], "qexp_display": "q-\\beta _{4}q^{2}-q^{4}+(-\\beta _{2}+\\beta _{5})q^{5}+(-\\beta _{1}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "e", "char_is_real": true, "Nk2": 4680, "analytic_conductor": 9.342497036489805, "hecke_ring_index": 4, "level_radical": 390, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [1170, 2, [911, 937, 1081], [2, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 13], "conrey_indexes": [469], "field_disc": -350464, "field_disc_factorization": [[-1, 1], [2, 8], [37, 2]], "field_poly": [2, -4, 4, 2, 2, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.055", "prec": 17}, {"__RealLiteral__": 0, "data": "5.483", "prec": 17}, {"__RealLiteral__": 0, "data": "0.686", "prec": 17}, {"__RealLiteral__": 0, "data": "168.670", "prec": 24}, {"__RealLiteral__": 0, "data": "102.543", "prec": 24}, {"__RealLiteral__": 0, "data": "8074.326", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 6, 0, 0, -6, 0, 0, 0, 0, 0, 2, -12, 0, 0, 8, 0, 6, 0, 0, -4, 0, 0, 0, 0, 0, 2, -6, 0, 0, 20, 0, -12, 0, 0, -8, -12, 0, 0, 0, 0, -2, -28, 0, 0, 12, 0, 0, 0, 0, 10, -8, 0, 0, 0, 0, 0, -8, 0, 0, 28, 0, -4, 0, 0, -6, 2, 0, 0, 0, 0, 12, -8, 0, 0, 20, 0, 4, 0, 0, 16, 0, 0, 0, 0, 0, 4, 0, 0, 0, 44, 0, 8, 0, 0, 8, -20, 0, 0, 0, 0, -2, -44, 0, 0, 6, 0, 0, 0, 0, 12, -4, 0, 0, 0, 0, -44, -20, 0, 0, 56, 0, -42, 0, 0, 12, -48, 0, 0, 0, 0, 0, -28, 0, 0, 12, 0, 8, 0, 0, 16, 12, 0, 0, 0, 0, 4, 24, 0, 0, 72, 0, 4, 0, 0, -16, -32, 0, 0, 0, 0, 2, -16, 0, 0, 28, 0, -8, 0, 0, -6, -44, 0, 0, 0, 0, -8, -12, 0, 0, 76, 0, 12, 0, 0, 0, -60, 0, 0, 0, 0, 16, -32, 0, 0, 56, 0, -10, 0, 0, 8, 8, 0, 0, 0, 0, 8, 20, 0, 0, 8, 0, 24, 0, 0, -24, -80, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, -24, 0, 0, -20, -28, 0, 0, 0, 0, 16, -28, 0, 0, 88, 0, 60, 0, 0, 4, -16, 0, 0, 0, 0, -26, 36, 0, 0, -12, 0, 6, 0, 0, -64, -2, 0, 0, 0, 0, 64, -8, 0, 0, 52, 0, 28, 0, 0, 60, -4, 0, 0, 0, 0, -12, -20, 0, 0, 8, 0, 12, 0, 0, -42, -56, 0, 0, 0, 0, -40, -20, 0, 0, 0, 0, -56, 0, 0, -4, -88, 0, 0, 0, 0, 4, 0, 0, 0, 20, 0, -16, 0, 0, -40, 0, 0, 0, 0, 0, -8, 28, 0, 0, 32, 0, 92, 0, 0, 0, -20, 0, 0, 0, 0, -4, 24, 0, 0, 0, 0, 24, 0, 0, 76, -40, 0, 0, 0, 0, 48, -44, 0, 0, 32, 0, -74, 0, 0, -8, -36, 0, 0, 0, 0, -16, 104, 0, 0, 16, 0, -8, 0, 0, -44, 20, 0, 0, 0, 0, 24, 24, 0, 0, 20, 0, -40, 0, 0, 28, -64, 0, 0, 0, 0, 2, -124, 0, 0, 44, 0, -32, 0, 0, -44, -36, 0, 0, 0, 0, -8, -6, 0, 0, 84, 0, -92, 0, 0, 0, -8, 0, 0, 0, 0, -24, -16, 0, 0, -40, 0, -12, 0, 0, 56, 4, 0, 0, 0, 0, 40, 8, 0, 0, 28, 0, 56, 0, 0, -8, 12, 0, 0, 0, 0, 44, 32, 0, 0, 20, 0, 40, 0, 0, 32, -24, 0, 0, 0, 0, 