# Stored data for newform 168.2.i.a, downloaded from the LMFDB on 25 April 2024. {"label": "168.2.i.a", "space_label": "168.2.i", "level": 168, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 549789368488, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 336094268233711210, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [2, 0, 1]], [11, [-6, 0, 1]], [13, [-2, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(-1+\\beta _{2})q^{3}+(1+\\beta _{3})q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 168, "char_orbit_label": "i", "char_is_real": true, "Nk2": 672, "analytic_conductor": 1.3414867539575104, "hecke_ring_index": 2, "level_radical": 42, "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": "0.750", "prec": 17}, "analytic_rank_proved": true, "char_values": [168, 2, [127, 85, 113, 73], [2, 1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [125], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.030", "prec": 17}, {"__RealLiteral__": 0, "data": "3.860", "prec": 17}, {"__RealLiteral__": 0, "data": "1.151", "prec": 17}, {"__RealLiteral__": 0, "data": "123.523", "prec": 24}, {"__RealLiteral__": 0, "data": "57.060", "prec": 20}, {"__RealLiteral__": 0, "data": "5022.133", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -4, 0, -8], "traces": [0, 4, 0, -4, 4, 0, -4, -8, 0, -4, -4, 0, -4, 8, 0, -8, -8, 0, 8, -16, 0, 8, 12, 0, -16, 12, 0, 20, 4, 0, 4, 0, 0, 0, 36, 0, -4, 0, 0, -8, -16, 0, 20, 0, 0, 16, -4, 0, 8, 4, 0, 0, 8, 0, -4, 0, 0, 16, -24, 0, -8, -40, 0, 8, -32, 0, -12, 0, 0, -8, 20, 0, 32, 0, 0, -12, -16, 0, -8, 32, 0, -28, -12, 0, -4, 0, 0, 0, 0, 0, 4, -16, 0, 0, -24, 0, -16, 0, 0, 0, 12, 0, -36, 0, 0, 16, 0, 0, 20, 0, 0, 0, 40, 0, 16, -8, 0, -8, -16, 0, 16, -20, 0, 0, 48, 0, -40, -16, 0, 0, -8, 0, -24, 32, 0, -8, 0, 0, 4, 56, 0, 0, -4, 0, 8, 0, 0, -4, 72, 0, -12, 32, 0, 0, -12, 0, -8, 56, 0, 0, -16, 0, -16, 0, 0, 0, 32, 0, 32, -36, 0, 16, 24, 0, 24, -24, 0, -32, -36, 0, 16, -88, 0, 40, -16, 0, 48, 72, 0, -40, 16, 0, 32, -16, 0, -16, -44, 0, -12, 0, 0, 0, -28, 0, -72, 0, 0, 16, -16, 0, -20, 0, 0, -8, 36, 0, -16, -48, 0, 0, -24, 0, 72, 0, 0, -12, -40, 0, 16, 56, 0, 24, 0, 0, 16, 0, 0, -32, -36, 0, 16, 0, 0, -4, -40, 0, 12, -32, 0, 64, -32, 0, -4, 0, 0, 0, -32, 0, 24, -72, 0, 0, 32, 0, 0, 0, 0, 0, -24, 