# Stored data for newform 170.2.d.c, downloaded from the LMFDB on 16 April 2024.
{"label": "170.2.d.c", "space_label": "170.2.d", "level": 170, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007405446725802, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 1275892196604968439, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-8, 0, 1]]], "qexp_display": "q+\\zeta_{8}^{2}q^{2}+(-2\\zeta_{8}+2\\zeta_{8}^{3})q^{3}-q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 85, "char_orbit_label": "d", "char_is_real": true, "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": "0.768", "prec": 17}, "analytic_rank_proved": true, "char_values": [170, 2, [137, 71], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 5, 17], "conrey_indexes": [169], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.808", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "124.718", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5178.417", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -4, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 8, 4, 0, 0, 8, 0, -48, 0, 0, 0, -16, 24, 0, 0, 0, -24, 0, 0, 0, 12, -12, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, -12, 32, 0, 0, 0, 0, 0, 0, 0, -48, -8, 0, 0, 0, -4, 0, 0, 0, 0, -16, 36, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 4, 0, 0, 48, 8, -24, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 24, 0, 0, -24, 0, 24, 0, 0, 0, 0, -48, 0, 0, 0, -4, 0, 0, 0, -48, 24, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 16, -12, 0, 0, 0, 12, 0, 0, 0, 20, -36, 0, 0, 0, 24, 0, -32, 0, 0, 0, -36, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -24, 0, 0, -92, -24, 40, 0, 0, -48, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -12, -48, 0, 0, -96, 0, 96, 0, 0, 0, 144, -44, 0, 0, 0, 12, 0, 0, 0, -32, 72, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, -72, 0, 0, 0, -80, 0, 0, 0, 56, 12, 0, 0, 0, 120, 0, 48, 0, 0, 0, 8, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 24, 0, 0, 0, 72, 4, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, -80, 0, 0, -48, 0, 16, 0, 0, 0, -36, 48, 0, 0, 0, 16, 0, 0, 0, -4, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -36, 60, 0, 0, 0, -12, 0, 0, 0, -72, -60, 0, 0, 0, 0, 0, -64, 0, 0, -4, 72, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, -48, 0, 0, 160, -8, 0, 0, 0, 24, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -36, -48, 0, 0, 48, 0, -60, 0, 0, 0, -24, -48, 0, 0, 0, 36, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 48, -16, 0, 0, 0, 36, 0, 0, 0, -96, -16, 0, 0, 0, -24, 0, 72, 0, 0, -128, 24, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -104, 0, 0, -24, 36, -48, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 220, 0, 0, 48, 0, -48, 0, 0, 0, -60, 0, 0, 0, 0, -216, 0, 0, 0, 64, 4, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, -32, 48, 0, 0, 0, -24, 0, 0, 0, -44, 0, 0, 0, 0, 96, 0, 120, 0, 0, 48, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -24, 24, 144, 0, 0, 96, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 192, 0, 0, 0, -84, 0, -240, 0, 0, 0, -16, 48, 0, 0, 0, -16, 0, 0, 0, 12, -36, -288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, -12, 0, 0, 0, 0, 40, 0, 0, 0, -24, -48, 0, 0, 0, -144, 0, -20, 0, 0, 0, 36, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 80, 0, 0, 0, -108, -24, 0, 