4, -56, 0, 0, 72, 0, 20, 0, 0, 42, -28, 0, 0, 0, 0, -42, -84, 0, 0, 4, 0, -12, 0, 0, 84, 48, 0, 0, 0, 0, -76, 0, 0, 0, -8, 0, -96, 0, 0, 64, 76, 0, 0, 0, 0, 0, 136, 0, 0, 28, 0, 64, 0, 0, -22, -40, 0, 0, 0, 0, -64, -12, 0, 0, -20, 0, 60, 0, 0, -8, 36, 0, 0, 0, 0, 16, -80, 0, 0, 60, 0, -16, 0, 0, 0, -12, 0, 0, 0, 0, -44, 96, 0, 0, 8, 0, 24, 0, 0, -56, -88, 0, 0, 0, 0, -4, -56, 0, 0, -24, 0, -36, 0, 0, 48, 44, 0, 0, 0, 0, 16, -72, 0, 0, 16, 0, -84, 0, 0, -4, 0, 0, 0, 0, 0, -4, 8, 0, 0, -124, 0, 16, 0, 0, 36, 32, 0, 0, 0, 0, 22, 8, 0, 0, 32, 0, 108, 0, 0, -68, 68, 0, 0, 0, 0, -2, -8, 0, 0, 16, 0, 48, 0, 0, -56, -2, 0, 0, 0, 0, 84, -28, 0, 0, -28, 0, 44, 0, 0, 8, -24, 0, 0, 0, 0, -64, 8, 0, 0, -32, 0, 6, 0, 0, -96, 44, 0, 0, 0, 0, -92, 8, 0, 0, 0, 0, 36, 0, 0, -16, 80, 0, 0, 0, 0, 8, 20, 0, 0, 12, 0, -84, 0, 0, -100, -64, 0, 0, 0, 0, -4, -76, 0, 0, -8, 0, 120, 0, 0, -12, 124, 0, 0, 0, 0, 36, 8, 0, 0, -76, 0, 0, 0, 0, 36, 60, 0, 0, 0, 0, 96, 84, 0, 0, -48, 0, -152, 0, 0, -20, -8, 0, 0, 0, 0, -16, -68, 0, 0, 32, 0, -40, 0, 0, 20, -24, 0, 0, 0, 0, 44, -56, 0, 0, -16, 0, 16, 0, 0, 10, 52, 0, 0, 0, 0, 120, 40, 0, 0, 4, 0, -8, 0, 0, -80, -8, 0, 0, 0, 0, 0, 12, 0, 0, -96, 0, -148, 0, 0, -40, 76, 0, 0, 0, 0, -8, 16, 0, 0, -20, 0, 32, 0, 0, 164, 56, 0, 0, 0, 0, 16, -8, 0, 0, -208, 0, 202, 0, 0, -24, 0, 0, 0, 0, 0, 88, -176, 0, 0, -96, 0, 24, 0, 0, 40, 80, 0, 0, 0, 0, -16, 16, 0, 0, -32, 0, 12, 0, 0, 72, 92, 0, 0, 0, 0, 0, 128, 0, 0, 8, 0, 40, 0, 0, 120, -20, 0, 0, 0, 0, -76, -8, 0, 0, -48, 0, -184, 0, 0, 24, 120, 0, 0, 0, 0, 12, 56, 0, 0, 32, 0, 20, 0, 0, -40, 28, 0, 0, 0, 0, -80, 104, 0, 0, -28, 0, -36, 0, 0, -96, -8, 0, 0, 0, 0, -16, -120, 0, 0, 28, 0, 0, 0, 0, 24, 40, 0, 0, 0, 0, -104, -88, 0, 0, -160, 0, -98, 0, 0, -60, 20, 0, 0, 0, 0, 12, 204, 0, 0, -48, 0, -4, 0, 0, -88, 16, 0, 0, 0, 0, 28, 24, 0, 0, -264, 0, 40, 0, 0, -24, 64, 0, 0, 0, 0, 26, -16, 0, 0, -36, 0, -56, 0, 0, -44, -8, 0, 0, 0, 0, 144, 12, 0, 0, -20, 0, 108, 0, 0, -6, 28, 0, 0, 0, 0, -64, -104, 0, 0, -16, 0, 64, 0, 0, 32, 2, 0, 0, 0, 0, 40, 144, 0, 0, -24, 0, 52, 0, 0, 104, 136, 0, 0, 0, 0, -64, 104, 0, 0, 8, 0, 28, 0, 0, 60, 8, 0, 0, 0, 0, -160, -52, 0, 0, -8, 0, 32, 0, 0, -28, 32, 0, 0, 0, 0, 32, 100, 0, 0, -8, 0, -60, 0, 0, -104, 4, 0, 0, 0, 0, -44, 72, 0, 0, -228, 0, 88, 0, 0, -68, -60, 0, 0, 0, 0, 12, 56, 0, 0, 20, 0, -8, 0, 0, -20, -60, 0, 0, 0, 0, 88, -8, 0, 0, -160, 0, -96, 0, 0, -12, 68, 0, 0, 0, 0, -32, 136, 0, 0, -24, 0, 42, 0, 0, 88, 56, 0, 0, 0, 0, -100, 0, 0, 0, -48, 0, -120, 0, 0, 136, 48, 0, 0, 0, 0, 40, -8, 0, 0, 20, 0, -92, 0, 0, 32, 64, 0, 0, 0, 0, 16, 0, 0, 0, -24, 