# Stored data for newform 546.2.s.c, downloaded from the LMFDB on 24 March 2023.
{"level_primes": [2, 3, 7, 13], "is_polredabs": true, "sato_tate_group": "1.2.3.c6", "rm_discs": [], "conrey_indexes": [43, 127], "cm_discs": [], "trace_hash": 151492537465044723, "level_radical": 546, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 5, "is_cm": false, "hecke_orbit": 3, "analytic_conductor": 4.359831950361909, "inner_twist_count": 2, "field_disc_factorization": [[2, 4], [3, 2]], "is_rm": false, "char_order": 6, "level_is_square": false, "weight_parity": 1, "label": "546.2.s.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "546.2.s.c", "field_poly_is_cyclotomic": true, "dim": 4, "trace_zratio": {"__RealLiteral__": 0, "data": "0.193", "prec": 17}, "traces": [0, 4, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, -4, 0, -4, 12, -2, 6, 0, 12, 12, 0, 8, 8, 0, -28, 14, 4, 0, -16, 0, 0, 0, 0, 0, 0, 2, -24, 16, 0, 0, -24, 2, 2, 0, -12, 6, 0, -2, 2, 0, -12, 0, -40, 0, 0, -2, 0, 0, 6, 0, 0, 6, 0, -4, 0, -16, 18, -6, 8, 0, 24, 0, 0, 4, 14, 12, -16, -4, -24, 12, -2, 0, 0, 0, 36, 0, -16, -8, -6, 0, -4, 16, 12, -8, -24, 0, 36, 0, 0, -14, 0, -12, -8, 10, 0, 6, -24, 2, 0, 48, 24, 0, -12, -8, -48, -32, 0, -32, -12, 0, 10, 0, 24, 12, 0, 2, 24, 0, -4, -12, 76, 0, -8, 4, 0, -12, -48, 0, 8, 0, 12, -20, 56, 4, 96, -8, 2, 0, 12, 0, 0, 8, 6, 0, -48, 0, 16, -12, 20, 0, 0, 0, -30, 0, 0, 0, 0, 4, 2, 48, -12, -2, 16, 0, 0, 0, 0, -20, -20, -12, -16, 0, 0, 6, -48, 6, 0, 12, 0, 0, 8, 2, 48, 8, 0, 4, -36, 8, -20, 0, -18, 0, 0, -6, -48, -30, -16, 0, 64, -12, 32, -20, 0, 12, 12, 0, 6, 24, -24, 0, 48, -8, 12, 2, 14, 0, -60, -12, 0, -12, 8, 0, -40, -10, -48, 6, 12, -6, 0, -12, 48, 0, -2, 0, -12, 0, 16, 12, -6, 0, -34, 0, 24, -24, 0, -2, -6, -12, -8, 0, 32, 0, 0, -8, 0, -12, 6, 0, -24, 0, 12, -12, -10, 0, 0, -8, -20, 0, -12, -12, 0, -8, -16, 24, 48, 0, 0, 0, -8, 0, 0, -24, -12, 0, -12, -4, 0, -60, -6, 28, -12, -24, 0, 0, 0, 12, 0, -8, 4, -36, 16, -14, 72, -24, 0, -12, 0, -6, 0, 0, -24, -8, 84, -4, 0, 40, 0, 0, -8, 0, 60, -6, 0, 40, 36, 0, -24, 0, 24, 36, 24, -8, 0, -12, 48, 0, 4, 16, -120, 28, 0, -16, -30, 16, -48, 0, 12, -24, 0, 0, 18, -72, -20, -14, 96, -18, 28, 8, 0, 24, -6, 0, 4, -24, -24, -16, 0, -4, 36, 24, 24, 0, 60, 0, 0, 8, 2, 36, 24, 48, 72, 0, -38, 26, 0, 0, -72, 0, -8, 14, -36, -8, -30, 0, 12, 16, 16, 0, 36, 0, 0, -4, 16, -6, 24, -4, -16, 48, 10, 0, 0, -24, -12, 0, -42, 