# Stored data for newform 722.2.c.b, downloaded from the LMFDB on 24 April 2024. {"label": "722.2.c.b", "space_label": "722.2.c", "level": 722, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503737099879122, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1001997916840868064, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1, -1, 1]], [5, [0, 1]], [7, [4, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}+(1-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "c", "char_is_real": false, "Nk2": 2888, "analytic_conductor": 5.765199025936444, "hecke_ring_index": 1, "level_radical": 38, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.013", "prec": 17}, "analytic_rank_proved": true, "char_values": [722, 3, [363], [2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [429, 653], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.977", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.742", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "106.353", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 1, 0, -8], "traces": [0, 2, -1, 1, -1, 0, 1, -8, 2, 2, 0, 6, -2, 2, 4, 0, -1, 6, -4, 0, 0, -4, -3, 6, 1, 5, -4, 10, 4, 0, 0, -4, -1, 3, 6, 0, 2, 20, 0, 4, 0, 9, -4, 4, -3, 0, -12, 0, 1, 18, -10, -6, 2, 6, -5, 0, -8, 0, 0, -9, 0, 4, 2, -8, 2, 0, 3, -7, -12, 12, 0, -6, 2, 1, -10, 10, 0, -24, -2, -4, 0, -1, 9, 6, 8, 0, 4, 0, 6, 6, 0, -8, 6, -2, 0, 0, -2, 17, -9, 6, 5, 0, 12, -4, 2, 0, -12, 0, -5, -16, 0, 10, 4, -30, 0, 0, 0, -4, -9, -24, 0, -4, -8, -9, 2, 0, 16, 2, -1, -4, 0, -9, -6, 0, 14, 0, 6, -9, -6, -11, 0, 0, -6, 6, -4, 0, 1, 9, -10, -18, -5, 20, 0, 24, 12, 0, -2, 16, -4, 12, 0, -24, -1, -38, -18, 0, -3, -24, -4, 9, 0, 0, -8, 6, 0, -20, -3, 9, -12, -18, 0, 2, 16, 8, 6, 0, -2, 18, 0, -40, 0, 24, 1, 2, 17, 0, -9, 36, -12, 10, 5, -14, 0, 0, -6, 0, 2, -12, -4, 0, 0, 20, 6, 6, 0, 0, 10, 16, -16, -1, 0, 24, 10, 14, 4, -10, 15, -6, 0, -32, 0, -12, 0, -3, -4, 0, 18, 4, -24, -24, 0, 5, 2, 16, 4, 0, 18, 0, -4, 3, 0, 3, -8, 18, -4, 0, -1, 3, 8, -80, 0, 0, -9, 12, 3, 0, 0, 12, -7, 12, 0, 16, 6, -16, 18, 15, -6, 16, 22, -4, 0, 27, 0, -5, 12, 0, -12, -36, 2, -19, 0, -17, -2, -48, 9, 0, 20, 30, -18, -12, -5, -16, -10, 0, 0, 0, -12, -7, 12, -2, 0, -60, 4, 19, 16, 0, 8, -18, -6, 0, 0, 0, 48, 0, 2, -10, 19, 16, 9, 0, 0, -10, -3, 20, 48, 0, -4, 11, 9, -15, 0, -12, 0, -16, 4, 0, 6, 9, 0, -8, 40, 10, -3, 6, -18, 0, 6, 24, 9, 6, 0, 0, -4, -2, -8, 0, -4, 22, -12, 36, 0, -24, 4, 8, 18, 0, 0, 0, 20, 56, 0, 4, -12, -36, 1, 0, 2, 16, -34, 36, 0, 72, 18, 9, -18, 0, 6, 10, -20, 0, -10, -27, 7, -4, 0, 0, 0, 60, -6, 5, 0, -18, 2, 36, -12, 0, 2, -22, 0, -24, 0, -10, 20, 0, 6, 60, -12, -16, 0, 12, 0, -30, -5, 26, -8, 0, 32, 0, 2, 14, 0, 18, -12, -9, -20, 0, 14, 18, -8, -18, -10, 27, 15, 10, 3, 0, 0, 10, 16, 30, 0, -6, -12, -68, 0, 0, -3, -54, 8, 28, 0, -16, -9, 12, -8, 0, 48, -12, 12, -36, 0, 20, -10, -48, 2, 0, -32, -4, 4, -19, 0, 0, -9, 0, 0, 0, 2, 24, 3, 25, 0, -48, -6, -6, -8, 0, -36, -9, 