0, -20, 0, 0, 16, 32, 0, -8, 0, 0, 0, 32, 0, 24, -16, 0, 32, 24, 0, 32, 148, 0, 0, 0, 0, -52, -32, 0, 0, -48, 0, -12, -24, 0, -56, 32, 0, -36, -16, 0, 0, 48, 0, -32, 0, 0, -32, 32, 0, 0, -48, 0, 0, 20, 0, -28, 24, 0, 0, 0, 0, -24, 0, 0, 0, 96, 0, -40, 8, 0, -80, -72, 0, -32, 40, 0, 8, -4, 0, 48, 56, 0, 40, -48, 0, 16, -8, 0, 72, -108, 0, 16, -12, 0, 20, 8, 0, 40, 0, 0, 0, 72, 0, -48, 0, 0, -64, 0, 0, 20, 0, 0, 16, 44, 0, 32, 24, 0, 0, 96, 0, 8, 0, 0, 64, 72, 0, 48, 8, 0, -32, -24, 0, -24, 0, 0, -32, 24, 0, 0, 0, 0, 64, -96, 0, 4, 64, 0, -56, -48, 0, -8, 0, 0, 0, 0, 0, 4, 80, 0, 0, 24, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, -4, 72, 0, -72, 0, 0, 0, 64, 0, 24, -24, 0, -32, 8, 0, 64, -40, 0, 0, -8, 0, 12, -16, 0, 0, -40, 0, -8, 24, 0, -56, -64, 0, -32, -48, 0, 0, -76, 0, 16, 0, 0, 16, -20, 0, 44, -16, 0, 0, -52, 0, 24, -144, 0, 0, 96, 0, -32, 0, 0, 0, -40, 0, -64, -56, 0, 36, -16, 0, -72, 0, 0, -80, -12, 0, -24, -48, 0, -8, -32, 0, 24, -88, 0, 24, -28, 0, -48, 84, 0, 64, -16, 0, 36, 0, 0, 0, 68, 0, -8, 0, 0, 88, -144, 0, 40, 0, 0, 40, 36, 0, 16, -64, 0, 0, 56, 0, -96, 0, 0, -72, 8, 0, 48, -80, 0, 56, -16, 0, -16, 0, 0, 88, 12, 0, 32, 0, 0, 16, 48, 0, 96, 0, 0, 32, -4, 0, 44, 0, 0, 0, 144, 0, 60, 72, 0, 0, -8, 0, -48, 0, 0, 0, 32, 0, 28, 0, 0, -48, 40, 0, 144, 0, 0, 0, 48, 0, -96, -40, 0, -8, -120, 0, 16, -4, 0, 0, 56, 0, -20, 128, 0, 0, -96, 0, 0, 8, 0, 16, 32, 0, -36, 80, 0, 0, -144, 0, -64, 0, 0, 48, 72, 0, 0, 64, 0, 0, 24, 0, 24, 56, 0, 0, 128, 0, -144, 0, 0, 0, -24, 0, -16, 32, 0, 60, -36, 0, 40, -96, 0, 16, 48, 0, 16, 64, 0, -56, 48, 0, 8, -40, 0, -48, -12, 0, 0, -72, 0, -80, 12, 0, -8, 0, 0, 0, -60, 0, -32, 0, 0, -32, 0, 0, 36, 0, 0, -152, -76, 0, -32, 96, 0, 0, -88, 0, 20, 0, 0, 92, 0, 0, 40, 56, 0, -8, -16, 0, 12, 0, 0, 32, 0, 0, 0, 0, 0, -128, 72, 0, 32, 128, 0, -80, -48, 0, 20, 0, 0, 0, 64, 0, 16, 0, 0, 0, 24, 0, 32, 0, 0, 0, -16, 0, -48, 0, 0, 72, 120, 0, -16, 0, 0, 0, -104, 0, -32, 8, 0, -56, -32, 0, 0, -80, 0, 0, 72, 0, -80, -144, 0, 0, 32, 0, 24, 16, 0, 136, -112, 0, 28, 8, 0, 0, 72, 0, -144, 0, 0, 16, 24, 0, -32, 80, 0, 0, 80, 0, 16, -136, 0, 0, -64, 0, -56, 0, 0, 0, 32, 0, -32, -20, 0, 16, -168, 0, 24, 40, 0, 16, 108, 0, -8, -40, 0, -64, 0, 0, -24, 80, 0, -24, -52, 0, -16, -8, 0, -148, -144, 0, 48, 0, 0, 