# Stored data for newform 72.2.n.a, downloaded from the LMFDB on 24 April 2024.
{"label": "72.2.n.a", "space_label": "72.2.n", "level": 72, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 893386752072, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1508533291294644190, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [16, 0, -4, 0, 1]]], "qexp_display": "q+(-\\zeta_{12}-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(-\\zeta_{12}+\\cdots)q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 72, "char_orbit_label": "n", "char_is_real": false, "Nk2": 288, "analytic_conductor": 0.5749228945532188, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [72, 6, [55, 37, 65], [6, 3, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [13, 61], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.784", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "84.715", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2852.061", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [-2, 0, 0, -8], "traces": [0, 4, -2, 0, 0, 0, 6, -8, -8, -6, 8, 0, 0, 0, -8, 0, 8, 20, 12, 0, -8, 0, -6, -4, -12, -2, -8, 0, 0, 0, 12, 8, 8, -18, -10, 0, 0, 0, 2, 0, -8, 10, 0, 0, 24, 0, 8, 12, 0, -18, -2, 0, 8, 0, -18, -24, 16, -6, 0, 0, 0, 0, -16, 48, 0, -8, 0, 0, 0, 0, -16, -24, 12, 36, 4, 0, 4, 0, -12, 28, 0, -18, -20, 0, -48, 0, 22, 0, -12, -56, -12, 0, 0, 0, 12, -4, 0, -2, 36, 0, 0, 0, 30, 12, 8, 48, 0, 0, 36, 0, 12, -12, 32, -12, 6, 0, 0, 0, 4, -40, 0, -4, -24, 0, 0, 0, -24, -8, -16, 66, -8, 0, 0, 0, -12, -36, -40, 18, -12, 0, -32, 0, 12, 24, -48, 0, -18, 0, 8, 0, 0, 12, -8, -30, 48, 0, 0, 0, 28, 0, 16, 32, -18, 0, 0, 0, -8, 4, 48, -18, 40, 0, -88, 0, 0, -8, 0, 0, 28, 0, 48, 0, 16, -72, 8, -8, 24, 0, 0, 0, 8, 32, 48, 30, -2, 0, 0, 0, -18, -32, 4, 0, -28, 0, 0, 0, -24, -12, 0, -6, -48, 0, 0, 0, 6, 88, 0, -64, -40, 0, 0, 0, 12, -4, -64, 12, 24, 0, 0, 0, -8, 0, 0, 52, 12, 0, -4, 0, -40, 60, -48, -34, 8, 0, 96, 0, 30, 4, -16, -24, -24, 0, 0, 0, 4, 0, -32, -30, 0, 0, 0, 0, 16, 16, 36, 0, 8, 0, 12, 0, 0, 48, 40, -48, 18, 0, 24, 0, -52, 24, 64, 12, 0, 0, 0, 0, -12, -80, 24, 32, 0, 0, 0, 0, -54, 4, -16, 54, -72, 0, -12, 0, 12, -84, 0, -96, 60, 0, -48, 0, 16, -40, 0, 2, 16, 0, 0, 0, 0, 0, 32, -18, -16, 0, 0, 0, -8, 120, -20, 48, -36, 0, 32, 0, -8, -12, 0, -14, -18, 0, -40, 0, -12, 32, 44, -24, 48, 0, 0, 0, 16, 36, -48, -30, 6, 0, 0, 0, 40, -16, -24, 72, 20, 0, 32, 0, 0, -36, -32, 30, 16, 0, -48, 0, -30, 72, -24, 0, 72, 0, 0, 0, 32, -36, -48, 48, -60, 0, 0, 0, 0, -20, 36, 0, 16, 0, -36, 0, 16, 24, 8, 30, -18, 0, 112, 0, 0, -12, -60, -62, 20, 0, 0, 0, -12, -32, -16, 0, -6, 0, 0, 0, 64, -72, 0, -10, -36, 0, 12, 0, -44, -144, 0, 20, 32, 0, -80, 0, 54, 0, 48, -54, -40, 0, 0, 0, -4, 0, 0, 84, -6, 0, 0, 0, 14, -32, 12, 74, 80, 0, 32, 0, 72, -20, 0, 48, -26, 0, -48, 0, 24, 0, -4, -66, 0, 0, 0, 0, -120, -32, 48, 8, -34, 0, 0, 0, 0, 80, -48, 24, -36, 0, -60, 0, -8, 36, 64, 48, 0, 0, -48, 0, -30, 144, -96, -112, -12, 0, 0, 0, 60, -72, 64, 0, 60, 0, 0, 0, 16, 144, 16, 60, 0, 0, -16, 0, 16, 40, 0, 38, 0, 0, -32, 0, -84, -12, 12, -120, 24, 0, 0, 0, -24, -60, 40, 80, 48, 0, 0, 0, 12, 0, 0, 112, -4, 0, 52, 0, 24, -88, 0, -90, 12, 0, 72, 0, -80, -72, 48, -78, -12, 0, 0, 0, 40, 8, 0, -132, -16, 0, 0, 0, 0, 0, -72, 48, -48, 0, 108, 0, 4, -48, 0, -120, -54, 0, 72, 0, 8, -76, 12, -10, -176, 0, 0, 0, 0, 40, -8, 0, 48, 0, 