# Stored data for newform 1386.2.k.t, downloaded from the LMFDB on 25 April 2024.
{"label": "1386.2.k.t", "space_label": "1386.2.k", "level": 1386, "weight": 2, "hecke_orbit": 20, "hecke_orbit_code": 85569080148362602, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 2052671613377138141, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [4, 8, 14, 4, 1]], [13, [-7, 2, 1]], [17, [784, -112, 44, 4, 1]], [23, [196, -56, 30, 4, 1]]], "qexp_display": "q-\\beta _{2}q^{2}+(-1-\\beta _{2})q^{4}+(-\\beta _{1}+2\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "k", "char_is_real": false, "Nk2": 5544, "analytic_conductor": 11.06726572014946, "hecke_ring_index": 1, "level_radical": 462, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": "0.023", "prec": 17}, "analytic_rank_proved": true, "char_values": [1386, 3, [155, 199, 1135], [3, 1, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7, 11], "conrey_indexes": [793, 991], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.048", "prec": 17}, {"__RealLiteral__": 0, "data": "3.761", "prec": 17}, {"__RealLiteral__": 0, "data": "0.054", "prec": 17}, {"__RealLiteral__": 0, "data": "52.795", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1291.239", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 0, -4, -2], "traces": [0, 4, 2, 0, -2, -4, 0, -2, -4, 0, 4, 2, 0, -4, 2, 0, -2, -4, 0, 4, 8, 0, 4, -4, 0, -2, -2, 0, 4, 12, 0, 8, 2, 0, -8, 8, 0, 16, -4, 0, 4, 16, 0, 0, 2, 0, 4, -4, 0, 10, -4, 0, 2, -4, 0, -8, 2, 0, 6, -14, 0, -18, 16, 0, 4, -4, 0, -14, -4, 0, -8, 16, 0, 16, -16, 0, -8, -4, 0, 18, -4, 0, 8, -8, 0, 48, 0, 0, -2, 8, 0, -22, 8, 0, 4, 12, 0, -4, 20, 0, -2, 18, 0, -24, 4, 0, -8, 8, 0, -16, -4, 0, -2, 44, 0, 4, -6, 0, -28, 8, 0, -2, 18, 0, 8, 0, 0, 12, 2, 0, 4, -4, 0, -8, -28, 0, 4, -22, 0, 0, -16, 0, 8, -2, 0, -28, 32, 0, -32, 24, 0, 6, -4, 0, -2, -32, 0, -24, -18, 0, -8, -40, 0, 6, -8, 0, -4, -4, 0, -16, 24, 0, 0, -14, 0, 4, -4, 0, -8, -18, 0, -8, -26, 0, 4, 28, 0, 4, 8, 0, 24, -20, 0, -24, -2, 0, 10, 36, 0, -20, 2, 0, 36, -54, 0, -12, 24, 0, 2, 8, 0, 24, -4, 0, -8, -16, 0, -16, -32, 0, 4, -28, 0, 40, -4, 0, 22, -52, 0, -24, 8, 0, -12, 0, 0, 16, -14, 0, 52, 4, 0, -16, 2, 0, 36, -40, 0, 4, -8, 0, 0, 48, 0, -8, 6, 0, -2, -22, 0, 28, 8, 0, 4, 14, 0, 72, 8, 0, -14, 16, 0, 22, 8, 0, -44, 2, 0, 2, 0, 0, -8, 16, 0, 44, -8, 0, -4, 4, 0, -38, 28, 0, 16, 32, 0, 64, -16, 0, -24, 28, 0, -48, 12, 0, 4, -28, 