# Stored data for newform 546.2.e.b, downloaded from the LMFDB on 08 May 2024.
{"label": "546.2.e.b", "space_label": "546.2.e", "level": 546, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538832418, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1759403302443497814, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [3, 0, 1]], [17, [-3, 1]], [19, [2, 1]], [71, [9, 1]]], "qexp_display": "q-q^{2}+(1+\\zeta_{6})q^{3}+q^{4}+(1-2\\zeta_{6})q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 273, "char_orbit_label": "e", "char_is_real": true, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [546, 2, [365, 157, 379], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [545], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "1.895", "prec": 17}, {"__RealLiteral__": 0, "data": "0.131", "prec": 17}, {"__RealLiteral__": 0, "data": "14.879", "prec": 20}, {"__RealLiteral__": 0, "data": "1.503", "prec": 17}, {"__RealLiteral__": 0, "data": "150.889", "prec": 24}], "related_objects": ["ModularForm/GL2/TotallyReal/2.2.273.1/holomorphic/2.2.273.1-4.1-a", "EllipticCurve/2.2.273.1/4.1/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, 3, 0, 5], "traces": [0, 2, -2, 3, 2, 0, -3, 5, -2, 3, 0, 0, 3, -2, -5, 3, 2, 6, -3, -4, 0, 6, 0, 0, -3, 4, 2, 0, 5, 0, -3, 16, -2, 0, -6, 3, 3, 0, 4, -9, 0, 0, -6, -22, 0, 9, 0, 0, 3, 11, -4, 9, -2, 0, 0, 0, -5, -6, 0, 0, 3, 0, -16, 3, 2, 12, 0, 0, 6, 6, -3, -18, -3, 4, 0, 6, -4, 0, 9, 20, 0, -9, 0, 0, 6, 0, 22, 12, 0, 0, -9, -11, 0, 24, 0, 0, -3, -16, -11, 0, 4, -24, -9, 0, 2, 12, 0, 0, 0, 0, 0, -3, 5, 0, 6, -12, 0, -21, 0, 15, -3, -22, 0, 0, 16, 0, -3, -4, -2, -33, -12, -30, 0, -10, 0, 18, -6, -36, -6, 0, 3, -21, 18, 0, 3, -24, -4, 9, 0, -12, -6, 0, 4, 9, 0, 0, -9, 0, -20, 6, 0, 6, 9, 0, 0, 0, 0, 0, -6, -22, 0, -6, -22, -12, -12, 10, 0, -18, 0, 0, 9, 0, 11, 12, 0, 6, -24, 0, 0, -9, 0, 0, 3, 0, 16, 15, 11, 30, 0, 0, -4, 24, 24, 12, 9, 0, 0, 18, -2, 0, -12, -26, 0, -27, 0, 0, 0, 40, 0, 6, 0, -6, 3, 14, -5, 6, 0, 0, -6, 10, 12, 0, 0, 0, 21, 42, 0, 30, -15, 30, 3, -20, 22, -27, 0, 15, 0, 4, -16, 6, 0, 24, 3, 0, 4, 9, 2, 42, 33, -3, 12, 36, 30, 0, 0, -12, 10, 6, 0, 0, -18, 2, 6, -30, 36, 0, 6, -32, 0, 24, -3, -60, 21, 0, -18, -6, 0, 0, -3, -16, 24, -24, 4, 0, -9, 36, 0, 0, 12, 24, 6, -55, 0, -36, -4, -24, -9, 28, 0, 6, 0, 60, 9, 0, 0, 27, 20, 12, -6, 0, 0, -18, -6, -12, -9, -4, 0, 9, 0, -21, 0, 0, 0, -9, 0, -48, 6, 10, 22, 12, 0, 0, 6, 20, 22, -18, 12, 0, 12, -2, -10, -36, 0, 0, 18, 0, 0, 18, 0, 0, -9, -30, 0, -33, -11, 0, -12, 0, 0, 0, -6, 6, 24, 32, 0, 21, 0, 48, 9, 0, 0, -6, 0, 0, -3, 0, 0, -33, -16, 0, -15, 0, -11, -45, -30, 0, 0, 44, 0, -12, 4, -12, -24, -16, -24, 27, -12, 0, -9, -28, 0, -54, 0, -18, -18, -12, 2, 33, 0, -54, 12, 0, 26, -63, 0, 12, 27, 12, 0, 0, 0, 66, 0, 0, -40, -36, 0, 0, -6, 0, 0, -6, 6, 0, -3, -12, -14, -18, 5, 0, -6, 0, 0, 33, 0, 27, 6, 0, -10, 0, -12, 0, 0, 0, 0, 24, 0, 72, -21, 24, -42, -18, 0, 0, -30, -8, 15, 18, -30, 0, -3, -12, 20, 24, -22, 0, 27, 0, 0, -30, -15, 0, 0, 0, -4, 0, 16, -45, -6, 0, 