# Stored data for newform 1728.2.i.a, downloaded from the LMFDB on 16 April 2024.
{"label": "1728.2.i.a", "space_label": "1728.2.i", "level": 1728, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 549789370048, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2181448126396180491, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [16, 4, 1]], [7, [4, 2, 1]]], "qexp_display": "q-4\\zeta_{6}q^{5}+(-2+2\\zeta_{6})q^{7}+(-5+5\\zeta_{6})q^{11}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "i", "char_is_real": false, "Nk2": 6912, "analytic_conductor": 13.79814946927725, "hecke_ring_index": 1, "level_radical": 6, "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": [1728, 3, [703, 325, 1217], [3, 3, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [577, 1153], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.023", "prec": 17}, {"__RealLiteral__": 0, "data": "1.879", "prec": 17}, {"__RealLiteral__": 0, "data": "0.050", "prec": 17}, {"__RealLiteral__": 0, "data": "10.394", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "90.034", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, -4, -2], "traces": [0, 2, 0, 0, 0, -4, 0, -2, 0, 0, 0, -5, 0, -2, 0, 0, 0, 6, 0, 2, 0, 0, 0, 6, 0, -11, 0, 0, 0, 2, 0, -4, 0, 0, 0, 16, 0, 16, 0, 0, 0, 1, 0, 7, 0, 0, 0, -2, 0, 3, 0, 0, 0, -8, 0, 40, 0, 0, 0, 5, 0, 0, 0, 0, 0, -8, 0, 13, 0, 0, 0, 16, 0, 6, 0, 0, 0, -10, 0, 8, 0, 0, 0, 12, 0, -12, 0, 0, 0, 20, 0, 8, 0, 0, 0, -4, 0, 11, 0, 0, 0, -12, 0, 6, 0, 0, 0, -10, 0, -16, 0, 0, 0, -2, 0, 24, 0, 0, 0, -6, 0, -14, 0, 0, 0, 48, 0, -4, 0, 0, 0, 16, 0, -2, 0, 0, 0, -3, 0, 13, 0, 0, 0, 20, 0, -16, 0, 0, 0, 18, 0, -18, 0, 0, 0, -16, 0, 20, 0, 0, 0, -24, 0, -40, 0, 0, 0, 16, 0, 9, 0, 0, 0, -18, 0, -22, 0, 0, 0, -24, 0, -4, 0, 0, 0, -32, 0, -15, 0, 0, 0, 6, 0, 3, 0, 0, 0, 8, 0, -4, 0, 0, 0, 4, 0, 4, 0, 0, 0, -5, 0, -28, 0, 0, 0, -56, 0, 16, 0, 0, 0, -6, 0, -14, 0, 0, 0, 3, 0, 14, 0, 0, 0, 42, 0, 16, 0, 0, 0, -6, 0, 23, 0, 0, 0, 12, 0, -2, 0, 0, 0, 42, 0, -60, 0, 0, 0, -5, 0, -16, 0, 0, 0, -6, 0, 16, 0, 0, 0, 0, 0, 24, 0, 0, 0, -55, 0, -14, 0, 0, 0, -18, 0, 28, 0, 0, 0, -4, 0, -16, 0, 0, 0, -30, 0, 20, 0, 0, 0, 12, 0, 14, 0, 0, 0, 0, 0, -18, 0, 0, 0, -18, 0, -13, 0, 0, 0, -18, 0, 10, 0, 0, 0, 6, 0, 44, 0, 0, 0, -4, 0, 4, 0, 0, 0, 52, 0, 