0, 0, 2, 0, -16, 8, 0, 30, -48, 0, -36, 40, 0, 6, -4, 0, -8, -48, 0, -30, -6, 0, -16, -76, 0, 34, 4, 0, -2, 80, 0, -96, -8, 0, -24, -8, 0, -68, 0, 0, 14, 32, 0, 0, 50, 0, -2, -28, 0, 4, -16, 0, -36, 30, 0, 26, -4, 0, -4, -56, 0, -4, -4, 0, 56, 8, 0, 6, -4, 0, 4, 52, 0, 4, 12, 0, 20, 24, 0, 16, -48, 0, 2, -20, 0, -80, -10, 0, 18, 24, 0, -44, -40, 0, 4, 14, 0, -8, 18, 0, -42, 32, 0, 20, 12, 0, 48, 28, 0, 48, -2, 0, 4, 48, 0, 48, 12, 0, 4, -68, 0, -42, -16, 0, 16, -38, 0, 48, -8, 0, -16, -4, 0, 18, 8, 0, -56, -20, 0, -8, 20, 0, -2, -112, 0, 8, -22, 0, -104, 32, 0, 12, 24, 0, 4, -12, 0, 40, -6, 0, 0, -68, 0, 28, 32, 0, 14, 0, 0, -40, 44, 0, 2, -38, 0, -24, -32, 0, 4, -4, 0, 8, 18, 0, 4, -88, 0, -76, -4, 0, -16, 52, 0, -16, 0, 0, 24, 68, 0, -88, -4, 0, -6, -4, 0, -32, -4, 0, 22, -44, 0, -8, 32, 0, 4, 0, 0, 0, 8, 0, 28, 16, 0, 2, 36, 0, 16, -32, 0, 36, 14, 0, 32, -10, 0, 54, -22, 0, 4, 16, 0, 32, -22, 0, -2, 28, 0, 54, 4, 0, 0, 32, 0, 64, 8, 0, 8, 4, 0, -52, 88, 0, -16, -8, 0, -16, -2, 0, 20, -88, 0, 42, 38, 0, 56, 124, 0, 4, -16, 0, 16, 140, 0, 32, 32, 0, 16, -12, 0, -144, -48, 0, -28, 40, 0, -8, -48, 0, 6, -4, 0, 52, 8, 0, -56, 52, 0, -12, 0, 0, 4, 100, 0, -24, 16, 0, 16, 80, 0, -6, -30, 0, -24, -32, 0, 144, -18, 0, -40, 24, 0, 38, 12, 0, 4, -26, 0, 12, 32, 0, -24, -16, 0, 14, -60, 0, -12, 0, 0, -12, -8, 0, -8, 48, 0, -4, -34, 0, 8, -24, 0, 36, 2, 0, 40, -36, 0, -40, -48, 0, 8, -48, 0, -22, -48, 0, 8, 30, 0, 56, -34, 0, 0, -52, 0, -42, 28, 0, 64, 0, 0, 0, 0, 0, 46, -20, 0, -28, 2, 0, -56, -36, 0, -24, -4, 0, -8, -32, 0, -8, -18, 0, -30, -20, 0, -36, 52, 0, 4, -70, 0, -24, 22, 0, -28, -64, 0, 26, -8, 0, -8, 14, 0, 20, 28, 0, 88, 8, 0, 32, -6, 0, -8, -52, 0, -80, -4, 0, 26, 48, 0, 56, 2, 0, -12, 28, 0, 32, 40, 0, -24, 6, 0, 24, 8, 0, -24, 24, 0, 8, 4, 0, -40, 12, 0, 8, -40, 0, -20, 64, 0, 4, -18, 0, 48, -46, 0, 34, 44, 0, -20, 8, 0, -176, 2, 0, -14, -16, 0, -8, -16, 0, -18, -48, 0, 16, 12, 0, 16, 48, 0, 16, 40, 0, 24, -42, 0, 36, 24, 0, 26, -56, 0, -52, -48, 0, -4, -76, 0, -32, -4, 0, 24, 40, 0, 48, 24, 0, -12, 32, 0, -2, 8, 0, 68, 44, 0, 56, -36, 0, -8, -24, 0, -14, 32, 0, -76, 28, 0, -20, 24, 0, 8, 36, 0, -10, 16, 0, -8, -48, 0, 6, -18, 0, 4, 76, 0, 12, -28, 0, 20, -26, 0, 102, -16, 0, -20, -16, 0, 128, 2, 0, -56, 24, 0, -120, 16, 0, -44, -8, 0, -44, -52, 0, -8, 88, 0, -4, -12, 0, 48, 8, 0, -16, -4, 0, -6, -96, 0, 0, 20, 0, 6, -30, 0, 40, 0, 0, 68, 24, 0, -72, 