# Stored data for newform 1216.2.i.b, downloaded from the LMFDB on 07 October 2024. {"Nk2": 4864, "analytic_conductor": 9.709808885787695, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 19, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [1216, 3, [191, 837, 705], [3, 3, 1]], "cm_discs": [], "conrey_index": 577, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[3, [1, 1, 1]], [5, [16, 4, 1]], [7, [0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504149416740032, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1216.2.i.b", "level": 1216, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 19], "level_radical": 38, "minimal_twist": "152.2.i.b", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+(-1+\\zeta_{6})q^{3}+(-4+4\\zeta_{6})q^{5}+2\\zeta_{6}q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1216.2.i", "trace_display": [0, -1, -4, 0], "trace_hash": 726220335524297580, "trace_moments": [{"__RealLiteral__": 0, "data": "0.061", "prec": 17}, {"__RealLiteral__": 0, "data": "1.908", "prec": 17}, {"__RealLiteral__": 0, "data": "0.245", "prec": 17}, {"__RealLiteral__": 0, "data": "11.095", "prec": 20}, {"__RealLiteral__": 0, "data": "1.147", "prec": 17}, {"__RealLiteral__": 0, "data": "99.337", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, "traces": [0, 2, 0, -1, 0, -4, 0, 0, 0, 2, 0, 6, 0, 2, 0, -4, 0, -2, 0, 1, 0, 0, 0, 6, 0, -11, 0, -10, 0, -4, 0, 20, 0, -3, 0, 0, 0, -4, 0, -4, 0, -9, 0, 4, 0, -16, 0, -12, 0, -14, 0, -2, 0, -2, 0, -12, 0, -8, 0, 1, 0, -8, 0, 0, 0, -16, 0, -9, 0, -12, 0, -6, 0, 9, 0, 22, 0, 0, 0, -4, 0, -1, 0, -10, 0, -8, 0, 8, 0, 18, 0, 0, 0, -10, 0, -32, 0, -1, 0, 6, 0, 12, 0, 28, 0, 0, 0, 32, 0, 0, 0, 2, 0, -2, 0, -48, 0, -4, 0, 0, 0, -4, 0, -9, 0, 48, 0, -6, 0, 4, 0, 15, 0, 0, 0, 20, 0, -9, 0, 13, 0, 24, 0, 6, 0, 32, 0, 7, 0, -10, 0, -4, 0, -8, 0, -40, 0, 8, 0, 4, 0, 0, 0, -22, 0, -12, 0, 16, 0, 9, 0, -14, 0, -26, 0, 0, 0, 1, 0, 18, 0, 14, 0, 16, 0, 8, 0, -6, 0, 0, 0, -24, 0, 6, 0, 8, 0, 36, 0, -18, 0, 18, 0, 0, 0, -36, 0, -12, 0, 3, 0, 12, 0, -6, 0, 16, 0, 0, 0, 9, 0, -8, 0, 10, 0, 22, 0, 38, 0, 16, 0, 0, 0, -11, 0, 96, 0, -4, 0, -24, 0, -21, 0, -16, 0, 28, 0, -14, 0, 5, 0, -5, 0, 18, 0, 16, 0, -3, 0, 0, 0, 8, 0, 16, 0, 16, 0, -36, 0, 4, 0, -20, 0, 0, 0, -33, 0, -24, 0, 20, 0, 13, 0, -13, 0, 28, 0, 0, 0, 13, 0, -1, 0, 8, 0, 4, 0, -30, 