25, 0, 0, 0, 40, 0, -40, 0, 0, 0, -1, 0, 16, 0, 0, 0, 35, 0, -32, 0, 0, 0, -28, 0, -36, 0, 0, 0, -12, 0, 0, 0, 0, 0, 8, 0, -22, 0, 0, 0, -8, 0, 2, 0, 0, 0, -20, 0, -40, 0, 0, 0, 6, 0, 18, 0, 0, 0, -64, 0, 64, 0, 0, 0, 5, 0, -8, 0, 0, 0, -40, 0, -25, 0, 0, 0, -20, 0, -96, 0, 0, 0, 4, 0, 8, 0, 0, 0, -33, 0, 0, 0, 0, 0, 60, 0, 2, 0, 0, 0, 6, 0, -8, 0, 0, 0, -27, 0, -40, 0, 0, 0, 62, 0, -10, 0, 0, 0, -16, 0, 7, 0, 0, 0, 18, 0, -16, 0, 0, 0, -14, 0, -52, 0, 0, 0, 35, 0, -11, 0, 0, 0, -18, 0, -16, 0, 0, 0, -88, 0, -44, 0, 0, 0, 7, 0, 6, 0, 0, 0, -16, 0, -21, 0, 0, 0, 48, 0, 96, 0, 0, 0, -24, 0, -6, 0, 0, 0, 24, 0, -10, 0, 0, 0, 6, 0, -24, 0, 0, 0, -12, 0, -13, 0, 0, 0, 2, 0, 20, 0, 0, 0, -30, 0, 64, 0, 0, 0, 32, 0, -33, 0, 0, 0, 2, 0, 16, 0, 0, 0, 20, 0, -28, 0, 0, 0, 15, 0, -8, 0, 0, 0, -11, 0, -13, 0, 0, 0, -132, 0, 6, 0, 0, 0, 24, 0, 20, 0, 0, 0, 9, 0, -4, 0, 0, 0, -12, 0, 48, 0, 0, 0, 40, 0, -19, 0, 0, 0, -56, 0, 20, 0, 0, 0, 8, 0, -24, 0, 0, 0, -45, 0, -21, 0, 0, 0, -20, 0, -41, 0, 0, 0, 48, 0, 56, 0, 0, 0, 8, 0, 6, 0, 0, 0, 5, 0, 15, 0, 0, 0, 12, 0, -50, 0, 0, 0, 22, 0, 64, 0, 0, 0, -12, 0, 32, 0, 0, 0, 16, 0, 24, 0, 0, 0, 0, 0, -2, 0, 0, 0, 28, 0, 22, 0, 0, 0, 30, 0, 24, 0, 0, 0, 8, 0, 8, 0, 0, 0, 52, 0, 3, 0, 0, 0, 84, 0, 16, 0, 0, 0, -24, 0, -20, 0, 0, 0, 24, 0, -40, 0, 0, 0, 64, 0, -24, 0, 0, 0, 22, 0, -30, 0, 0, 0, 21, 0, -34, 0, 0, 0, -130, 0, 98, 0, 0, 0, 6, 0, 72, 0, 0, 0, 10, 0, -52, 0, 0, 0, 144, 0, -36, 0, 0, 0, -30, 0, 16, 0, 0, 0, 10, 0, -10, 0, 0, 0, -84, 0, 88, 0, 0, 0, 1, 0, -40, 0, 0, 0, 80, 0, 36, 0, 0, 0, 8, 0, 0, 0, 0, 0, -24, 0, -6, 0, 0, 0, -15, 0, 48, 0, 0, 0, -34, 0, 110, 0, 0, 0, 80, 0, 7, 0, 0, 0, 50, 0, 28, 0, 0, 0, -56, 0, -28, 0, 0, 0, 9, 0, 64, 0, 0, 0, 4, 0, 25, 0, 0, 0, -72, 0, 56, 0, 0, 0, 48, 0, 30, 0, 0, 0, -10, 0, -5, 0, 0, 0, -56, 0, 144, 0, 0, 0, 40, 0, 26, 0, 0, 0, -48, 0, 40, 0, 0, 0, -60, 0, -26, 0, 0, 0, -36, 0, 4, 0, 0, 0, -2, 0, 48, 0, 0, 0, -16, 0, -24, 0, 0, 0, 8, 0, -7, 0, 0, 0, 24, 0, 60, 0, 0, 0, -64, 0, -108, 0, 0, 0, -16, 0, -88, 0, 0, 0, -6, 0, 3, 0, 0, 0, 120, 0, -116, 0, 0, 0, 28, 0, -6, 0, 0, 0, -27, 0, -6, 0, 0, 0, 78, 0, -48, 0, 0, 0, -6, 0, 15, 0, 0, 0, 12, 0, -42, 0, 0, 0, 40, 0, -52, 0, 0, 0, -11, 0, -50, 0, 0, 0, -36, 0, -16, 0, 0, 0, 84, 0, 32, 0, 0, 0, 8, 0, 60, 0, 0, 