50, 0, 16, 38, 0, -28, 28, 0, 0, 64, 0, -24, -20, 0, -8, 40, 0, -48, -2, 0, -76, 44, 0, 30, 24, 0, -16, 40, 0, -32, 2, 0, 4, 70, 0, 0, 16, 0, -18, 80, 0, 16, 44, 0, -44, -20, 0, -60, -152, 0, -8, 48, 0, 40, -8, 0, 68, 136, 0, -32, 16, 0, 0, 4, 0, -44, -24, 0, 34, -72, 0, 144, -44, 0, 4, -52, 0, 104, -12, 0, 4, 20, 0, 192, -4, 0, -2, 8, 0, -42, 44, 0, -88, -38, 0, -20, -4, 0, 4, 8, 0, 4, -4, 0, 0, 72, 0, -12, 0, 0, 4, 12, 0, -16, 14, 0, -16, -20, 0, -12, 4, 0, -36, -12, 0, 32, 8, 0, -16, -2, 0, -4, 72, 0, 28, 32, 0, -64, 16, 0, 10, -152, 0, -80, -54, 0, -44, 64, 0, -24, -4, 0, 8, -56, 0, -160, 16, 0, 22, -24, 0, 48, -4, 0, -28, 0, 0, 112, 36, 0, 2, 24, 0, -18, 0, 0, 64, -44, 0, 78, 32, 0, 16, -64, 0, -94, -8, 0, 8, -40, 0, 12, 52, 0, 44, -48, 0, 192, -8, 0, 8, -76, 0, -102, -32, 0, 2, -16, 0, 128, 16, 0, -44, 34, 0, -64, 84, 0, 76, -56, 0, 28, 28, 0, 116, 64, 0, -4, -4, 0, -32, -106, 0, -30, -16, 0, 70, -184, 0, 16, 16, 0, -32, 28, 0, 56, 32, 0, 12, -72, 0, 16, -96, 0, -24, 62, 0, -64, -56, 0, 80, 16, 0, 0, -4, 0, 0, 40, 0, 64, -6, 0, -8, -38, 0, -8, -52, 0, 4, 160, 0, -152, -28, 0, -52, 6, 0, -86, -24, 0, 0, -6, 0, -28, 2, 0, 50, 20, 0, -44, -48, 0, 32, 16, 0, 22, 8, 0, 16, 128, 0, -40, 6, 0, -60, 36, 0, -8, 24, 0, -16, -180, 0, 36, 72, 0, 18, -4, 0, -44, -80, 0, -24, 32, 0, -80, -20, 0, 6, -32, 0, -40, 8, 0, -52, -68, 0, -4, 6, 0, 40, 40, 0, -22, 24, 0, -32, -56, 0, 40, -14, 0, -30, -24, 0, -48, -6, 0, 0, 8, 0, -44, -24, 0, 8, -2, 0, -192, 68, 0, 24, -6, 0, 62, -8, 0, -68, -116, 0, 78, 4, 0, -60, -4, 0, 0, -36, 0, 4, 4, 0, 32, -40, 0, -18, 24, 0, -96, -20, 0, 48, -4, 0, 48, 16, 0, 48, 88, 0, 32, -26, 0, -24, 28, 0, 84, 16, 0, 60, -16, 0, -58, 28, 0, 34, -72, 0, 0, 0, 0, -104, -90, 0, 30, 42, 0, 14, -24, 0, 56, 32, 0, 0, 32, 0, 40, 0, 0, 0, 6, 0, -180, -4, 0, -10, -60, 0, -52, -56, 0, 4, 62, 0, 168, -28, 0, -42, -168, 0, 64, 24, 0, -8, 126, 0, 12, 8, 0, -16, -8, 0, 28, -4, 0, 18, -66, 0, 12, -60, 0, 20, 48, 0, -8, -48, 0, 26, -140, 0, -6, 8, 0, -140, -52, 0, -24, -12, 0, 26, -32, 0, -28, 28, 0, -128, -16, 0, -24, -26, 0, -4, -12, 0, -36, -4, 0, -14, -30, 0, 0, 40, 0, -28, 28, 0, 132, 80, 0, 4, -14, 0, 120, 64, 0, -12, -14, 0, 28, -4, 0, 16, 100, 0, -24, 80, 0, -8, 80, 0, 22, -26, 0, 24, -48, 0, 160, 28, 0, -2, 68, 0, -40, -24, 0, -28, 16, 0, -28, -56, 0, 20, 0, 0, 48, -48, 0, 12, 28, 0, -124, 12, 0, -8, -16, 0, -32, 24, 0, 48, 56, 0, 24, -8, 0, 2, -32, 0, 40, -20, 