# Stored data for newform 170.2.h.b, downloaded from the LMFDB on 23 April 2024. {"label": "170.2.h.b", "space_label": "170.2.h", "level": 170, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504080697262250, "dim": 8, "is_polredabs": true, "nf_label": "8.0.23045668864.1", "trace_hash": 1518090981518016798, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1156, 136, 8, -52, 101, -4, 0, 0, 1]]], "qexp_display": "q-\\beta _{2}q^{2}-\\beta _{7}q^{3}-q^{4}+\\beta _{4}q^{5}-\\beta _{6}q^{6}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 17, "char_orbit_label": "h", "char_is_real": false, "Nk2": 680, "analytic_conductor": 1.3574568343617666, "hecke_ring_index": 1, "level_radical": 170, "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": "0.250", "prec": 17}, "analytic_rank_proved": true, "char_values": [170, 4, [137, 71], [4, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5, 17], "conrey_indexes": [21, 81], "field_disc": 23045668864, "field_disc_factorization": [[2, 16], [593, 2]], "field_poly": [1156, 0, 892, 0, 237, 0, 26, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.536", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "231.490", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12083.782", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, -4], "traces": [0, 8, 0, 0, -8, 0, 0, -4, 0, 0, 0, 8, 0, -12, -4, 0, 8, -8, -28, 0, 0, 16, 8, -16, 0, 0, 0, 12, 4, 24, 4, 4, 0, 16, 12, 0, 0, -20, 20, -4, 0, 0, 0, 0, -8, -8, -16, 20, 0, 0, -8, 4, 12, 0, 12, -32, 4, 40, -24, 0, 0, -16, -4, -64, -8, -8, 0, -16, 8, 8, 0, 4, 28, 28, 20, 0, 0, 0, 4, 8, 0, -8, 0, 0, -16, 8, 32, 0, -8, -44, -8, -44, 16, 0, 0, 4, 0, 20, 48, -4, 0, 16, -48, -32, 0, 52, -20, -20, -12, -24, 0, 0, -4, -20, 40, -16, -24, 0, -4, -24, -4, 0, -16, 32, -4, 0, 64, 0, 0, 52, 8, 32, -16, 44, 0, 52, -12, -24, 0, -24, 0, -56, -4, 20, 0, 0, -28, -24, 20, 0, 0, 0, -20, 20, -8, 0, 4, 8, 8, 12, 0, 0, 0, 28, 0, -4, -56, 8, 0, -20, 12, 112, 0, 32, -44, -4, 8, -24, 0, 0, 8, 8, -44, 12, 16, 0, 20, 28, -20, 0, 4, 32, 0, 44, -20, 0, 0, -12, 4, -28, 8, -88, 0, -8, -4, 0, 0, -72, -12, -4, -52, 36, 0, 0, 20, -4, -12, 80, -24, 0, 32, 8, 0, 0, -4, -28, -20, 56, -40, 0, 0, -192, 24, -12, 8, -4, 0, -168, 48, -40, 0, 8, 56, 116, 16, 16, 0, 0, 4, 44, 0, -72, 64, 0, -12, 36, 8, 0, 52, 120, 8, -88, -32, 0, 0, -8, -44, 108, 16, 120, 0, 80, -8, -112, 0, 8, -8, 16, 24, 56, 0, 0, 56, -64, -4, -44, 20, 0, -28, -68, -12, 0, -28, -60, -24, -36, -20, 0, 0, 40, 0, 0, 8, -16, 0, 12, 40, 0, 0, -112, 28, -32, -4, -52, 0, 0, -8, 72, 12, 0, 0, 0, 16, 36, 8, 0, 28, -44, 0, -76, 4, 0, 0, 88, -8, -24, 16, 20, 0, -12, -8, 120, 0, 96, -32, 8, -32, -80, 0, 0, 4, -12, 8, -40, -24, 0, 44, -92, -16, 0, 8, -20, 8, 32, 44, 0, 0, 32, -16, -100, -32, -60, 0, -56, -28, 4, 0, -56, -128, -52, -4, 144, 0, 0, 0, 16, 