0, -12, 0, 0, 0, -24, 0, 64, 0, -25, 0, -14, 0, 4, 0, 19, 0, 0, 0, 6, 0, -12, 0, -16, 0, -16, 0, 22, 0, 0, 0, 0, 0, 26, 0, -4, 0, 72, 0, -3, 0, 1, 0, 60, 0, 0, 0, 24, 0, 9, 0, 56, 0, -10, 0, 22, 0, -24, 0, 0, 0, -2, 0, -37, 0, 2, 0, 36, 0, -26, 0, -36, 0, 0, 0, -8, 0, -24, 0, 8, 0, -24, 0, 12, 0, -8, 0, 0, 0, 16, 0, 4, 0, -24, 0, 15, 0, -16, 0, -14, 0, 0, 0, 3, 0, 20, 0, -4, 0, -12, 0, 35, 0, 18, 0, 0, 0, 20, 0, -26, 0, 24, 0, -22, 0, 24, 0, 44, 0, 0, 0, -12, 0, -30, 0, -10, 0, -16, 0, -42, 0, -14, 0, -14, 0, -1, 0, -144, 0, -10, 0, 66, 0, -27, 0, 2, 0, 0, 0, -22, 0, 10, 0, 6, 0, 68, 0, -40, 0, 10, 0, 0, 0, 8, 0, 12, 0, 77, 0, 4, 0, 20, 0, -4, 0, 0, 0, -4, 0, 52, 0, 11, 0, -16, 0, 16, 0, -48, 0, 0, 0, -7, 0, -32, 0, -6, 0, -96, 0, 9, 0, 16, 0, 0, 0, -5, 0, -56, 0, -36, 0, -26, 0, 2, 0, -20, 0, 0, 0, -20, 0, -13, 0, 4, 0, -36, 0, -64, 0, -9, 0, -42, 0, 4, 0, -28, 0, 0, 0, -28, 0, 16, 0, 28, 0, 0, 0, 8, 0, -40, 0, 16, 0, -6, 0, 22, 0, 4, 0, 0, 0, -92, 0, 34, 0, 12, 0, 66, 0, -74, 0, 6, 0, 0, 0, -6, 0, -16, 0, -4, 0, 10, 0, -18, 0, 21, 0, 0, 0, 36, 0, 38, 0, -26, 0, 18, 0, 8, 0, 0, 0, 0, 0, 24, 0, -22, 0, 72, 0, -3, 0, -40, 0, -30, 0, 0, 0, -41, 0, -24, 0, 4, 0, -8, 0, 12, 0, 48, 0, -14, 0, -24, 0, -33, 0, -5, 0, -32, 0, 28, 0, 3, 0, 0, 0, -72, 0, 60, 0, 36, 0, -12, 0, 20, 0, 4, 0, 0, 0, 24, 0, 10, 0, -24, 0, 60, 0, 55, 0, 4, 0, 0, 0, -19, 0, -56, 0, 72, 0, -8, 0, 4, 0, 72, 0, 0, 0, -104, 0, -18, 0, -11, 0, -12, 0, -2, 0, -48, 0, 0, 0, 18, 0, -16, 0, 60, 0, -48, 0, 12, 0, -34, 0, 0, 0, 42, 0, -44, 0, -8, 0, 26, 0, 8, 0, -44, 0, 28, 0, -27, 0, 5, 0, -2, 0, -6, 0, -40, 0, -10, 0, 0, 0, 38, 0, 10, 0, 8, 0, 14, 0, -36, 0, 34, 0, 0, 0, 16, 0, 4, 0, -2, 0, 6, 0, 52, 0, -110, 0, 0, 0, -72, 0, -18, 0, 20, 0, 32, 0, 82, 0, 16, 0, 0, 0, 16, 0, -8, 0, -84, 0, 48, 0, -36, 0, 27, 0, 0, 0, 4, 0, 42, 0, 0, 0, -20, 0, 44, 0, 32, 0, 0, 0, -38, 0, -26, 0, 66, 0, 55, 0, 24, 0, 12, 0, 14, 0, -128, 0, -100, 0, 0, 0, 13, 0, -26, 0, 36, 0, 0, 0, -13, 0, -12, 0, 42, 0, -8, 0, 35, 0, -29, 0, 0, 0, -12, 0, -104, 0, -26, 0, -12, 0, 18, 0, -4, 0, 0, 0, 40, 0, -4, 0, 14, 0, 43, 0, -8, 0, 32, 0, 0, 0, -3, 0, 84, 0, -36, 0, -12, 0, -40, 0, 8, 0, 0, 0, -112, 0, -49, 0, -24, 0, 28, 0, -30, 0, -32, 0, 0, 0, 52, 0, -25, 0, -24, 0, 22, 0, 28, 0, -21, 0, -7, 0, -2, 0, -24, 0, -11, 0, -38, 0, -10, 0, -108, 0, 0, 0, 28, 0, 36, 0, -12, 