# Stored data for newform 546.2.c.d, downloaded from the LMFDB on 18 April 2024.
{"label": "546.2.c.d", "space_label": "546.2.c", "level": 546, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510936354619938, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 191105832154368716, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [9, 0, 1]], [11, [25, 0, 1]]], "qexp_display": "q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 13, "char_orbit_label": "c", "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": 4, "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": "0.518", "prec": 17}, "analytic_rank_proved": true, "char_values": [546, 2, [365, 157, 379], [2, 2, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [337], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.960", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.967", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "162.372", "prec": 24}], "related_objects": ["EllipticCurve/2.2.13.1/1764.1/n", "ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1764.1-n"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 2, 0, 0], "traces": [0, 2, 0, 2, -2, 0, 0, 0, 0, 2, 6, 0, -2, -6, -2, 0, 2, 6, 0, 0, 0, 0, 10, -2, 0, -8, 4, 2, 0, 10, 6, 0, 0, 0, 0, 6, -2, 0, 2, -6, -6, 0, -2, -2, 0, 0, 0, 0, 2, -2, 0, 6, 6, 28, 0, -30, 2, 0, 0, 0, 0, -6, 0, 0, -2, -12, 10, 0, -6, -2, 0, 0, 0, 0, 14, -8, 0, 10, 4, 0, 0, 2, 0, 0, 0, 0, 0, 10, -10, 0, 6, 4, 2, 0, -16, -6, 0, 0, 0, 0, 8, -36, 0, -22, -4, 6, 0, 36, -2, 0, 0, 0, 0, -12, 2, 0, -10, -6, -28, 0, -6, -28, 0, 0, 0, 0, -2, -24, 0, -2, -18, 14, 0, 2, -16, 0, 0, 0, 0, 40, -6, 0, 20, -20, 2, 0, -22, -2, 0, 0, 0, 0, -2, 6, 0, 0, 6, 26, 0, 28, 6, 0, 0, 0, 0, -30, -12, 0, 2, 10, 18, 0, 2, -52, 0, 0, 0, 0, 32, 20, 0, 4, 6, -6, 0, -42, 0, 0, 0, 0, 0, 34, -2, 0, 4, -12, 2, 0, 10, -10, 0, 0, 0, 0, -6, 0, 0, -2, -6, -10, 0, -26, -28, 0, 0, 0, 0, 0, -18, 0, 30, -18, 14, 0, -2, -8, 0, 0, 0, 0, -6, 10, 0, 28, 4, 48, 0, 0, -6, 0, 0, 0, 0, 2, 6, 0, 0, -4, 0, 0, 6, 34, 0, 0, 0, 0, 2, 36, 0, 14, 12, 10, 0, 48, -10, 0, 0, 0, 0, 0, 6, 0, 6, 4, -6, 0, 2, 56, 0, 0, 0, 0, -16, 28, 0, -6, -30, 0, 0, -16, 30, 0, 0, 0, 0, 84, -14, 0, 12, 6, 8, 0, -30, -36, 0, 0, 0, 0, -10, -22, 0, -16, -4, -12, 0, 6, 0, 0, 0, 0, 0, 36, 2, 0, -2, 24, 8, 0, 0, -16, 0, 0, 0, 0, 14, 48, 0, 66, -24, -12, 0, 0, 2, 0, 0, 0, 0, 56, -10, 0, 8, -6, 10, 0, -28, -60, 0, 0, 0, 0, -6, 36, 0, -28, -4, 66, 0, -64, -2, 0, 0, 0, 0, -52, 30, 0, 16, -30, -2, 0, 6, -24, 0, 0, 0, 0, -32, -2, 0, -60, -18, -6, 0, 14, 4, 0, 0, 0, 0, 2, -8, 0, -16, 0, 36, 0, -10, -70, 0, 0, 0, 0, 22, -28, 0, 36, 4, 40, 0, -70, -6, 0, 0, 0, 0, -24, 20, 0, -36, -20, -6, 0, 2, 8, 0, 0, 0, 0, -22, -30, 0, -2, 12, -12, 0, -96, -32, 0, 0, 0, 0, 0, 12, 0, -16, -18, -2, 0, 52, 6, 0, 0, 0, 0, 10, 0, 0, -14, 6, -16, 0, 26, 28, 0, 0, 0, 0, 28, -8, 0, 6, -28, -20, 0, 28, -12, 0, 0, 0, 0, -6, -56, 0, 30, -6, -30, 