# Stored data for newform 170.2.g.f, downloaded from the LMFDB on 20 April 2024.
{"label": "170.2.g.f", "space_label": "170.2.g", "level": 170, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518410487267498, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 1768108921736543308, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, -4, 8, -4, 1]], [7, [2, 2, 1]]], "qexp_display": "q+q^{2}+(1-\\zeta_{8}^{2}-\\zeta_{8}^{3})q^{3}+q^{4}+(\\zeta_{8}+\\cdots)q^{5}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 85, "char_orbit_label": "g", "char_is_real": false, "Nk2": 680, "analytic_conductor": 1.3574568343617666, "hecke_ring_index": 1, "level_radical": 170, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.268", "prec": 17}, "analytic_rank_proved": true, "char_values": [170, 4, [137, 71], [2, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5, 17], "conrey_indexes": [89, 149], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "3.865", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "51.729", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1065.624", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c4", "trace_display": [4, 4, 0, -4], "traces": [0, 4, 4, 4, 4, 0, 4, -4, 4, 0, 0, -12, 4, 0, -4, 4, 4, 0, 0, 0, 0, -8, -12, 0, 4, -16, 0, 4, -4, 0, 4, 4, 4, 0, 0, 0, 0, -4, 0, -12, 0, 12, -8, -32, -12, 24, 0, 0, 4, 0, -16, -16, 0, 12, 4, -8, -4, 0, 0, 0, 4, 16, 4, 0, 4, 0, 0, 0, 0, 16, 0, 12, 0, 8, -4, -28, 0, 24, -12, 16, 0, 4, 12, 0, -8, 36, -32, -4, -12, 12, 24, -12, 0, 44, 0, 36, 4, 8, 0, 16, -16, 0, -16, 0, 0, 4, 12, 0, 4, -8, -8, 0, -4, -24, 0, -32, 0, 0, 0, 0, 4, 0, 16, 0, 4, 0, 0, -20, 4, -44, 0, 36, 0, 12, 0, 8, 0, 0, 16, -44, 0, 16, 12, 36, 0, 8, 8, -20, -4, 0, -28, 0, 0, -40, 24, -72, -12, 0, 16, 12, 0, 0, 4, -16, 12, -60, 0, -24, -8, 16, 36, -48, -32, -48, -4, 4, -12, -16, 12, 0, 24, -56, -12, 0, 0, 24, 44, 32, 0, 0, 36, 0, 4, -40, 8, 24, 0, -36, 16, -20, -16, 0, 0, 0, -16, -8, 0, 32, 0, -12, 4, -32, 12, 20, 0, 12, 4, 0, -8, 0, -8, 0, 0, 76, -4, 0, -24, 36, 0, 0, -32, 32, 0, 24, 0, -12, 0, 0, 0, 72, 4, 28, 0, 16, 16, 0, 0, 36, 4, 12, 0, 48, 0, -32, -20, 28, 4, 24, -44, 8, 0, -8, 36, -36, 0, 0, 12, -12, 0, -48, 8, 8, 0, 0, 0, 84, 16, -16, -44, 72, 0, 0, 16, 68, 12, 24, 36, -24, 0, -32, 8, 0, 8, 0, -20, 