0, -1, 0, 48, 0, 24, 0, 0, 0, 138, 0, 32, 0, 24, 0, 54, 0, 14, 0, -53, 0, 0, 0, 22, 0, -94, 0, 54, 0, 0, 0, 32, 0, -72, 0, 0, 0, 48, 0, 8, 0, -13, 0, 144, 0, -32, 0, 20, 0, 0, 0, 2, 0, -36, 0, 14, 0, 34, 0, -3, 0, -6, 0, 0, 0, -2, 0, 34, 0, -22, 0, -30, 0, 198, 0, -16, 0, 0, 0, 50, 0, -34, 0, -48, 0, 32, 0, -6, 0, 9, 0, 0, 0, -96, 0, -28, 0, 25, 0, -47, 0, -4, 0, 48, 0, 0, 0, -11, 0, 36, 0, -56, 0, 48, 0, -3, 0, 38, 0, 0, 0, 8, 0, -88, 0, -2, 0, -10, 0, 72, 0, 11, 0, 0, 0, 2, 0, -4, 0, -40, 0, 16, 0, -72, 0, 33, 0, 0, 0, 52, 0, 32, 0, 16, 0, 45, 0, 40, 0, 36, 0, 0, 0, 40, 0, -28, 0, 4, 0, 8, 0, -8, 0, 48, 0, -42, 0, 82, 0, 8, 0, 84, 0, -76, 0, 12, 0, 36, 0, 0, 0, 12, 0, -32, 0, -40, 0, -8, 0, 28, 0, 53, 0, 0, 0, -36, 0, 56, 0, -20, 0, 20, 0, -44, 0, -8, 0, 0, 0, 134, 0, 12, 0, -132, 0, 96, 0, 60, 0, -24, 0, 0, 0, 32, 0, 39, 0, 72, 0, -14, 0, 6, 0, 48, 0, 0, 0, 0, 0, 53, 0, 3, 0, 168, 0, -12, 0, -40, 0, 0, 0, 28, 0, 128, 0, -122, 0, 12, 0, 6, 0, -36, 0, 77, 0, -70, 0, -6, 0, -40, 0, 18, 0, -8, 0, 34, 0, 0, 0, 18, 0, -6, 0, 20, 0, -32, 0, -11, 0, -26, 0, 0, 0, 40, 0, -12, 0, 43, 0, -4, 0, -22, 0, -144, 0, 0, 0, 60, 0, -90, 0, 63, 0, -22, 0, 22, 0, 50, 0, 0, 0, 21, 0, 24, 0, -12, 0, 21, 0, -110, 0, 60, 0, 0, 0, 47, 0, 20, 0, 2, 0, 72, 0, 32, 0, -49, 0, 0, 0, -6, 0, -24, 0, 64, 0, -14, 0, 52, 0, -42, 0, 70, 0, -22, 0, 66, 0, 2, 0, -78, 0, 40, 0, 72, 0, 0, 0, 28, 0, -40, 0, -8, 0, 16, 0, -33, 0, -48, 0, 0, 0, -27, 0, -80, 0, 12, 0, -4, 0, 92, 0, -48, 0, 0, 0, -36, 0, -66, 0, 11, 0, 10, 0, 144, 0, -2, 0, 0, 0, -42, 0, 6, 0, 48, 0, 72, 0, -34, 0, 32, 0, 0, 0, -160, 0, -18, 0, 52, 0, -5, 0, 48, 0, -104, 0, 0, 0, -21, 0, 10, 0, 32, 0, -52, 0, 0, 0, 12, 0, 28, 0, -44, 0, 11, 0, -39, 0, -6, 0, 10, 0, -114, 0, 0, 0, -40, 0, 40, 0, 45, 0, 8, 0, -104, 0, -28, 0, 0, 0, 8, 0, 60, 0, 8, 0, -120, 0, 59, 0, -26, 0, 0, 0, -16, 0, -22, 0, -2, 0, -36, 0, -16, 0, -22, 0, 0, 0, -8, 0, -90, 0, 94, 0, 60, 0, 18, 0, 66, 0, 0, 0, -44, 0, -48, 0, -7, 0, -53, 0, -32, 0, -32, 0, 0, 0, -27, 0, 12, 0, 30, 0, -72, 0, 48, 0, 18, 0, -140, 0, 36, 0, 21, 0, -88, 0, -32, 0, 39, 0, -110, 0, 0, 0, -100, 0, -8, 0, -8, 0, 54, 0, -4, 0, -56, 0, 0, 0, -6, 0, 72, 0, 30, 0, -8, 0, -104, 0, -84, 0, 0, 0, -1, 0, -152, 0, -68, 0, 40, 0, 59, 0, -4, 0, 0, 0, -5, 0, 43, 0, -20, 0, 12, 0, -48, 0, -13, 0, 0, 0, -8, 0, -5, 0, 96, 0, -16, 0, 