0, -124, 0, 0, 56, -56, 0, 0, 0, 0, -14, -8, 0, 0, -180, 0, 4, 0, 0, 152, 88, 0, 0, 0, 0, 126, 28, 0, 0, 48, 0, 112, 0, 0, 44, 16, 0, 0, 0, 0, -4, 168, 0, 0, 0, 0, 64, 0, 0, -100, -80, 0, 0, 0, 0, 44, -20, 0, 0, -260, 0, 56, 0, 0, 16, 88, 0, 0, 0, 0, -40, 40, 0, 0, -10, 0, 40, 0, 0, 172, 0, 0, 0, 0, 0, -108, 148, 0, 0, -164, 0, -160, 0, 0, 160, -40, 0, 0, 0, 0, 8, -20, 0, 0, -28, 0, 40, 0, 0, -112, 56, 0, 0, 0, 0, -68, -32, 0, 0, -40, 0, 36, 0, 0, -92, 128, 0, 0, 0, 0, -8, 216, 0, 0, -192, 0, 0, 0, 0, 20, 20, 0, 0, 0, 0, -84, 64, 0, 0, -104, 0, 32, 0, 0, -112, 184, 0, 0, 0, 0, 4, 80, 0, 0, -24, 0, -56, 0, 0, -58, 8, 0, 0, 0, 0, 96, 0, 0, 0, 48, 0, 36, 0, 0, -24, 28, 0, 0, 0, 0, -64, -24, 0, 0, 40, 0, -76, 0, 0, 36, 40, 0, 0, 0, 0, 72, 56, 0, 0, -156, 0, 168, 0, 0, -128, -96, 0, 0, 0, 0, -48, 276, 0, 0, 44, 0, 56, 0, 0, -36, 0, 0, 0, 0, 0, 128, -32, 0, 0, -208, 0, 56, 0, 0, 74, 32, 0, 0, 0, 0, -152, 4, 0, 0, -20, 0, 8, 0, 0, -152, 36, 0, 0, 0, 0, -4, 52, 0, 0, -24, 0, 20, 0, 0, -24, 20, 0, 0, 0, 0, 16, -248, 0, 0, -104, 0, -112, 0, 0, -188, 0, 0, 0, 0, 0, -28, -16, 0, 0, 20, 0, 168, 0, 0, 8, 0, 0, 0, 0, 0, 28, 112, 0, 0, -44, 0, 44, 0, 0, 12, -20, 0, 0, 0, 0, 180, 80, 0, 0, -32, 0, -240, 0, 0, -28, 92, 0, 0, 0, 0, -24, -112, 0, 0, -24, 0, 36, 0, 0, 4, 32, 0, 0, 0, 0, -8, -20, 0, 0, -272, 0, 112, 0, 0, 40, 64, 0, 0, 0, 0, 136, 212, 0, 0, -148, 0, -28, 0, 0, -76, 64, 0, 0, 0, 0, -36, 4, 0, 0, -48, 0, -320, 0, 0, -48, -8, 0, 0, 0, 0, -2, 84, 0, 0, 124, 0, -48, 0, 0, 52, -104, 0, 0, 0, 0, 64, -44, 0, 0, -28, 0, 140, 0, 0, 32, -26, 0, 0, 0, 0, 144, -40, 0, 0, 104, 0, 44, 0, 0, -144, 36, 0, 0, 0, 0, -16, 188, 0, 0, 120, 0, -12, 0, 0, 232, -92, 0, 0, 0, 0, 8, -8, 0, 0, 6, 0, 80, 0, 0, 116, 64, 0, 0, 0, 0, -16, -84, 0, 0, -48, 0, -62, 0, 0, 92, 16, 0, 0, 0, 0, -2, -104, 0, 0, -56, 0, 0, 0, 0, -72, 8, 0, 0, 0, 0, 64, -116, 0, 0, -80, 0, -40, 0, 0, -192, 48, 0, 0, 0, 0, 24, 212, 0, 0, 16, 0, -16, 0, 0, -8, -32, 0, 0, 0, 0, -104, 40, 0, 0, 48, 0, -44, 0, 0, 12, -12, 0, 0, 0, 0, -52, -248, 0, 0, 44, 0, -56, 0, 0, 152, -4, 0, 0, 0, 0, -44, 32, 0, 0, 88, 0, 32, 0, 0, 88, 24, 0, 0, 0, 0, -40, 60, 0, 0, -8, 0, 0, 0, 0, 108, 32, 0, 0, 0, 0, 144, -28, 0, 0, -72, 0, 212, 0, 0, -56, 48, 0, 0, 0, 0, -100, -92, 0, 0, -184, 0, 8, 0, 0, 64, -12, 0, 0, 0, 0, -24, 16, 0, 0, 24, 0, 108, 0, 0, 112, -124, 0, 0, 0, 0, -44, -192, 0, 0, -32, 0, 8, 0, 0, -222, -68, 0, 0, 0, 0, 0, -20, 0, 0, 12, 0, -132, 0, 0, -40, 36, 0, 0, 0, 0, 88, 200, 0, 0, 104, 0, -32, 0, 0, -132, 24, 0, 0, 0, 0, -56, -88, 0, 0, -168, 0, 184, 0, 0, -40, 132, 0, 0, 0, 0, -4, -180, 0, 0, 56, 0, -88, 