0, 16, 0, 0, 0, 0, -8, -48, 0, 104, 0, 0, 32, 84, 0, 0, 32, 0, 0, -120, 0, 48, 0, 0, -16, 104, 0, -12, 0, 0, 24, -160, 0, -32, 0, 0, 112, 40, 0, -32, 0, 0, 80, 56, 0, 180, -160, 0, 16, -28, 0, 72, 0, 0, 0, 96, 0, -48, -16, 0, 0, -88, 0, 64, 0, 0, 0, 48, 0, -56, 0, 0, 16, 24, 0, -32, 0, 0, 0, 144, 0, 0, 88, 0, 48, -24, 0, 64, -68, 0, 0, -48, 0, -20, -16, 0, 0, 96, 0, -4, -112, 0, -24, 80, 0, 72, -72, 0, 0, -84, 0, 0, 0, 0, -48, -32, 0, 48, -208, 0, 0, 20, 0, 64, 248, 0, 0, -128], "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, 3, 2, -1, 2, 0], [1, 1, 56, 8, -1, 2, 0], [1, 1, 168, 9, 1, 2, 0]], "char_orbit_index": 9, "prim_orbit_index": 9, "minimal_twist": "168.2.i.a", "char_is_minimal": true, "conrey_index": 125, "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, 1, 0, 0], [-1, 0, 1, 0], [1, 0, 0, 1], [0, 0, 1, 0], [-1, -1, 0, 1], [-2, 0, 0, -1], [0, 0, 2, 0], [-1, 0, -2, 0], [-1, 0, 0, 1], [0, 2, -1, 0], [-1, -2, 2, -1], [2, 0, 0, 0], [0, -1, -2, 0], [-2, 0, -1, 0], [-2, 0, 0, 2], [0, 6, -3, 0], [2, -1, 0, -2], [-4, 0, 0, 0], [0, -2, 2, 0], [2, 2, -3, 1], [3, 0, 0, 1], [0, 0, 1, 0], [-4, 0, -2, 0], [3, 0, 0, 0], [0, 2, 0, 0], [5, 0, 1, 0], [1, 0, 0, -3], [0, -4, 2, 0], [1, -2, 0, -1], [0, 0, 0, -4], [0, -4, 4, 0], [0, -2, 1, 2], [9, 0, 0, 3], [0, 2, -3, 0], [-1, 4, -4, -1], [0, 0, 0, -6], [0, -4, 0, 0], [-2, 0, 2, 0], [-4, 0, 0, 0], [0, -2, 1, 0], [5, 1, 2, -1], [0, 0, 0, -2], [0, 2, 2, 0], [4, 0, -1, 0], [-1, 0, 0, 1], [0, -4, 2, 0], [2, -4, 0, -2], [1, 0, 0, 4], [0, 3, 0, 0], [0, -6, 3, 6], [2, 0, 0, 2], [0, 0, 0, 0], [-1, 5, 0, 1], [0, 0, 0, 2], [0, 4, -6, 0], [4, 0, -4, 0], [-6, 0, 0, -2], [0, 0, 4, 0], [-2, 2, -2, -2], [-10, 0, 0, 0], [0, 4, -8, 0], [2, -4, 6, 1], [-8, 0, 0, 0], [0, 0, 2, 0], [-3, -2, 4, -1], [0, 0, 0, 2], [0, 6, 6, 0], [-2, 0, -1, 0], [5, 0, 0, -1], [0, 0, 1, 0], [8, 0, -2, 0], [0, 0, 0, 0], [0, 6, -12, 0], [-3, 0, 3, 0], [-4, 0, 0, -4], [0, -4, -1, 0], [-2, -2, 0, 2], [8, 0, 0, 0], [0, -4, 0, 0], [-7, 0, 4, 0], [-3, 0, 0, -1], [0, 0, -8, 0], [-1, 6, -2, 3], [0, 0, 0, 6], [0, 2, -4, 0], [0, 4, -2, -4], [0, 0, 0, 4], [0, -6, 3, 0], [1, 4, 0, -1], [-4, 0, 0, -2], [0, -2, 2, 0], [0, 8, -4, 4], [-6, 0, 0, -2], [0, 0, -4, 0], [-4, 4, -4, -4], [0, 0, 0, -8], [0, -3, 8, 0], [0, -2, 1, -4], [3, 0, 0, 3]]}