0, 20, -12, 0, 0, 0, 0, -12, 2, 0, -10, 10, 24, 0, 18, -22, 0, 0, 0, 0, 2, 80, 0, -52, 18, 54, 0, -32, -14, 0, 0, 0, 0, -44, 84, 0, -2, 0, 32, 0, 16, 20, 0, 0, 0, 0, 0, 4, 0, 54, 6, 56, 0, -6, -40, 0, 0, 0, 0, -42, -40, 0, 0, 6, 6, 0, 20, 18, 0, 0, 0, 0, -20, -60, 0, 64, 20, 34, 0, 8, -2, 0, 0, 0, 0, -12, 4, 0, 22, -12, -12, 0, 2, 0, 0, 0, 0, 0, 10, 18, 0, -10, -4, -90, 0, -96, 2, 0, 0, 0, 0, 46, 2, 0, -18, 32, -6, 0, -16, 0, 0, 0, 0, 0, 0, -2, 0, 32, -6, -58, 0, -10, -26, 0, 0, 0, 0, -26, -16, 0, -28, 6, 50, 0, -6, -16, 0, 0, 0, 0, 6, -4, 0, 140, -16, 0, 0, -2, -18, 0, 0, 0, 0, -60, 30, 0, -40, -18, 12, 0, 14, -10, 0, 0, 0, 0, -2, -22, 0, -8, -10, 16, 0, 4, -18, 0, 0, 0, 0, 18, 2, 0, -2, -84, -6, 0, 52, 10, 0, 0, 0, 0, 32, 28, 0, 4, 4, -14, 0, 48, 48, 0, 0, 0, 0, 0, -32, 0, -6, 90, -20, 0, -68, -40, 0, 0, 0, 0, -4, -40, 0, -14, -6, 2, 0, -6, 6, 0, 0, 0, 0, 80, 0, 0, 42, -4, -28, 0, 0, -36, 0, 0, 0, 0, 6, -96, 0, 34, 20, 90, 0, 36, -8, 0, 0, 0, 0, -18, -34, 0, -62, 56, 2, 0, 30, 36, 0, 0, 0, 0, -4, 14, 0, 0, 12, -100, 0, 10, -2, 0, 0, 0, 0, 48, 0, 0, -10, 18, 24, 0, 10, 36, 0, 0, 0, 0, 60, 110, 0, -6, 0, 0, 0, 0, 6, 0, 0, 0, 0, -24, 6, 0, -38, 4, 0, 0, -6, 88, 0, 0, 0, 0, 2, -50, 0, 56, 6, -6, 0, -42, 10, 0, 0, 0, 0, -8, 60, 0, 26, 72, -16, 0, 28, 28, 0, 0, 0, 0, 6, -6, 0, -84, -30, -100, 0, 0, 60, 0, 0, 0, 0, -16, 0, 0, 30, 32, 18, 0, -2, 6, 0, 0, 0, 0, -30, 14, 0, -82, 18, 84, 0, -4, -14, 0, 0, 0, 0, 16, 12, 0, 2, 6, 42, 0, 8, 84, 0, 0, 0, 0, -30, -24, 0, -36, 12, 94, 0, 60, -16, 0, 0, 0, 0, 20, 6, 0, -30, -40, -10, 0, -22, -22, 0, 0, 0, 0, -28, -16, 0, -90, -4, -64, 0, -12, -48, 0, 0, 0, 0, 6, -10, 0, 0, 44, -8, 0, 6, 108, 0, 0, 0, 0, 42, -6, 0, 62, -42, 36, 0, 96, 2, 0, 0, 0, 0, -56, -2, 0, 64, 24, -6, 0, 8, -160, 0, 0, 0, 0, 0, -12, 0, -16, 4, 2, 0, -56, 0, 0, 0, 0, 0, 76, -28, 0, -6], "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, 13, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "546.2.c.d", "char_is_minimal": true, "conrey_index": 337, "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, 0], [-1, 0], [0, -3], [0, 1], [0, 1], [0, -1], [1, 0], [3, 0], [0, -5], [-1, 0], [-3, -2], [-1, 0], [0, -3], [1, 0], [3, 0], [0, 1], [0, -1], [0, 3], [0, 1], [5, 0], [-1, 0], [0, -1], [-4, 0], [2, -3], [1, 0], [0, -1], [5, 0], [3, 0], [0, 0], [0, 1], [0, -5], [0, 3], [3, 0], [-1, 0], [0, -7], [1, 0], [-3, -2], [-3, 0], [0, 0], [-1, 0], [-1, 0], [0, 5], [0, -3], [0, -1], [0, 8], [1, 0], [-1, 0], [0, -4], [3, 0], [3, 2], [14, 0], [0, 1], [-15, 0], [1, 0], [0, -1], [0, 5], [0, 14], [0, 3], [-3, 0], [0, 0], [0, 1], [-1, 0], [-6, 9], [5, 0], [0, 8], [-3, 0], [-1, 0], [0, 3], [0, -10], [0, -1], [0, 11], [7, 0], [-4, 0], [0, 1], [5, 0], [2, -3], [0, 0], [0, -3], [1, 0], [0, 0], [0, 6], [0, -1], [0, -9], [0, -1], [5, 0], [-5, 0], [0, -16], [3, 0], [2, -3], [1, 0], [0, 0], [-8, 0], [-3, 0], [0, 1], [0, -2], [0, -1], [0, -5], [4, 0]]}