10, -18, -48, -16, 48, 48, -2, -8, 0, -96, 0, 0, -8, -48, 48, -4, 30, -48, 24, -12, -22, 0, 0, 0, 0, 0, 12, 0, 16, 48, -16, 18, 26, 6, 0, 24, 0, 0, -16, 24, -12, 20, 0, -8, 48, -8, -16, 0, 12, -84, 0, 20, 2, -36, 0, 28, 8, -6, -10, -72, 0, 36, -18, 0, 0, 8, 24, -96, 36, 0, 12, 10, 0, 0, -24, 0, 0, 0, -2, 0, 64, 44, 48, -84, -24, -8, 0, 12, 12, 0, -2, -32, 24, -32, 36, -120, 0, -16, 38, 0, 60, 72, 0, 8, 12, -6, -16, 0, 40, 144, -4, -20, 0, 0, 12, 0, 18, 8, -12, 0, 0, -80, -48, 0, -56, 0, -6, 12, 0, -48, -8, -36, -12, 48, 0, -48, 16, 0, 0, -72, -12, 0, -10, 24, 48, -28, 40, -16, 24, -56, 2, 0, -72, -48, 0, 0, -4, 24, -16, 0, -120, 42, -2, -48, 0, 36, 24, 0, 8, -24, 12, 40, 16, 0, 0, 0, -2, 0, 0, 60, 0, 20, -8, 0, 72, 40, 12, 36, -44, -48, 0, -48, 30, 0, -24, 8, -60, 40, 0, -44, -60, -32, 8, 0, 12, 24, 0, 32, -26, -144, 40, 0, -128, -24, 0, 16, 0, -84, -6, 0, 48, 40, 0, -128, -98, -12, -30, 44, 24, 0, 24, 24, 0, -24, 0, 96, 16, -36, 0, 48, 4, 64, 0, -12, 24, 0, 2, 10, 0, -28, 46, 32, -36, -4, 24, 0, 48, 108, 0, 96, -2, 24, -4, 18, 24, -108, -16, 8, 0, 48, 0, 0, -2, 20, 0, -40, 14, -64, 0, 24, 36, 0, -6, -96, 0, 12, 20, -66, 12, -48, -40, -48, -16, 76, 0, 30, 96, 0, -8, 112, 0, -40, 0, 4, 48, -30, 0, 0, 66, 12, 0, 16, 0, 6, -96, 40, 40, 72, -6, -24, 0, 6, -48, 0, 0, 24, 12, 68, -32, 0, 0, -12, -40, 0, 48, 24, 0, 24, -8, -36, -40, -32, 4, 120, 0, -6, 0, 24, 12, 0, 4, 4, 30, -96, 0, -80, 66, -16, 2, 0, 0, -36, 0, 0, -24, -36, 16, 72, -36, -120, 20, 36, 0, -12, 0, 0, -12, -32, -18, 24, -12, 48, 0, 24, 0, 0, 0, -12, 0, 60, 6, 60, -16, 14, -96, 84, 0, 68, 0, 0, -6, 0, -8, 56, 0, 40, 0, 12, 24, 0, 32, 0, 0, 36, 0, -70, 24, -36, 64, -180, 16, 0, 20, -16, 0, -84, -24, 0, 0, -24, 12, 24, 0, -8, 12, 0, -18, 0, 0, 96, 0, -8, -6, -48, 0, 28, 48, -36, 44, 0, 0, 96, 36, 0, 0, -26, 0, -68, 12, 24, -36, 4, -4, 0, -120, 0, 0, 8, 30, 120, 4, 24, 72, 96, -14, -48, 0, 12, -36, 0, -24, -30, -60, 0, 0, -16, -12, 0, -8, 0, 24, 0, 0, 52, 12, 0, -48, -20, 16, 168, -32, 4, 0, -42, 36, 0, -20, -8, 120, 192, 4, -152, -18, -36, -24, 0, 24, -96, 0, 0, -8, 84, 24, 40, -112, -12, 6, 60, 0, 48, -48, 0, 12, 0, -12, 40, -96, 48, 48, 96, -8, 0, 0, -84, 0, -34, 2, 24, -40, 0, 0, -48, -20, -80, 0, 0, -48, 0, 0, -72, -96, 16, 56, 40, -48, -28, 6, 0, -24, -120, 0, -16, 4, -24, 0], "hecke_ring_index_factorization": [], "nf_label": "4.0.144.1", "field_poly": [1, 0, -1, 0, 1], "has_non_self_twist": 1, "char_values": [546, 