# Stored data for newform 28.2.f.a, downloaded from the LMFDB on 20 April 2024.
{"label": "28.2.f.a", "space_label": "28.2.f", "level": 28, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 343630938140, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 2158202316746619870, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-\\zeta_{12}-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(\\zeta_{12}+\\cdots)q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 28, "char_orbit_label": "f", "char_is_real": false, "Nk2": 112, "analytic_conductor": 0.22358112565958507, "hecke_ring_index": 1, "level_radical": 14, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.591", "prec": 17}, "analytic_rank_proved": true, "char_values": [28, 6, [15, 17], [3, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 7], "conrey_indexes": [3, 19], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.728", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "86.137", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2759.154", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [-2, 0, -6, 0], "traces": [0, 4, -2, 0, 0, -6, 0, 0, -8, 0, 6, 0, 12, 0, 2, 0, 8, -6, 0, 0, 0, 6, -4, 0, -12, -4, -12, 0, -20, 16, -6, 0, 8, 6, 0, 0, 0, -6, 18, 0, 12, 0, 12, 0, 4, 0, -2, 0, 0, -4, 8, 0, 0, 2, -18, 0, 16, -36, -8, 0, -12, -18, 0, 0, 0, 12, -6, 0, 0, 0, 6, 0, 0, 30, -6, 0, 0, -10, 24, 0, -24, 18, 12, 0, 0, 12, -4, 0, 4, 54, 0, 0, 8, 6, -30, 0, -24, 0, -22, 0, 0, -30, 6, 0, 0, -24, -4, 0, 36, -18, 6, 0, 0, -64, 18, 0, 0, 0, 0, 0, 24, -20, 18, 0, -12, 0, 0, 0, -16, 12, 12, 0, 0, 54, -12, 0, 12, -2, -6, 0, 24, 60, 28, 0, 0, -24, 0, 0, 0, -2, -12, 0, -36, 0, 8, 0, -24, 6, -18, 0, 0, -2, -36, 0, 0, -6, 48, 0, -12, 4, -6, 0, -8, -42, 0, 0, 0, 18, -54, 0, 0, 0, -36, 0, -4, 18, 6, 0, 0, -36, -36, 0, 48, 30, 60, 0, 0, 64, 0, 0, 8, 18, 0, 0, -24, -12, 30, 0, 48, 0, -6, 0, 0, -84, 26, 0, 0, -6, 36, 0, -12, -12, 18, 0, 40, 0, 32, 0, 0, -54, 0, 0, -32, 14, 0, 0, -36, 0, -12, 0, 0, -18, -20, 0, 0, 30, -24, 0, 12, -48, -42, 0, 0, 4, -12, 0, -32, 18, 0, 0, 0, 0, -18, 0, -12, 0, -18, 0, 12, 78, 18, 0, 0, 60, 4, 0, 0, 26, -24, 0, -36, -16, -30, 0, 56, 54, 0, 0, 0, -28, 24, 0, 0, 0, 48, 0, 12, 18, -2, 0, 0, -16, 28, 0, 0, 18, 0, 0, 0, -60, 6, 0, -24, 6, 0, 0, 72, -22, 6, 0, 0, 0, 10, 0, 0, 24, -42, 0, 0, -90, 12, 0, -96, 0, -60, 0, -48, 0, -2, 0, 0, -6, 0, 0, 16, 6, 42, 0, 48, 0, 16, 0, -8, -102, 18, 0, 0, 6, 76, 0, 0, -16, -24, 0, 24, -60, -18, 0, 0, 0, 0, 0, 0, 58, 6, 0, 60, 0, 54, 0, 36, 36, 2, 0, 0, 12, -60, 0, 0, 38, -36, 0, 8, 36, -32, 0, 0, 66, 0, 0, -32, 46, -18, 0, 0, 0, 8, 0, 12, 90, -12, 0, 0, -18, 0, 0, -48, 24, -18, 0, 0, -80, -20, 0, -4, 12, 0, 0, -104, -12, 12, 0, 0, 0, -12, 0, 0, -18, -30, 0, 0, 0, 24, 0, -36, -54, 24, 0, -64, 32, 0, 0, 0, -42, 0, 0, 72, -30, 54, 0, -12, 0, -6, 0, 32, -18, 14, 0, 0, -30, 60, 0, 36, -4, -54, 0, 36, 0, -40, 0, 24, -36, 0, 0, 0, -60, 0, 0, 36, 0, 18, 0, 24, -24, 36, 0, 0, 112, 96, 0, 0, 60, -12, 0, 0, 60, -2, 0, -24, 42, 0, 0, 64, -54, -18, 0, 0, 0, -30, 0, -24, 6, 0, 0, 0, -36, -92, 0, 24, -44, 6, 0, 0, 48, 54, 0, 12, -114, 0, 0, -72, 38, 54, 0, -24, 0, -48, 0, 0, 0, 4, 0, 0, -18, -52, 0, 48, -74, 0, 0, 0, -12, 8, 0, 0, 96, 0, 0, -112, 26, -54, 0, 24, 0, 36, 0, 0, -114, -28, 0, 0, 96, -120, 0, -60, 0, 72, 0, -60, 36, 18, 0, 