0, 0, -18, 60, -48, -10, 36, 0, -64, 0, 80, 112, 48, 38, 2, 0, -16, 0, 96, 136, -56, 0, 44, 0, 0, 0, 0, 36, -64, 62, 18, 0, 0, 0, 10, 96, 36, -12, 4, 0, -16, 0, -120, 16, 80, -54, -96, 0, 0, 0, 40, 0, -16, 32, -24, 0, 0, 0, -12, 72, 96, -52, 28, 0, 0, 0, -36, -8, -40, 42, 24, 0, 12, 0, -16, 0, 0, 0, 0, 0, -192, 0, -52, -52, 0, 50, -32, 0, 0, 0, 0, -8, 48, -72, -30, 0, 0, 0, -48, -168, 112, 16, 0, 0, 80, 0, 8, -136, 0, -96, -36, 0, 40, 0, -12, -12, -64, 108, 72, 0, 0, 0, -36, -108, 16, 36, 30, 0, 0, 0, 0, 88, 0, -72, 104, 0, 120, 0, -72, -4, -48, 90, 0, 0, 0, 0, -10, 36, 8, -28, -12, 0, 0, 0, 72, -4, 0, -68, 48, 0, 0, 0, 66, -16, 4, 48, 16, 0, -48, 0, 40, 0, -144, 16, 24, 0, 32, 0, 56, 96, 72, 96, 44, 0, 0, 0, 0, 60, -16, 84, -60, 0, 0, 0, -16, -72, -56, -36, -36, 0, 0, 0, -12, 16, 0, 22, 124, 0, -80, 0, 0, -52, -24, 0, -8, 0, 0, 0, 16, -12, -32, -90, -78, 0, 0, 0, -144, -8, -96, -58, 44, 0, -64, 0, 36, 32, 0, 0, -10, 0, 0, 0, 192, -12, -24, -12, 36, 0, 0, 0, 72, 24, -72, 192, -10, 0, 0, 0, 0, 12, 160, 12, -8, 0, 0, 0, 0, 0, -48, -8, -54, 0, 40, 0, -18, -60, 24, 16, -112, 0, 0, 0, -108, -80, -64, 24, -42, 0, 0, 0, 30, 0, 24, -40, 0, 0, -56, 0, 64, -24, -24, 24, 74, 0, -80, 0, -90, -168, -16, 54, -12, 0, 0, 0, 40, 36, 0, -28, 0, 0, 0, 0, -58, -120, 24, 8, 24, 0, 48, 0, 24, 20, 0, 0, 132, 0, 168, 0, 2, 132, 80, -84, 0, 0, 0, 0, -32, 72, 0, 30, -16, 0, 0, 0, 48, 8, 8, -30, -4, 0, -108, 0, -40, -12, 0, 62, -24, 0, 144, 0, 76, -92, 0, -32, 0, 0, 0, 0, -72, 224, -32, 120, 48, 0, 0, 0, 60, 0, 96], "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, 8, 2, 1, 2, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 72, 14, 1, 6, 0]], "char_orbit_index": 14, "prim_orbit_index": 14, "minimal_twist": "72.2.n.a", "char_is_minimal": true, "conrey_index": 13, "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, -1, 1], [0, -1, 0, -1], [0, 2, 0, 0], [0, -2, 0, 0], [1, -1, 1, 2], [0, 0, -4, 0], [-2, 0, 0, -2], [-3, 0, 3, 0], [2, 0, 0, 2], [0, 3, 0, -3], [2, 0, -4, 0], [0, 2, 0, 0], [-4, 4, 4, 0], [-2, 0, 4, 0], [0, 0, 4, 0], [5, 0, 0, 0], [3, 0, 0, -3], [0, 0, 0, -1], [0, 0, -4, 0], [0, -4, 0, 8], [-3, -3, 3, 0], [-2, 0, 2, 0], [-4, 2, 2, 2], [0, 0, -1, 0], [-2, 0, 0, -2], [0, 6, 0, -3], [0, 0, 0, -8], [0, 0, 0, 0], [4, -2, -2, -2], [4, 0, -4, 0], [4, -4, -4, 0], [-3, 0, -3, 0], [0, -5, -5, 5], [0, 0, 0, 8], [0, -6, 0, 6], [0, 0, 0, -2], [0, -1, 1, 1], [2, 0, -4, 0], [-4, 4, 4, 0], [5, 0, -5, 0], [4, 8, -8, -4], [0, -11, 0, 11], [6, 0, 0, 0], [0, 6, 0, -6], [2, 0, 0, -2], [0, 0, 6, 0], [0, 4, 0, -8], [-9, 0, 9, 0], [-1, 1, 1, 0], [0, -5, 0, -5], [0, 0, 4, 0], [0, 0, 0, 0], [-6, -3, 3, -3], [-6, 0, 0, 0], [0, -8, 8, 8], [-2, 0, 1, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, -4, 0, 8], [0, 12, 0, -12], [-4, 0, 0, 4], [12, 0, 0, 0], [0, 0, 0, 8], [0, 0, -4, 0], [-3, 6, 6, -3], [0, 3, 0, 0], [0, 10, 0, 0], [0, 4, 0, -2], [0, 8, -8, -8], [-6, 0, 0, 0], [6, 6, -6, 0], [9, 0, 0, 0], [0, -2, 2, 2], [0, -1, 0, 2], [2, 0, -2, 0], [0, -12, 0, 0], [-4, 2, 2, 2], [0, 0, 14, 0], [0, 0, 0, -8], [0, 0, -9, 0], [-5, 0, 0, 5], [0, 4, 0, -4], [-16, 0, 8, 0], [0, -10, 0, 0], [11, 11, -11, 0], [0, 0, 0, 0], [0, -6, -6, 6], [-14, 0, 0, 0], [-6, -6, 6, 0], [0, 0, 0, -8], [0, -4, 0, 4], [0, -8, 0, 4], [6, -6, -6, 0], [-2, 0, 2, 0], [-4, -8, 8, 4], [0, 0, -1, 0], [9, 0, 0, -9], [0, 0, 0, 9], [0, 0, 0, -2]]}