0, -144, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -12, 0, 0, 0, 120, 0, 0, 0, 0, 0, 36, -32, 0, 0, 0, 28, 0, 0, 0, -48, 180, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -144, 24, 0, 0, 0, -96, 0, 0, 0, -48, 144, 0, 0, 0, -48, 0, -88, 0, 0, 24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 24, -32, 0, 0, -40, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 48, 0, 0, -224, 0, -24, 0, 0, 0, 0, 72, 0, 0, 0, -12, 0, 0, 0, -144, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -172, 72, 72, 0, 0, 0, 88, 0, 0, 0, 136, 12, 0, 0, 0, 48, 0, 24, 0, 0, 96, 72, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, -24, 0, 0, -96, 40, -96, 0, 0, 56, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -144, 0, 0, 0, 44, 0, 192, 0, 0, 0, 12, -240, 0, 0, 0, 144, 0, 0, 0, 0, -12, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 32, 0, 0, 0, -72, 0, 0, 0, -48, 0, 0, 0, 0, 152, 0, -240, 0, 0, 0, -4, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, -48, 24, 0, 0, 72, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 44, -24, 0, 0, 0, 0, 288, 0, 0, 0, 156, 96, 0, 0, 0, 0, 0, 0, 0, 72, -96, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 80, -72, 0, 0, 0, 180, 0, 0, 0, 120, -72, 0, 0, 0, -72, 0, -56, 0, 0, -224, -12, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 88, 0, 0, 48, 0, -120, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -24, -176, 0, 0, 120, 0, 0, 0, 0, 0, -8, 52, 0, 0, 0, 0, 0, 0, 0, 64, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 20, -48, 0, 0, 0, 0, 0, 0, 0, 72, -108, 0, 0, 0, -96, 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, 5, 2, 1, 2, 0], [1, 1, 17, 2, 1, 2, 0], [1, 1, 85, 3, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 3, "minimal_twist": "170.2.d.c", "char_is_minimal": true, "conrey_index": 169, "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], [0, 0, 1, 0], [0, -2, 0, 2], [-1, 0, 0, 0], [0, -2, 0, -1], [0, -2, 0, -2], [0, 3, 0, -3], [0, 0, -1, 0], [5, 0, 0, 0], [0, 1, 0, -2], [0, 0, 0, 0], [0, 2, 0, -2], [0, 0, -6, 0], [0, 3, 0, 3], [2, 0, 6, 0], [1, 0, 0, 0], [0, -2, -3, 2], [0, 0, 5, 0], [2, 0, 0, 0], [0, 2, 0, 1], [-12, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, 2, 0, 2], [-4, 0, 3, 0], [6, 0, 0, 0], [0, -4, 0, 4], [0, -3, 0, 3], [0, -3, 0, -3], [-6, 0, 2, 0], [0, -3, 0, -3], [0, 0, 1, 0], [0, 0, 0, 0], [3, -2, 0, -2], [-3, 0, -9, 0], [-5, 0, 0, 0], [0, 3, 0, -3], [0, 0, 2, 0], [0, 12, 0, 12], [0, -1, 0, 2], [0, 6, 0, 6], [0, 0, -12, 0], [0, 0, 6, 0], [0, 0, 0, 0], [0, -10, 0, -5], [0, 1, 0, 1], [0, 0, 0, 0], [0, -2, 0, 2], [11, 0, 0, 0], [-3, 0, -4, 0], [8, 6, 0, 6], [0, 0, 6, 0], [0, 0, -6, 0], [0, -4, 0, -4], [0, 0, 0, 0], [0, -3, 0, -3], [0, -4, 0, 4], [0, 3, 0, -3], [-12, 0, 0, 0], [-2, 0, -6, 0], [0, -3, 0, -3], [0, 3, 0, -3], [0, 15, 0, -15], [-1, 0, 0, 0], [0, -6, 0, 12], [0, 0, 0, 0], [0, 0, 12, 0], [0, 2, 3, -2], [-4, 0, 0, 0], [9, 0, -3, 0], [0, -3, 0, -3], [0, 0, -5, 0], [0, 6, 0, -6], [0, 3, 0, 3], [0, 2, 0, -14], [-2, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 12], [0, 3, 0, 3], [0, -2, 0, -1], [1, 0, 0, 0], [0, -6, 0, 6], [0, 0, 6, 0], [12, 0, 0, 0], [2, -3, 6, 6], [-6, 0, 0, 0], [0, 0, 12, 0], [0, 0, 0, 0], [12, 0, 0, 0], [0, 5, 0, -10], [0, -18, 0, -18], [0, -1, 0, 1], [0, 0, 12, 0], [0, 0, 0, 0], [0, -4, 0, -2], [0, -2, 0, -2], [0, 0, 0, 0], [0, 0, 11, 0], [0, 0, 0, 0], [4, 0, -3, 0]]}