0, -6, -24, -12, -3, 0, 0, -21, -4, 0, -9, 10, -2, 0, -42, -12, -33, 0, 3, -18, -12, -54, -36, 0, -30, 12, 0, 48, 0, 22, 12, -54, -10, 0, -6, 36, 0, -21, 0, 0, 18, 0, -2, -6, -6, -18, 30, 34, -36, 36, 0, 0, -6, 50, 32, 9, 0, 66, -24, 22, 3, 0, 60, -42, -21, -24, 0, -36, 18, 0, 6, 26, 0, 36, 0, 0, 3, 92, 16, 30, -24, 6, 24, 0, -4, 9, 0, 0, 9, -32, -36, 45, 0, 0, 0, 9, -12, -12, -24, 0, -6, 0, 55, 72, 0, 0, 36, 0, 4, 48, 24, -84, 9, 0, -28, 0, 0, 72, -6, 80, 0, 36, -60, 6, -9, -22, 0, 0, 0, 0, -27, 0, -20, -39, -12, 0, 6, -41, 0, -27, 0, 0, 18, -80, 6, -33, 12, 60, 9, 0, 4, 48, 0, 0, -9, 0, 0, 6, 21, 0, 0, -44, 0, -27, 0, -6, 9, -48, 0, 21, 48, 0, -6, -34, -10, 0, -22, -36, -12, -40, 0, 0, 0, 60, -6, 0, -20, 15, -22, 24, 18, -40, -12, 0, 0, -66, -12, 0, 2, -15, 10, 0, 36, 0, 0, 63, 0, -60, -18, 0, 0, 30, 0, 0, -18, 0, 0, 45, 0, 24, 9, 6, 30, -30, 0, 0, 33, 0, 11, -54, 0, -66, 12, -38, 0, 39, 0, 0, 0, 0, 6, 18, -6, -66, -24, 0, -32, 18, 0, -18, -21, 8, 0, 36, -48, -66, -9, 76, 0, 0, 0, 0, 6, 9, 0, 27, 0, -72, 3, -8, 0, 63, 0, 0, 33, 32, 16, -12, 0, 0, 15, 0, 0, 72, 11, 36, 45, -64, 30, -24, 0, 12, 0, 48, -44, -18, 0, 84, 12, 0, -4, 18, 12, 0, 24, -30, 16, 0, 24, 0, -27, -32, 12, 3, 0, 60, 9, 44, 28, -57, 0, 30, 54, 76, 0, 0, 18, -60, 18, 0, 12, -48, -2, 33, -33, 12, 0, 0, 54, 0, -12, -38, 0, -90, -26, -24, 63, -55, 0, -18, -12, 12, -27, 38, -12, -18, 0, 36, 0, 0, 0, 0, -66, 66, 0, 0, 0, -24, 40, 0, 36, 96, 0, -24, 0, 21, 6, 0, 0, 33, 0, -30, 6, 34, -6, 54, 0, -48, 3, -10, 12, 0, 14, 0, 18, 42, -5, 30, 0, 0, 6, 0, 0, -66, 0, 12, -33, 106, 0, -36, -27, 0, -6, 0, 0, -36, 10, -75, 0, -104, 12, 42, 0, 18, 0, 0, 0, 18, 0, 0, -24, -22, 0, 90, -72, 0, 21, 0, -24, 15, 42, 0, 18, 0, 0, 45, 0, -72, 30, -4, 8, 18, -15, 0, -18, -72, 30, 0, 0, -90, 3, 66, 12, -54, -20, -60, -24, 0, 22, -18, 0, 18, -27, 33, 0, -18, 0, 48, 30, 0, 15, 27, 0, 0, 0, 0, 0, -84, 4, 0, 0, 20, -16, -30, 45, 24, 6, 0, 0, -18, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 273, 7, 1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 7, "minimal_twist": "546.2.e.a", "char_is_minimal": true, "conrey_index": 545, "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, 0], [1, 1], [1, 0], [1, -2], [-1, -1], [2, 1], [-1, 0], [0, 3], [-1, 2], [0, 0], [1, 1], [-3, 4], [-2, -1], [3, -3], [1, 0], [3, 0], [0, -3], [-2, 0], [1, -2], [1, 4], [0, 0], [2, -4], [-1, -1], [2, 0], [3, -4], [-3, 6], [2, 1], [4, -8], [-3, 3], [8, 0], [-1, 0], [0, 0], [-3, 0], [4, -5], [0, 3], [-1, 2], [2, 0], [-7, 5], [-1, 2], [0, 0], [-1, -4], [-11, 0], [0, 0], [6, -3], [-2, 4], [-7, 14], [1, 1], [3, 5], [-2, 0], [3, 3], [-3, 4], [2, -4], [3, -6], [0, 0], [-2, -1], [-2, -2], [-4, 8], [-6, 12], [3, -3], [4, -8], [-8, 0], [-3, 9], [1, 0], [5, 2], [0, 0], [8, -16], [3, 0], [6, -6], [-4, 5], [-9, 0], [0, -3], [2, 0], [1, -2], [2, 2], [-2, 0], [0, 0], [7, -5], [10, 0], [1, -2], [-9, 9], [0, 0], [2, -4], [1, 4], [3, -6], [11, 0], [12, -12], [0, 0], [2, -4], [-6, 3], [-10, 9], [2, -4], [8, 8], [7, -14], [-2, 4], [-1, -1], [-8, 0], [-3, -5], [0, 0], [2, 0]]}