0, -20, 0, 15, 0, 0, 0, -8, 0, -76, 0, 0, 0, 40, 0, 16, 0, 0, 0, 27, 0, 60, 0, 0, 0, -22, 0, -32, 0, 0, 0, 44, 0, -19, 0, 0, 0, 0, 0, 34, 0, 0, 0, -72, 0, 40, 0, 0, 0, 14, 0, 55, 0, 0, 0, -112, 0, -36, 0, 0, 0, 60, 0, 64, 0, 0, 0, 55, 0, 52, 0, 0, 0, 16, 0, 77, 0, 0, 0, -48, 0, -24, 0, 0, 0, -32, 0, -46, 0, 0, 0, 1, 0, -14, 0, 0, 0, -38, 0, -80, 0, 0, 0, -18, 0, -24, 0, 0, 0, -32, 0, -60, 0, 0, 0, 112, 0, 0, 0, 0, 0, 5, 0, 40, 0, 0, 0, -18, 0, 43, 0, 0, 0, -60, 0, -24, 0, 0, 0, 39, 0, 40, 0, 0, 0, 56, 0, -32, 0, 0, 0, 96, 0, 62, 0, 0, 0, -20, 0, 0, 0, 0, 0, 55, 0, -84, 0, 0, 0, -64, 0, -86, 0, 0, 0, -22, 0, 25, 0, 0, 0, 28, 0, 18, 0, 0, 0, -94, 0, 4, 0, 0, 0, 51, 0, -24, 0, 0, 0, 40, 0, -31, 0, 0, 0, -184, 0, 48, 0, 0, 0, -36, 0, 52, 0, 0, 0, -41, 0, -24, 0, 0, 0, -20, 0, -66, 0, 0, 0, -18, 0, 62, 0, 0, 0, -8, 0, 8, 0, 0, 0, 18, 0, 20, 0, 0, 0, -14, 0, -3, 0, 0, 0, 24, 0, -84, 0, 0, 0, 10, 0, -44, 0, 0, 0, 120, 0, 4, 0, 0, 0, 4, 0, 13, 0, 0, 0, -12, 0, 88, 0, 0, 0, -37, 0, -20, 0, 0, 0, 35, 0, 49, 0, 0, 0, 128, 0, 58, 0, 0, 0, -18, 0, -30, 0, 0, 0, -12, 0, -30, 0, 0, 0, 48, 0, 48, 0, 0, 0, -56, 0, -9, 0, 0, 0, 44, 0, 44, 0, 0, 0, 30, 0, -56, 0, 0, 0, 12, 0, 12, 0, 0, 0, 24, 0, 0, 0, 0, 0, 16, 0, -12, 0, 0, 0, -48, 0, -30, 0, 0, 0, -43, 0, 4, 0, 0, 0, -124, 0, 54, 0, 0, 0, 48, 0, -120, 0, 0, 0, -8, 0, -46, 0, 0, 0, 112, 0, 6, 0, 0, 0, 10, 0, 4, 0, 0, 0, 10, 0, -4, 0, 0, 0, 0, 0, 144, 0, 0, 0, 21, 0, 36, 0, 0, 0, 112, 0, 16, 0, 0, 0, 12, 0, 124, 0, 0, 0, -3, 0, -22, 0, 0, 0, -54, 0, 8, 0, 0, 0, -144, 0, -160, 0, 0, 0, 32, 0, -62, 0, 0, 0, 40, 0, -14, 0, 0, 0, 16, 0, 40, 0, 0, 0, -10, 0, -120, 0, 0, 0, -4, 0, -26, 0, 0, 0, -110, 0, 112, 0, 0, 0, -57, 0, 16, 0, 0, 0, 2, 0, -26, 0, 0, 0, -132, 0, -96, 0, 0, 0, -39, 0, 8, 0, 0, 0, 56, 0, -15, 0, 0, 0, -4, 0, 60, 0, 0, 0, 8, 0, 12, 0, 0, 0, -51, 0, 0, 0, 0, 0, -130, 0, -72, 0, 0, 0, 36, 0, -8, 0, 0, 0, -78, 0, -72, 0, 0, 0, 24, 0, 12, 0, 0, 0, -49, 0, -72, 0, 0, 0, 8, 0, -28, 0, 0, 0, 104, 0, -56, 0, 0, 0, -45, 0, -28, 0, 0, 0, 12, 0, -28, 0, 0, 0, 4, 0, 144, 0, 0, 0, 6, 0, 56, 0, 0, 0, 40, 0, 42, 0, 0, 0, -86, 0, -56, 0, 0, 0, -12, 0, 6, 0, 0, 0, 14, 0, -12, 0, 0, 0, -30, 0, 144, 0, 0, 0, -48, 0, -4, 0, 0, 0, -42, 0, 48, 0, 0, 0, 72, 0, -180, 0, 0, 0, 16, 0, -16, 0, 0, 0, 33, 0, 4, 0, 0, 