84, -4, -16, 0, 0, -28, 32, 0, 0, 0, -12, -40, 0, 24, 0, -72, 0, -12, 56, 0, -16, 16, 0, 12, 8, 0, 0, 0, -60, 4, -36, -16, 0, 12, 12, -60, 0, 0, -48, -24, -72, -8, 8, 16, -68, 36, -96, -48, -48, -32, -16, -48, -60, -4, 0, 4, 12, -12, 0, -16, 8, 12, 12, 0, 0, 24, -32, -56, -92, -12, -36, 0, 56, 0, 16, 24, -12, 44, 0, 32, 8, 0, 0, 0, -32, 36, 16, 0, 36, 4, -8, -40, 0, 8, 0, 24, 16, 0, 80, -36, 24, 16, 32, -20, 0, -16, -48, 0, 12, 0, -24, 0, 0, -16, 68, -8, 28, 0, 12, 32, -12, 0, -88, -12, 0, 4, 8, -32, 16, 12, 0, 20, -32, 0, 96, 12, 48, 4, 40, 0, 4, -8, 48, 0, 16, -8, 0, 0, 0, 0, 24, 76, 36, -4, -36, 0, 0, -24, -48, 36, 0, 0, -8, 0, -4, -32, 0, 32, 0, 0, -40, 24, 24, 0, -24, -12, 48, 0, 120, 0, 36, 0, 0, 72, -60, 4, 12, 28, -16, 0, 12, 16, -28, 16, -80, 0, 0, 0, -4, 36, -96, 4, 0, 12, -68, 0, 0, 48, -24, 0, 0, -32, 16, -20, 0, 28, -16, 4, -24, 24, 0, -44, -44, 8, 0, 0, 0, -8, 0, 36, 32, -36, 36, 0, 0, 0, -112, 12, -36, -12, -16, 0, 80, -48, 60, 8, 16, 8, 0, 0, -60, 0, -52, 0, 24, 84, -12, 16, -32, -16, 60, -44, 0, 72, 0, 0, 100, 0, 48, 16, 40, 68, -4, 12, 0, 24, 4, 36, -60, -24, 0, 0, 0, -32, -32, 8, 0, 0, -36, 8, 24, 0, -96, -20, 96, 84, -104, -4, -72, -16, -44, 0, -28, 0, -48, -28, 64, 32, 96, 0, 144, 0, -4, 0, 4, -12, 36, -40, 0, 0, 12, 24, 24, 0, 40, -72, 0, 0, -12, -12, 28, 56, 24, 0, -96, -16, 0, 16, 0, 0, -36, 12, -60, 8, -8, 0, -48, 0, 32, 0, -56, -60, 0, 4, 20, -36, -44, -16, 60, 0, -16, 12, 72, 12, 36, -60, 0, 0, -12, 0, -24, -48, 0, -24, 64, -72, 0, -8, -112, 8, -4, 16, -84, -68, -16, 36, 100, -96, -84, -48, -12, -48, 60, -32, 0, -16, 4, -48, 0, -60, 0, -4, 32, 0, 0, 4, -48, 12, -84, -12, -40, 0, 0, -16, -32, 8, -48, 12, 0, 12, -48, 0, 60, 0, -12, 24, 0, -32, 80, -56, 0, -92, 0, -12, 0, -36, 36, 0, 64, 56, 40, 0, 24, 16, 0, 24, 0, -12, 60, 44, -36, 0, 0, 32, 0, 8, 52, 0, 24, 0, 0, 0, 4, -32, -80, 36, 48, 16, 16, 0, 0, 36, 36, 4, 44, -8, 60, -40, 96, 0, -4, 8, -16, 0, 60, 24, -64, 16, 0, 0, 0, 80, 20, -36, -48, 24, 0, 16, -48, 32, 12, -20, 48, 0, 20, -16, 0, -48, 0, 0, 48, 12, -100, 0, 84, -24, 4, 0, 32, 0, 96, -16, 0, 68, 0, -8, -24, 28, 8, 0, 96, 12, 24, 32, 56, -12, 0, 0, 0, -88, -40, -12, 0, 0, -60, 4, 0, 8, -52, -32, 0, 16, -44, 12, 124, 0, 96, 20, 68, -32, -24, 0, -48, 96, 0, 12, -16, 48, 0, 4, 32, 40, 28, 0, 0, 