# Stored data for newform 546.2.i.b, downloaded from the LMFDB on 23 April 2024.
{"label": "546.2.i.b", "space_label": "546.2.i", "level": 546, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504149416739362, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 617803979065879103, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [1, -1, 1]], [17, [36, -6, 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": "0.010", "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": "1.894", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.785", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "94.438", "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, 1, -1], "traces": [0, 2, -1, -1, -1, 1, 2, -1, 2, -1, 1, 1, -1, -2, -4, -2, -1, 6, -1, 4, -2, 5, -2, 6, -1, 4, 1, 2, 5, 6, 1, 11, -1, 1, -12, 4, 2, -4, 4, 1, 1, 24, -1, -16, 1, 1, 6, 8, 2, -13, -8, 6, 1, 5, -1, 2, -1, -8, -3, 5, 1, -12, 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"char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "546.2.i.b", "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, 1], [1, 0], [1, -3], [1, 0], [0, -1], [1, -1], [1, -1], [0, -1], [-1, 0], [-3, 2], [-1, 0], [0, -1], [6, -6], [-1, 1], [0, 4], [-1, 0], [2, 1], [-1, 0], [0, 6], [-1, 1], [4, -4], [0, 1], [1, 0], [2, 1], [3, 0], [0, 1], [11, -11], [-1, 1], [0, 1], [-6, 0], [3, -2], [1, 0], [0, -4], [4, -4], [1, -1], [0, 1], [12, 0], [1, -3], [-8, 0], [0, 1], [1, -1], [6, -6], [0, 8], [1, 0], [-8, 3], [-4, 0], [0, 6], [1, -1], [5, -5], [0, -1], [1, 0], [1, -3], [-4, 0], [0, -3], [5, -5], [1, -1], [0, -12], [-11, 0], [-3, 2], [1, 0], [0, -1], [1, -1], [-16, 16], [0, 6], [-6, 0], [-2, -1], [6, 0], [0, -1], [10, -10], [-4, 4], [0, 4], [-4, 0], [-2, -1], [-1, 0], [0, -7], [1, -1], [-1, 1], [0, -12], [-17, 0], [-3, 2], [6, 0], [0, 8], [-3, 3], [1, -1], [0, 12], [-1, 0], [-1, 3], [-6, 0], [0, 11], [8, -8], [-4, 4], [0, -1], [13, 0], [3, 5], [-1, 0], [0, 4]]}