0, 0, 24, 40, 0, 0, 0, 0, 104, -72, 0, 0, 112, 0, -160, 0, 0, -20, 16, 0, 0, 0, 0, -36, -156, 0, 0, -176, 0, -42, 0, 0, 72, 28, 0, 0, 0, 0, -52, 32, 0, 0, 188, 0, -56, 0, 0, 52, -32, 0, 0, 0, 0, 42, 256, 0, 0, 84, 0, -48, 0, 0, -152, -48, 0, 0, 0, 0, -96, -4, 0, 0, 36, 0, -232, 0, 0, 12, 156, 0, 0, 0, 0, -112, -24, 0, 0, 156, 0, -84, 0, 0, 96, -48], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "1170.2.e.g", "char_is_minimal": true, "conrey_index": 469, "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], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0], [-2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 3, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, 0, -1], [0, 0, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0], [0, 1, 0, -2, -1, 2], [0, 0, 0, 0, 0, 0], [1, 0, 2, -1, -2, 1], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, -1, 0], [5, 0, 1, 2, 0, 2], [0, 0, 0, 0, 0, 0], [-2, 0, 2, -1, 0, -1], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 3, -1, 0, -1], [-1, 0, 1, 1, 2, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 2, 2], [0, -1, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, 0], [-4, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, -3, -2, 3], [2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 1, -2, 0, -2], [0, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0], [3, 0, 2, 1, 0, 1], [-2, -2, 0, -1, -1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 4, 0, 1, 2, -1], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, -2], [-1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, -2, -5, 2], [4, 0, 2, -2, 0, -2], [0, 0, 0, 0, 0, 0], [0, 0, 6, -2, 0, -2], [0, -2, 0, 1, 2, -1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 4, 0, -2, 2, 2], [0, -3, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0], [2, -1, 0, -1, 1, 1], [0, 0, -2, 3, 0, 3], [0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 3, 0], [2, 0, 0, -2, 0, -2], [0, 0, 0, 0, 0, 0], [1, 0, -1, 1, 0, 1], [0, 2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, -5, 0, -5], [0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 4, 1], [0, -4, 0, 1, -2, -1], [0, 0, 0, 0, 0, 0], [-1, -2, -1, -2, -8, -2], [-2, 0, 0, -3, 0, -3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0], [8, 0, -2, 2, 0, 2], [0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0], [0, -1, 0, 2, 1, -2], [0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 0], [-4, -1, 0, 0, 3, -2], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 9, 0], [0, -2, 0, -1, -3, 1], [0, 0, 0, 0, 0, 0], [-1, 0, -2, 1, 2, -1]]}