# Stored data for newform 546.2.i.g, downloaded from the LMFDB on 25 September 2023.
{"label": "546.2.i.g", "space_label": "546.2.i", "level": 546, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27022147553591842, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1379815403610865255, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4, -2, 1]], [17, [1, 1, 1]]], "qexp_display": "q+\\zeta_{6}q^{2}+(1-\\zeta_{6})q^{3}+(-1+\\zeta_{6})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 2184, "analytic_conductor": 4.359831950361909, "hecke_ring_index": 1, "level_radical": 546, "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": [546, 3, [365, 157, 379], [3, 1, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [79, 235], "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": "1.845", "prec": 17}, {"__RealLiteral__": 0, "data": "0.105", "prec": 17}, {"__RealLiteral__": 0, "data": "9.747", "prec": 17}, {"__RealLiteral__": 0, "data": "1.828", "prec": 17}, {"__RealLiteral__": 0, "data": "79.680", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 1, 2, -1], "traces": [0, 2, 1, 1, -1, 2, 2, -1, -2, -1, -2, -3, 1, -2, -5, 4, -1, -1, 1, 3, -4, 4, -6, 0, -1, 1, -1, -2, -4, 6, 2, 4, 1, 3, -2, -10, 2, 2, -3, -1, -2, 4, -1, 12, -3, 2, 0, 9, -2, -13, 2, 1, 1, -1, -1, -12, 1, 6, 3, -11, -2, -11, 8, 5, 2, -2, -3, 7, -1, 0, -8, 30, 1, 12, -2, -1, -6, -12, -2, -2, 2, -1, 2, 0, -5, -4, 6, 3, 3, -10, 4, 1, 0, -4, -9, -6, -1, -24, -2, 6, 1, 14, -1, -14, 2, -2, -2, 4, 1, 8, -6, 4, 5, 6, 3, 0, -3, 1, -22, -4, -4, 2, 11, 2, 4, 24, 4, 16, 1, 6, 2, 12, -6, -15, 14, -2, 1, -18, 0, -28, 2, 18, 15, 3, -1, 6, 24, -11, -4, 0, 1, 17, -3, 2, 3, 16, -1, 11, 2, 1, 4, 0, -2, 25, -2, -6, 0, -38, -4, 2, -2, 3, -6, -7, 6, 4, 6, 11, 10, 6, 2, -10, 5, -22, 0, -4, 4, -3, -18, 1, -12, 12, 1, 14, -12, -4, 11, 16, 3, -12, -1, -7, 28, -3, -2, 4, 14, 0, 1, -18, -10, -32, -1, 15, -4, 12, 2, 16, 16, -12, 6, 1, 2, -2, 4, -2, 3, -8, -3, 2, 0, -15, -6, -7, -1, -18, -11, -4, 1, -22, -2, -12, -2, 1, 22, -4, 4, -3, -4, 0, 12, -20, -1, 0, 8, -2, -1, 26, 12, -10, 4, -3, -12, -10, -3, -4, -12, -20, 7, 21, 2, -15, 2, -4, -36, 3, 0, -5, -14, -8, 10, -48, 9, 4, -15, 6, 6, -2, -2, 16, -6, -12, 12, -24, -13, -44, -2, 3, 0, 0, 2, -6, 34, -14, 3, 22, 1, -30, 15, -28, 8, -14, 1, 14, 22, 8, 4, -18, -1, -9, 2, 8, 0, -6, -1, -1, -25, -8, -4, -45, -12, 28, 0, 2, -19, 28, 1, 14, 1, 3, 2, 12, 6, 20, -12, 0, 7, -2, 3, 40, -1, 2, 3, 18, -11, 30, 20, -5, 12, -16, -2, 10, -5, 4, 4, 48, -11, -18, 0, -2, -8, -4, 8, 11, 3, 12, -9, -6, 5, 72, -6, 8, -12, 32, 2, 6, 28, -6, 12, -13, -2, 0, 13, 24, 8, 4, -3, 20, -24, -3, -2, -12, 7, -4, 14, -4, -15, -12, -1, 38, -4, 18, 28, -44, 0, 0, -1, -14, -9, -12, -8, 0, -16, 9, 1, 1, 30, 55, -8, -3, -12, 40, 1, -22, -4, 12, 8, 0, 12, -16, 12, 2, 2, -6, -2, 20, -1, 0, -1, -80, -1, -6, -3, -17, -16, 10, -6, 32, -2, 1, 0, -40, -12, -64, -3, 8, 7, 0, -2, 28, -36, -11, 11, -18, -2, 6, 5, 2, -11, -15, 2, -2, -24, 0, -4, -24, -1, 33, 11, 50, 22, 44, 2, -3, 3, 6, -8, -15, 0, -28, -12, -19, -10, -40, -5, 56, 0, 1, -8, -12, -4, 