0, -32, 0, 26, 0, 0, 0, -90, 0, -56, 0, 0, 0, -57, 0, -4, 0, 0, 0, 24, 0, -286, 0, 0, 0, 18, 0, 40, 0, 0, 0, 100, 0, 46, 0, 0, 0, 20, 0, 4, 0, 0, 0, 30, 0, -55, 0, 0, 0, 32, 0, -80, 0, 0, 0, -56, 0, 20, 0, 0, 0, 80, 0, -36, 0, 0, 0, -5, 0, -23, 0, 0, 0, -200, 0, 8, 0, 0, 0, -18, 0, -4, 0, 0, 0, -16, 0, 20, 0, 0, 0, -128, 0, -88, 0, 0, 0, 18, 0, 61, 0, 0, 0, -42, 0, 6, 0, 0, 0, 14, 0, -280, 0, 0, 0, 0, 0, 60, 0, 0, 0, -88, 0, 17, 0, 0, 0, 12, 0, -24, 0, 0, 0, -68, 0, -58, 0, 0, 0, 100, 0, 56, 0, 0, 0, 20, 0, 110, 0, 0, 0, 72, 0, 26, 0, 0, 0, 59, 0, 24, 0, 0, 0, 96, 0, -30, 0, 0, 0, -42, 0, -33, 0, 0, 0, 20, 0, 14, 0, 0, 0, 0, 0, -160, 0, 0, 0, -12, 0, 11, 0, 0, 0, 10, 0, -6, 0, 0, 0, -48, 0, -64, 0, 0, 0, 45, 0, -42, 0, 0, 0, -88, 0, 23, 0, 0, 0, 60, 0, -76, 0, 0, 0, 44, 0, 28, 0, 0, 0, 0, 0, 16, 0, 0, 0, 98, 0, 0, 0, 0, 0, -4, 0, -24, 0, 0, 0, -36, 0, -90, 0, 0, 0, -66, 0, 144, 0, 0, 0, 27, 0, -80, 0, 0, 0, -12, 0, -6, 0, 0, 0, 220, 0, -4, 0, 0, 0, -67, 0, 36, 0, 0, 0, 36, 0, -28, 0, 0, 0, 52, 0, -48, 0, 0, 0, -30, 0, -14, 0, 0, 0, 72, 0, 6, 0, 0, 0, -64, 0, 72, 0, 0, 0, -36, 0, 60, 0, 0, 0, -6, 0, 88, 0, 0, 0, -168, 0, -112, 0, 0, 0, -128, 0, 4, 0, 0, 0, 10, 0, -1, 0, 0, 0, 116, 0, 56, 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, 9, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "288.2.i.a", "char_is_minimal": false, "conrey_index": 577, "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, 0], [0, 0], [0, 0], [0, -4], [0, 0], [-2, 2], [0, 0], [0, 0], [0, 0], [-5, 5], [0, 0], [0, -2], [0, 0], [0, 0], [0, 0], [3, 0], [0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 6], [0, 0], [-11, 11], [0, 0], [0, 0], [0, 0], [2, -2], [0, 0], [0, -4], [0, 0], [0, 0], [0, 0], [8, 0], [0, 0], [8, 0], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [7, -7], [0, 0], [0, 0], [0, 0], [-2, 2], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [-4, 0], [0, 0], [20, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-8, 8], [0, 0], [0, 13], [0, 0], [0, 0], [0, 0], [8, 0], [0, 0], [3, 0], [0, 0], [0, 0], [0, 0], [0, -10], [0, 0], [8, -8], [0, 0], [0, 0], [0, 0], [12, -12], [0, 0], [0, -12], [0, 0], [0, 0], [0, 0], [10, 0], [0, 0], [4, 0], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [11, -11], [0, 0], [0, 0], [0, 0]]}