6, [365, 157, 379], [6, 6, 1]], "Nk2": 2184, "field_poly_root_of_unity": 12, "analytic_rank": 0, "char_orbit_label": "s", "weight": 2, "trace_display": [0, -2, 0, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+\\zeta_{12}q^{2}+(-1+\\zeta_{12}^{2})q^{3}+\\zeta_{12}^{2}q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 144, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[5, [12, 0, 1]], [11, [256, 0, -16, 0, 1]]], "space_label": "546.2.s", "level": 546, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 5, 1, 6, 0]], "char_degree": 2, "char_conductor": 13, "char_orbit_index": 19, "hecke_ring_generator_nbound": 2, "hecke_orbit_code": 9008436238877218, "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "3.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "61.143", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1447.215", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [-1, 0, 1, 0], [0, 0, 1, 0], [2, 0, -4, 0], [0, -1, 0, 1], [0, -1, 0, 1], [0, 0, 0, 1], [0, 0, -1, 0], [0, 2, 0, -4], [0, 4, 0, 0], [-1, 0, 0, 0], [0, 3, 0, -4], [-1, 0, 0, 0], [2, 0, 2, 0], [-1, 0, 1, 0], [0, 2, 3, 2], [0, 0, 0, -1], [4, 4, -2, -4], [4, 0, -2, 0], [0, 0, 0, -1], [0, 0, 4, 0], [4, 1, -4, -2], [0, -1, 0, 0], [-7, 0, 0, 0], [4, 0, -1, 0], [1, 0, 0, 0], [0, -1, 0, 0], [-8, 0, 8, 0], [0, 2, 0, 2], [2, 0, -4, -3], [0, -1, 0, 1], [0, -4, 0, 4], [-2, 0, 4, 3], [0, 2, 0, 2], [1, 0, -1, 0], [-4, 2, -4, 0], [4, 4, 0, -2], [0, 1, 0, 3], [0, 4, 0, -2], [-4, 0, -4, 0], [1, 0, -1, 0], [0, 2, 1, 2], [0, 0, 0, 4], [-4, 0, 2, 0], [2, 4, -1, -4], [2, 0, -4, 4], [0, 0, -1, 0], [1, 0, -1, 0], [0, -7, 0, 0], [-3, -4, 0, 2], [0, 4, 0, -1], [-10, 2, 0, -1], [0, 1, 0, 0], [0, 8, 0, -16], [0, 0, -1, 0], [-2, 0, 4, 4], [0, -8, 0, 8], [2, -8, -1, 8], [-2, 0, 4, 0], [0, 3, 0, 3], [3, 2, -3, -4], [0, 1, 0, 0], [-1, 0, 0, 0], [0, -10, 0, -4], [-4, 0, 0, 0], [3, 2, 3, 0], [-3, -2, 3, 4], [0, 1, 4, 1], [-2, 0, 4, 0], [8, -5, -4, 5], [0, 1, 0, -1], [-4, 0, 8, 4], [0, -4, 2, -4], [7, 0, -7, 0], [2, 4, 2, 0], [-4, 0, 0, 0], [-3, 0, 4, 0], [-6, -4, 0, 2], [2, 0, 2, 0], [-1, 0, 1, 0], [0, -4, 0, -4], [-1, 0, 2, 0], [0, 1, 0, -1], [12, 12, -6, -12], [-2, 0, 4, 1], [0, 0, -8, 0], [-4, 0, 4, 0], [-1, -10, -1, 0], [0, -4, 0, 2], [-3, 0, 4, 0], [4, 2, 0, -1], [2, 3, 2, 0], [-4, 2, 4, -4], [0, -8, -12, -8], [0, 0, 0, -1], [12, 2, -6, -2], [0, 1, 0, -1], [0, 0, 0, -4], [0, 0, -7, 0]]}