24, -54, 0, 0, 0, 78, 12, 0, 24, 0, -4, 0, -28, 60, 30, 0, 0, 24, -36, 0, 0, 62, 72, 0, 20, 80, 30, 0, 12, 18, 0, 0, 0, 22, -6, 0, 0, 0, 0, 0, -36, 60, -22, 0, 0, -96, -16, 0, 48, 26, 78, 0, 0, -24, -18, 0, -36, -18, 0, 0, 168, -62, -54, 0, -48, 0, 30, 0, 0, -138, 14, 0, 0, -90, 0, 0, 120, -24, 18, 0, 72, 96, 0, 0, 0, -150, 0, 0, -24, -66, 6, 0, 0, 0, -74, 0, 0, -12, 6, 0, 0, 0, 52, 0, -48, 12, -36, 0, 8, -104, 36, 0, -16, -90, 0, 0, 0, 18, -84, 0, -108, 0, -30, 0, -76, 120, -46, 0, 0, 90, 32, 0, 0, -16, 60, 0, 48, 108, 30, 0, -36, 150, 0, 0, -16, 6, 0, 0, 0, 0, -8, 0, -12, 6, 58, 0, 0, 26, 84, 0, 0, 12, -48, 0, 0, -192, 16, 0, 36, 66, 0, 0, -8, 0, 18, 0, 0, 0, -18, 0, 0, 90, 0, 0, 0, 36, -76, 0, 72, 28, 6, 0, 88, -12, -18, 0, 0, 138, 0, 0, 0, 36, -66, 0, -156, 0, -18, 0, 16, 0, 46, 0, 0, -6, -24, 0, 60, -86, 54, 0, -80, -108, 6, 0, 0, 36, 0, 0, 0, 22, -6, 0, -60, 0, -36, 0, 0, -30, -48, 0, 0, -18, -48, 0, 0, -18, -72, 0, 48, -52, 40, 0, -40, -6, 0, 0, 16, -42, -12, 0, 0, 0, 18, 0, 52, -90, -12, 0, 0, -60, 92, 0, -72, 42, 36, 0, 0, 36, -24, 0, 36, 0, 0, 0, 120, -2, -78, 0, 0, 0, 0, 0, 0, -54, 34, 0, 0, -48, 108, 0, -48, 90, 6, 0, -16, -24, -16, 0, 0, -6, 0, 0, 128, 24, 42, 0, 132, 0, 60, 0, -72, -48, -30, 0, 0, -54, 36, 0, 12, -72, 60, 0, -24, 24, 60, 0, 32, 30, 0, 0, 0, -30, 30, 0, 0, 0, 24, 0, -60, 198, -6, 0, 0, 18, 8, 0, 0, 60, -36, 0, -12, -32, 0, 0, -80, 24, 0, 0, -96, 56, 36, 0, 0, 0, -18, 0, 40, 54, -60, 0, 0, -48, -124, 0, -72, 62, -126, 0, 0, 0, -64, 0, 24, -96, 0, 0, -144, 4, 0, 0, 24, 0, 28, 0, 0, 78, 70, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 28, 6, 1, 6, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "28.2.f.a", "char_is_minimal": true, "conrey_index": 3, "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, 0, 0], [1, 0, 0, 0], [0, -1, -1, 1], [0, 1, 0, -2], [0, 2, 0, 0], [-2, 0, 1, 0], [-1, -2, 2, 1], [0, -2, 0, 3], [-2, 0, 0, -2], [0, 0, 0, 0], [1, 1, 1, -2], [0, 1, 0, 0], [4, 0, -2, 0], [2, 0, -4, 0], [2, 3, -3, -1], [0, 0, 0, 3], [0, 0, 4, 0], [-1, 0, -1, 0], [0, 0, 0, 0], [0, -3, 0, -3], [0, -4, 0, 2], [-1, 0, 5, 0], [-1, 0, 0, -1], [0, 1, 0, -1], [-2, -2, -2, 4], [-2, 0, 2, 0], [-4, 2, 2, 2], [0, 6, 0, -3], [-6, 0, 2, 0], [4, 0, 0, 0], [0, 3, -3, -3], [0, -1, 0, 2], [4, -4, -4, 0], [2, 0, -1, 0], [-1, 2, 2, -1], [0, 1, 0, -5], [0, 0, 0, 0], [0, 0, -3, 0], [3, -3, 3, 6], [0, -6, 0, 0], [4, 2, -2, 2], [-2, 0, 4, 0], [5, -4, -4, -1], [0, 0, 0, 2], [0, 0, 2, 0], [0, 0, 0, 0], [-1, -1, 1, 0], [0, 5, 0, 5], [0, 8, 0, -4], [3, 0, -8, 0], [2, 0, 0, -2], [0, -3, 0, 3], [0, 4, 0, -8], [1, 0, -1, 0], [-6, -3, 3, -3], [0, -2, 0, 1], [2, 4, 4, -6], [-9, 0, 0, 0], [0, -4, -4, 4], [0, -3, 0, 6], [-6, 0, 6, 0], [-6, 0, 3, 0], [1, 2, -2, -1], [0, 0, 0, 0], [0, 0, 0, 8], [0, 0, 6, 0], [-1, -1, -1, 2], [0, 3, 0, 0], [0, -2, 0, -2], [1, 0, -2, 0], [-1, -5, 5, 4], [0, 0, 0, -14], [0, 0, 0, 0], [5, 0, 5, 0], [-3, 3, 3, 0], [0, 2, 0, 2], [6, 0, -12, 0], [-3, 0, 1, 0], [6, 0, 0, 6], [0, 9, 0, -9], [-4, 0, -4, 0], [9, 0, -9, 0], [4, -2, -2, -2], [0, -16, 0, 8], [0, -2, 0, 10], [3, 0, 0, 0], [0, 2, -2, -2], [0, 4, 0, -8], [2, -2, -2, 0], [18, 0, -9, 0], [0, 0, 0, 0], [0, 8, 0, 2], [2, 0, 0, 0], [0, 0, 3, 0], [-5, 5, -5, -10], [0, 9, 0, 0], [-8, -4, 4, -4], [-10, 0, 20, 0], [-8, 5, 5, 3], [0, 0, 0, 0], [0, -4, 0, 4]]}