2, -24, 0, -4, 2, 0, -6, 0, -4, 0, 40, -6, 0, -18, 0, -28, 18, -40, 12, -12, 3, -13, 0, -36, 0, 36, -6, 0, -7, -9, 12, 54, 0, -44, 16, 4, -12, 0, 8, -4, -9, -8, -30, 0, 12, 16, -8, 0, -11, -24, 8, 16, 0, -18, -54, 42, 0, 0, -5, 4, -6, 12, 0, -14, 6, 12, -36, -30, 2, 22, 38, -2, 0, -24, 34, 18, 1, 0, 24, 12, -18, 0, 0, 18, -10, 21, -15, 0, 36, 20, -12, -6, 10, 26, -16, 14, -10, 0, 0, -40, 0, 0, 0, 0, -12, -2, -7, 0, -24, -3, -2, -8, 0, 30, 30, -24, -2, -25, -38, 0, -32, 60, 0, 28, -4, -20, 36, 0, -6, 18, 0, -24, 0, -39, 0, 43, -24, 0, 0, 36, -1, -27, -10, 8, 19, -24, -32, 0, 9, 4, 0, 36, 0, -40, 5, 12, 6, 0, -40, 0, -24, -14, 0, 12, 8, -28, 11, 25, -18, 84, -15, -68, 0, -3, 6, 72, 0, 0, 8, -16, 4, -12, 0, 88, -12, -24, 9, 0, 0, -54, 4, 3, -20, 24, -20, 0, 6, 0, -3, 0, 9, -14, 0, -16, 6, -12, -48, 0, 9, -12, 6, -30, 0, 16, 0, 10, 2, 0, -2, -32, -8, 26, 0, -24, -4, -44, -44, 0, 6, -21, -18, -35, 0, 0, 48, -18, -2, 0, -4, 6, -36, 0, 0, 38, 0, 6, 0, 0, 20, 10, -28, 36, 0, -78, -2, 64, -12, 0, -36, -36, -2, -2, 0, 6, -4, -48, -8, -10, 17, -40, -72, 0, 0, -18, -36, 0, -9, 0, -18, 14, -18, -12, 0, 120, 6, -8, 10, 0, 10, -12, 0, 0, 5, -12, -27, 3, 7, 0, 8, -12, 0, 90, 0, -16, 0, -16, -30, 0, 12, 0, -10, 16, 0, -18, 9, -14, -4, 30, 36, -39, 24, -88, 0, 8, 2, 54, 11, 0, 0, -20, 12, -12, 0, 29, -10, 54, -40, 0, 0, 16, -12, 5, -30, 60, 6, 22, 32, 0, 0, -3, -6, 43, 0, 36, 60, -36, -5, 0, -52, -38, -8, -12, 0, 14, -16, 68, 0, 0, -1, 20, 14, -24, 0, -18, -36, 19, -12, 0, 18, 48, 10, -8, 0, -3, -28, 0, -36, 0, 4, 12, 9, 0, 20, 72, 27, 16, -30, 0, 10, 17, 3, 0, 0, -60, 0, 18, -5, 0, 16, 36, 30, -20, 0, 7, -6, -24, 24, 50, 34, -4, 0, 3, 0, 0, 6, -30, 27, 0, -4, -35, -56, 38, 0, -42, 32, 108, -9, 0, 12, -60, 4, 4, 0, -36, -24, -15, -12, 0, 12, 0, 72, 36, 0, -54, -40, 0, 5, 0, 24, 34, -4, 0, 0, 21, 16, 44, 2, 10, -8, -66, -19, 18, 0, -64, 0, 24, -9, 0, 0, 0, 0, 48, 0, 8, 2, -5, 24, 0, -6, 4, 25, 100, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "38.2.c.a", "char_is_minimal": false, "conrey_index": 429, "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], [1, 0], [-1, 1], [1, -1], [0, -1], [0, 0], [0, 1], [-4, 0], [1, 0], [0, 2], [0, 0], [3, 0], [-1, 0], [0, 2], [4, -4], [0, 0], [-1, 1], [6, -6], [-2, 0], [0, 0], [0, 0], [-4, 4], [-3, 3], [0, 6], [1, -1], [0, 5], [-2, 0], [5, 0], [0, 4], [0, 0], [0, 0], [-2, 0], [0, -1], [3, -3], [0, 6], [0, 0], [2, -2], [10, 0], [0, 0], [2, 0], [0, 0], [9, -9], [0, -4], [4, -4], [0, -3], [0, 0], [-6, 0], [0, 0], [0, 1], [9, 0], [-5, 0], [0, -6], [2, -2], [0, 6], [-5, 5], [0, 0], [-4, 0], [0, 0], [0, 0], [-9, 9], [0, 0], [0, 4], [2, -2], [0, -8], [1, 0], [0, 0], [0, 3], [0, -7], [-6, 0], [6, 0], [0, 0], [-6, 6], [0, 2], [1, -1], [-10, 10], [5, 0], [0, 0], [-12, 0], [-2, 2], [-4, 4], [0, 0], [-1, 1], [0, 9], [3, 0], [4, 0], [0, 0], [0, 4], [0, 0], [3, 0], [0, 6], [0, 0], [0, -8], [6, -6], [-2, 2], [0, 0], [0, 0], [-1, 0], [17, -17], [-9, 9], [0, 6], [5, -5]]}