18, 0, 58, 0, 0, 0, -64, 0, -60, 0, 37, 0, 18, 0, 6, 0, 56, 0, 21, 0, -20, 0, 70, 0, -8, 0, 48, 0, -58, 0, -28, 0, 0, 0, -72, 0, 0, 0, 66, 0, -30, 0, 56, 0, -20, 0, 0, 0, 40, 0, -2, 0, 12, 0, 4, 0, -52, 0, -26, 0, 0, 0, -12, 0, 26, 0, 32, 0, 57, 0, -32, 0, 80, 0, 0, 0, -99, 0, -8, 0, 108, 0, -40, 0, -24, 0, -12, 0, 0, 0, -11, 0, -126, 0, -48, 0, 4, 0, 3, 0, 46, 0, 0, 0, 60, 0, -120, 0, 46, 0, -48, 0, -8, 0, -17, 0, 0, 0, -48, 0, -24, 0, -74, 0, -68, 0, 66, 0, 24, 0, 0, 0, 37, 0, 18, 0, 36, 0, 24, 0, 24, 0, 12, 0, 0, 0, -112, 0, 56, 0, 12, 0, -28, 0, 73, 0, 80, 0, 0, 0, -104, 0, -4, 0, 36, 0, -44, 0, -80, 0, -32, 0, 0, 0, 36, 0, 132, 0, 50, 0, -42, 0, 18, 0, 6, 0, 0, 0, -118, 0, 16, 0, 36, 0, -66, 0, -8, 0, -76, 0, 0, 0, 61, 0, 13, 0, 44, 0, -26, 0, 45, 0, 12, 0, 28, 0, 8, 0, -48, 0, -32, 0, 0, 0, -36, 0, -198, 0, 0, 0, 10, 0, 12, 0, 24, 0, 208, 0, 48, 0, -22, 0, 0, 0, -8, 0, 72, 0, 28, 0, 27, 0, 6, 0, 0, 0, 0, 0, 20, 0, 27, 0, 36, 0, -12, 0, 16, 0, -44, 0, 0, 0, 20, 0, -102, 0, -41, 0, -56, 0, 40, 0, -42, 0, 0, 0, 32, 0, 4, 0, 76, 0, -80, 0, 16, 0, 48, 0, 0, 0, 48, 0, -44, 0, -78, 0, -24, 0, -40, 0, -30, 0, 28, 0, -51, 0, -32, 0, 30, 0, -84, 0, 2, 0, -33, 0, 0, 0, 216, 0, -5, 0, 56, 0, -8, 0, -32, 0, -40, 0, 0, 0, -14, 0, -36, 0, -32, 0, 3, 0, 100, 0, 2, 0, 0, 0, 48, 0, 14, 0, 36, 0, 4, 0, -4, 0, -120, 0, 0, 0, 54, 0, -45, 0, -76, 0, 88, 0, 24, 0, -52, 0, 0, 0, -40, 0, -56, 0, -102, 0, -8, 0, 42, 0, -37, 0, 0, 0, -10, 0, -56, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [-1, 1], [0, 0], [-4, 4], [0, 0], [0, 0], [0, 0], [0, 2], [0, 0], [3, 0], [0, 0], [0, 2], [0, 0], [0, -4], [0, 0], [-2, 2], [0, 0], [-2, 5], [0, 0], [0, 0], [0, 0], [0, 6], [0, 0], [0, -11], [0, 0], [-5, 0], [0, 0], [0, -4], [0, 0], [10, 0], [0, 0], [-3, 3], [0, 0], [0, 0], [0, 0], [-2, 0], [0, 0], [-2, 0], [0, 0], [-9, 9], [0, 0], [4, -4], [0, 0], [-8, 0], [0, 0], [0, -12], [0, 0], [-7, 0], [0, 0], [0, -2], [0, 0], [0, -2], [0, 0], [-12, 12], [0, 0], [-3, -2], [0, 0], [1, -1], [0, 0], [0, -8], [0, 0], [0, 0], [0, 0], [-8, 0], [0, 0], [0, -9], [0, 0], [-6, 0], [0, 0], [-6, 6], [0, 0], [9, -9], [0, 0], [11, 0], [0, 0], [0, 0], [0, 0], [-4, 4], [0, 0], [-1, 1], [0, 0], [-5, 0], [0, 0], [0, -8], [0, 0], [4, 0], [0, 0], [0, 18], [0, 0], [0, 0], [0, 0], [-10, 10], [0, 0], [-12, -8], [0, 0], [-1, 1], [0, 0], [0, 6], [0, 0]]}