44, 88, -20, 0, 44, 64, -48, 0, -12, 0, 4, 136, 28, 0, 0, -52, 88, -20, -16, -40, 0, -168, 48, 92, 0, 148, 32, -36, 72, -20, 0, 0, 4, 92, -52, -16, 36, 0, 20, 12, 124, 0, 20, 168, -4, -24, 12, 0, 0, 4, 24, 48, -92, -40, 0, 300, -80, -136, 0, 32, -20, 68, 4, -64, 0, 0, 20, -16, 56, -8, -40, 0, -8, -116, 16, 0, -192, -100, 24, -40, 12, 0, 0, -24, 4, -32, 4, -48, 0, 20, 24, -136, 0, -12, 4, -52, -8, -136, 0, 0, -116, -108, 16, 24, 16, 0, -32, 32, -4, 0, 4, 48, 44, 8, 0, 0, 0, 72, -64, 32, 32, 108, 0, 56, -12, 88, 0, -48, 16, 24, -52, 36, 0, 0, -8, -36, -88, 144, -32, 0, -4, 16, 16, 0, -8, -120, -44, -100, -108, 0, 0, 72, -120, 16, -52, -56, 0, 64, 12, -12, 0, -16, 24, 48, -8, 108, 0, 0, -16, -60, 24, 36, 56, 0, 0, 4, -20, 0, 56, -44, -64, 236, 4, 0, 0, -48, -20, 36, 200, -16, 0, -40, -68, -184, 0, 56, 252, -12, 28, 32, 0, 0, 24, -80, -36, -192, -20, 0, -184, 52, 0, 0, 40, 40, 0, -116, 0, 0, 0, -64, 16, 4, 20, 76, 0, 44, -20, 36, 0, 100, 8, 124, 112, 52, 0, 0, 32, 204, -4, -8, -52, 0, -8, 72, 24, 0, -8, 112, 72, -4, -12, 0, 0, 32, 0, -124, 24, -36, 0, 0, 20, 84, 0, -140, 12, -140, -28, 4, 0, 0, 0, 12, -76, 100, 4, 0, 60, -104, 56, 0, 88, -120, -8, 96, 24, 0, 0, 44, -20, 12, 20, -84, 0, -200, -12, 204, 0, -128, -112, -28, -96, -116, 0, 0, -8, 128, -32, -32, -80, 0, 44, -68, 24, 0, 4, -88, -12, -68, -8, 0, 0, -8, 24, 16, 20, -40, 0, 40, 188, 32, 0, 20, -88, 76, -8, -16, 0, 0, -8, -24, 32, -44, 44, 0, 52, -4, -12, 0, 32, -124, -16, 80, 100, 0, 0, -40, 60, 28, -20, -36, 0, -152, -28, -80, 0, 52, 20, -128, 56, 0, 0, 0, 52, -24, -4, -56, 144, 0, -32, 104, -108, 0, 0, 60, 16, -228, -44, 0, 0, -4, 20, 152, -104, 68, 0, 88, -24, 84, 0, 96, -40, -144, 12, -104, 0, 0, -4, 104, 136, 60, 28, 0, 8, -76, -8, 0, -52, 264, 88, 8, 20, 0, 0, 72, 40, -8, 8, 272, 0, 48, 4, -160, 0, -96, 0, 0, -148, 16, 0, 0, 36, -156, 72, -24, -20, 0, 12, -28, -224, 0, 4, -220, 92, 84, 52, 0, 0, -36, -36, 32, -128, 28, 0, -36, 8, 16, 0, 4, -168, -8, -20, 20, 0, 0, 4, -32, -24, -112, 12, 0, 136, -16, -80, 0, 4, 104, 24, -132, -48, 0, 0, 52, 40, -12, -32, 52, 0, 144, -8, 36, 0, -132, 0, -4, -32, 152, 0, 0, -68, -8, 4, 104, -64, 0, 28, 8, 0, 0, 20, 8, -16, 48, -56, 0, 0, -48, 40, -24, -56, -84, 0, -200, 0, 24, 0, 156, 128, -12, 192, 20, 0, 0, -24, -8, -40, -204, 12, 0, -112, 28, -8, 0, -24, 168, 4, -24, 32, 0, 0, -92, 48, 32, 168, -48, 0, 64, -48, 136, 0, -36, 40, 60, 12, -40, 0, 0, 52, 4, -8, 64, -136, 0, -56, 92, 28, 0, -116, 88, -108, 4, -16, 0, 0, -172, -16, -88, 36, -20, 0, -48, 36, 104, 0, 56, 96, 228, -4, 168, 0, 0, -44, 36, 8, 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, 17, 3, 1, 4, 0]], "char_orbit_index": 8, "prim_orbit_index": 3, "minimal_twist": "170.2.h.b", "char_is_minimal": true, "conrey_index": 21, "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, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [-1, 1, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 1, -3, -1, 1, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [1, 0, 1, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [-1, 0, 0, -1, -1, -1, 0, 0], [-1, -1, 0, 0, 0, 1, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, 1, -1, 0, 0, -1], [-4, 0, 0, -1, -1, 1, 0, 0], [0, -1, 2, 1, -1, 0, 1, 1], [0, 0, 0, 0, -1, 0, 0, 0], [2, 0, 0, 6, 6, 0, -1, 1], [1, 0, -1, 0, -4, 0, 0, 0], [-2, 0, -2, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 1, 2, 1, -1, 0, 0, 0], [2, -1, 1, 6, 0, -1, -1, 0], [1, -1, 0, 0, 0, -1, 0, 0], [3, 0, -3, 0, 2, 0, 0, -1], [1, 0, 0, 0, 0, -1, 0, 0], [0, -1, -1, 0, -4, 1, 0, 1], [0, 0, -1, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, -4, 1, -1], [1, 0, 1, 1, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 1, -1], [0, -1, 3, 1, -1, 0, 0, 0], [-3, -1, 2, 0, 4, 1, 0, 0], [3, 0, 0, 1, 1, -1, 1, -1], [0, 1, 1, 0, -6, -1, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0], [-1, 2, 1, 0, 0, 2, 0, 0], [0, 0, -2, -6, 6, 0, 1, 1], [0, 0, 4, 0, 0, 0, 1, 1], [-1, 0, -1, 4, 0, 0, 0, 0], [-1, 0, -1, -3, 0, 0, 1, 0], [-2, 0, 2, 0, -2, 0, 0, 0], [3, 0, 0, -1, -1, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, -1], [0, -2, 5, 2, -2, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 2, -5, 5, 1, 1, 1, 1], [1, 0, 0, 1, 1, 1, 0, 0], [0, 1, -2, -1, 1, 0, 0, 0], [2, 1, -1, 0, 6, -1, 0, 1], [-4, 0, 0, 1, 1, 0, 0, 0], [1, 1, 0, 0, 0, -1, 0, 0], [5, 0, 5, -4, 0, 0, 3, 0], [-3, 0, -3, -2, 0, 0, -1, 0], [0, 1, 0, -5, 5, 0, -1, -1], [0, 1, 0, 0, 0, 0, 0, 0], [-1, -2, -3, 2, 0, -2, 1, 0], [0, -1, -1, 4, 0, -1, 1, 0], [-10, -4, 6, 0, -2, 4, 0, -2], [-1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, -2, 0, 0, 1], [0, 4, 0, 0, 0, 0, -1, -1], [-2, 0, 0, -4, -4, 0, -2, 2], [1, -1, -2, -1, 1, 0, 0, 1], [2, 0, 0, 0, 0, -2, -2, 2], [0, 0, 0, 0, 0, 0, -1, -1], [0, -1, -1, 0, -4, 1, 0, 3], [4, 0, 0, 1, 1, -1, 0, 0], [3, -1, -4, 0, -6, 1, 0, -1], [3, -1, 2, -4, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 1, -2, -1, 1, 0, -1, -1], [0, 2, 0, 0, 0, 0, -4, -4], [0, 1, 1, 6, 0, 1, 1, 0], [0, 2, 2, -2, 0, 2, -4, 0], [0, 0, 0, 0, 1, 0, 0, 0], [-3, 0, 0, -4, -4, 4, 2, -2], [-1, -2, -1, 0, 0, 2, 0, 0], [0, -2, -8, -2, 2, 0, 1, 1], [-2, 0, 0, -6, -6, 0, 1, -1], [1, -1, 1, 2, -1, 0, 1, 0], [4, 0, 0, 0, 0, 0, 1, -1], [0, -1, -6, -1, 1, 0, -3, -3], [-1, 0, 1, 0, 4, 0, 0, 0], [-7, 0, 0, 5, 5, 3, 2, -2], [-1, 0, 1, 0, -3, 0, 0, -1], [-5, -1, -6, -2, 0, -1, -2, 0], [2, 0, 2, 2, 0, 0, 0, 0], [0, 3, 4, -5, 5, 0, 0, 0], [0, 1, -2, 1, -1, 0, 1, 1], [0, 1, 1, 2, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, -1, 0], [3, 1, -2, 0, -6, -1, 0, 5], [7, 0, 0, 2, 2, -2, 0, 0], [0, 1, 1, 0, -10, -1, 0, -4], [0, 0, 1, 0, 0, 0, 0, 0]]}