4, -72, -8, -24, 48, 0, 0, 68, 16, -44, -8, -96, 0, 0, 0, 88, 0, 84, 0, 20, 24, -60, 76, -12, 36, -96, -4, 0, -36, 0, 0, 0, 0, 88, -24, 0, -48, -28, 36, 0, 0, -96, 0, -24, -8, 12, 0, 0, -4, -40, -32, 12, 0, 36, 32, 28, 0, 0, 0, -84, -40, 60, 24, 8, 24, -84, 0, -104, -24, 64, -12, 96, 48, -32, 0, -12, 120, -108, 0, -24, 36, -80, 0, 0, 0, 60, 72, 20, -60, 24, 4, 0, 12, 32, 28, -96, -16, -56, 0, -12, 12, 0, 16, 0, -28, 12, 16, 48, -80, 12, 0, 120, 0, 12, 0, 64, -4, 0, 36, -48, -96, 76, 4, 24, 0, -24, 12, -4, -68, -32, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 85, 10, 1, 4, 0]], "char_orbit_index": 7, "prim_orbit_index": 10, "minimal_twist": "170.2.g.e", "char_is_minimal": true, "conrey_index": 89, "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, 0, 0, 0], [1, 0, -1, -1], [1, 0, 0, 0], [0, 1, 0, 2], [1, 0, -1, -1], [-1, 0, -1, 0], [1, 0, 0, 0], [0, -2, 0, -2], [0, 1, 0, 2], [-3, 0, 3, 2], [1, 0, -1, -1], [0, 0, -3, 0], [-1, 0, -1, 0], [1, 3, 2, 1], [1, 0, 0, 0], [0, -4, 0, -1], [0, -2, 0, -2], [0, -3, 3, -3], [0, 1, 0, 2], [-2, -1, 0, 1], [-3, 0, 3, 2], [0, 4, 0, 0], [1, 0, -1, -1], [-4, 0, -3, 0], [0, 0, -3, 0], [1, -1, 1, 0], [-1, 0, -1, 0], [0, -1, 0, 0], [1, 3, 2, 1], [1, 9, 1, 0], [1, 0, 0, 0], [0, 5, 8, 5], [0, -4, 0, -1], [0, 1, 0, -3], [0, -2, 0, -2], [-1, 0, 1, -6], [0, -3, 3, -3], [-3, -3, -3, 0], [0, 1, 0, 2], [3, 0, -3, 2], [-2, -1, 0, 1], [-8, -3, 0, 3], [-3, 0, 3, 2], [6, 0, 2, 0], [0, 4, 0, 0], [0, 1, 3, 1], [1, 0, -1, -1], [0, 0, -5, 0], [-4, 0, -3, 0], [-4, -5, -1, 3], [0, 0, -3, 0], [3, 0, 0, 0], [1, -1, 1, 0], [-2, -9, -4, -3], [-1, 0, -1, 0], [0, -3, 0, 0], [0, -1, 0, 0], [0, -7, 3, -7], [1, 3, 2, 1], [4, 0, -4, 3], [1, 9, 1, 0], [0, 0, 0, 4], [1, 0, 0, 0], [0, 6, 0, -3], [0, 5, 8, 5], [0, 6, -6, 6], [0, -4, 0, -1], [4, 4, 0, -4], [0, 1, 0, -3], [3, -1, 3, 0], [0, -2, 0, -2], [2, 0, -2, 9], [-1, 0, 1, -6], [-7, -3, 1, 4], [0, -3, 3, -3], [6, 2, 0, -2], [-3, -3, -3, 0], [4, 0, -4, -6], [0, 1, 0, 2], [1, 6, 0, -6], [3, 0, -3, 2], [0, 3, 0, -3], [-2, -1, 0, 1], [9, 0, -2, 0], [-8, -3, 0, 3], [-1, -1, 0, 1], [-3, 0, 3, 2], [3, -6, 0, 6], [6, 0, 2, 0], [-3, 0, 3, 0], [0, 4, 0, 0], [11, 10, 0, -10], [0, 1, 3, 1], [9, -6, 3, 3], [1, 0, -1, -1], [2, 0, -2, -3], [0, 0, -5, 0], [4, 12, 4, 0], [-4, 0, -3, 0]]}