48, -2, -3, -26, 28, 6, -54, -8, -14, 2, 38, 3, -6, -24, 5, -20, 4, 3, 23, -2, 22, 3, -4, -10, -8, -7, -6, 42, 33, 4, -22, 15, -5, 1, 32, 1, 88, -18, -11, -3, 9, 0, 10, -10, 4, 14, 22, -4, -12, 8, -6, -24, -24, -9, 6, 8, -4, -30, -39, -6, -44, 3, 24, -10, 0, -1, 18, -16, -14, -12, 0, -24, -3, -12, -2, -12, 78, -2, 24, -22, 8, 2, 34, 6, 2, 0, 12, 0, 30, 1, -70, -30, -14, 17, -4, 14, -28, 6, 12, 44, -9, -1, 16, -15, 8, 12, -28, -14, -20, -8, 0, -28, 50, 2, 19, -14, -9, 11, -4, -2, -80, 2, -16, 18, 16, -2, 13, -18, -15, -2, 18, 4, 2, 0, 24, -3, 6, 1, -33, -2, 20, -50, 30, 8, -24, -2, -24, -36, 60, -6, -38, -28, -1, 0, -24, 4, 0, 19, -1, 14, 66, 5, -68, 7, -1, -1, -1, 6, 12, 4, 8, -12, 44, 3, -72, 37, 4, -6, 1, 0, -35, 14, -3, -4, -28, -3, -2, 20, -14, -5, 60, 1, -6, -3, 18, 36, 56, -22, 20, -30, -2, 10, 0, -4, 12, 6, -11, 16, -38, -4, 70, 20, 12, 5, 3, 2, -24, -1, 2, 24, -6, 11, 8, -36, -26, 0, 21, 2, 0, -4, -6, 1, -70, 4, 0, -11, 0, 6, -20, 24, -28, 9, -10, -3, 68, 4, 38, 36, 0, 6, -28, 16, 32, -24, 2, -32, 11, 1, -8, 30, 52, 14, -42, 6, -4, 24, -2, -26, 6, 2, -45, 0, -6, 2, 44, 12, -7, -8, 10, 8, -3, -6, 11, -20, -2, -12, 68, -15, -18, -1, -10, 12, 36, 14, 0, -8, -21, -14, -7, -2, 24, -12, -30, -6, -50, 1, 18, 76, -5, -8, 6, -18, -26, 14, 6, 11, -6, 0, -53, 0, 5, -2, 11, -28, -38, 9, -4, -6, 46, 2, -40, 0, -24, 16, 2, 18, -10, 2, -4, -1, 0, 15, -64, 44, 12, -4, -7, 3, -40, -24, 8, 80, -4, -1, 14, -11, 32, -20, 12, 6, -7, -8, 12, 0, -12, 24, 42, 16, -12, 6, -20, -11, -28, 1, -22, 6, 6, -4, -8, 40, -3, 1, -27, 0, 24, -5, 0, -40, 12, 1, -1, -12, 24, -6, -10, 17, 44, -8, -28, 8, -28, -3, 0, -32, -22, -4, -60, 2, -46, 0, -15, -20, -30, 3, 4, -32, -14, 3, -34, 16, -6, 14, 14, 0, 6, -1, -26, -7, 28, -18, 0, 11, 0, 22, 10, -36, 33, 2, -12, 3, -36, 4, -66, 1, -24, 11, 9, -30, -72, 4, 15, 2, 4, -12, 56, 0, 42, -2, -3, 24, -10, -2, 14, 66, 1, -11, -38, 25, 60, 26, -16, 22, -21, -2, 16, -6, -9, 6, 0, -6, 24, -4, 56, -75, -48, 0, -11, 28, -2, -24], "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, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "546.2.i.g", "char_is_minimal": true, "conrey_index": 79, "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], [0, 1], [1, -1], [-1, 1], [0, 2], [1, 0], [-2, 3], [-1, 0], [0, -1], [-2, 2], [-3, 3], [0, 1], [-1, 0], [-3, 1], [2, 0], [0, -1], [-1, 1], [1, -1], [0, 3], [-2, 0], [1, 2], [-3, 0], [0, 0], [-1, 1], [1, -1], [0, -1], [-1, 0], [-1, -2], [3, 0], [0, 2], [4, -4], [1, -1], [0, 3], [-1, 0], [-6, 2], [1, 0], [0, 2], [-3, 3], [-1, 1], [0, -2], [2, 0], [-2, 3], [6, 0], [0, -3], [2, -2], [0, 0], [0, 9], [-1, 0], [-5, -3], [1, 0], [0, 1], [1, -1], [-1, 1], [0, -1], [-6, 0], [2, -3], [3, 0], [0, 3], [-11, 11], [-2, 2], [0, -11], [4, 0], [3, -1], [1, 0], [0, -2], [-3, 3], [7, -7], [0, -1], [0, 0], [-2, -4], [15, 0], [0, 1], [12, -12], [-2, 2], [0, -1], [-3, 0], [-3, -6], [-1, 0], [0, -2], [2, -2], [-1, 1], [0, 2], [0, 0], [-3, 1], [-2, 0], [0, 6], [3, -3], [3, -3], [0, -10], [2, 0], [2, -3], [0, 0], [0, -4], [-9, 9], [-6, 6], [0, -1], [-12, 0], [3, -8], [3, 0], [0, 1]]}