0, -12, -36, 0, -32, 16, 0, 40, 44, 0, -8, -10, 0, 32, -18, 0, 2, 8, 0, -36, -48, 0, -44, 24, 0, -2, 60, 0, 112, -34, 0, 88, 104, 0, -16, 20, 0, 4, -56, 0, 12, -88, 0, -2, -64, 0, -120, -28, 0, 16, 44, 0, -16, -52, 0, -8, -126, 0, 88, -36, 0, -96, -20, 0, 36, 8, 0, 54, 64, 0, 56, -16, 0, 96, 12, 0, -76, -16, 0, 20, 64, 0, 48, 12, 0, 42, 16, 0, -32, 72, 0, -24, -28, 0, -156, -2, 0, -28, 48, 0, 20, -104, 0, -96, -6, 0, 80, -2, 0, -116, 16, 0, 64, 32, 0, -8, -182, 0, -62, -24, 0, 20, -88, 0, -92, 24, 0, -24, 84, 0, 32, -24, 0, -32, 8, 0, -28, -4, 0, 4, -2, 0, 2, 136, 0, 88, -4, 0, -16, 28, 0, 6, 64, 0, -58, 8, 0, -48, 104, 0, 68, 14, 0, 16, 20, 0, 168, -38, 0, -28, 24, 0, -32, -40, 0, -24, 64, 0, -120, 16, 0, 18, 56, 0, 4, -20, 0, 32, 0, 0, -8, -4, 0, -48, 64, 0, -26, -6, 0, -36, 96, 0, -24, -4, 0, 38, -32, 0, 176, 6, 0, 28, -22, 0, -32, 40, 0, 26, 72, 0, -8, 114, 0, -8, 54, 0, -8, -40, 0, -32, -70, 0, 22, 64, 0, 4, 12, 0, 48, 56, 0, 48, -142, 0, 120, 120, 0, 8, -72, 0, 0, -22, 0, 8, 132, 0, 160, -88, 0, 52, 72, 0, -192, -40, 0, 44, -22, 0, 0, -8, 0, -24, 56, 0, 20, 24, 0, -8, 88, 0, -2, 16, 0, -8, -28, 0, 4, 6, 0, -48, 204, 0, -44, 0, 0, -20, 64, 0, -228, 12, 0, 30, -8, 0, -180, -4, 0, 0, -36, 0, 92, 136, 0, 48, 4, 0, 66, -36, 0, 22, -168, 0, 4, -16, 0, 76, -32, 0, -60, 28, 0, 14, -32, 0, -144, 0, 0, -64, 72, 0, -110, -48, 0, 20, 4, 0, -28, -52, 0, 20, -66, 0, -112, -96, 0, -4, -108, 0, 100, -38, 0, -26, 88, 0, -76, -30, 0, 48, -46, 0, -40, 16, 0, 20, -24, 0, 4, -16, 0, -2, -56, 0, -4, 8, 0, -70, -90, 0, 8, 0, 0, 8, 62, 0, -28, -36, 0, 160, 72, 0, 44, 8, 0, 40, -8, 0, -78, 44, 0, -40, -116, 0, 18, 60, 0, -76, 160, 0, 60, -4, 0, -48, 60, 0, -88, 80, 0, 8, -88, 0, 56, 16, 0, 68, -4, 0, 116, -64, 0, 32, -34, 0, 90, 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, 7, 3, 1, 3, 0]], "char_orbit_index": 11, "prim_orbit_index": 3, "minimal_twist": "154.2.e.e", "char_is_minimal": true, "conrey_index": 793, "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, 0, -1, 0], [0, 0, 0, 0], [-1, 0, -1, 0], [0, -1, 2, -1], [0, 0, 0, 0], [0, 1, 1, -1], [-1, 0, 0, 0], [0, 0, 0, 0], [2, -1, 2, 0], [1, 0, 1, 0], [0, 0, 0, 0], [-1, 0, 0, 2], [1, -1, 1, -2], [0, 0, 0, 0], [0, 0, 1, 0], [-2, 4, -2, 0], [0, 0, 0, 0], [0, 1, -2, 1], [2, 0, 0, 1], [0, 0, 0, 0], [1, 0, 0, 0], [0, 3, 2, 3], [0, 0, 0, 0], [-1, 4, -1, 0], [0, 2, 1, 2], [0, 0, 0, 0], [1, -2, 0, -1], [3, 0, 0, 4], [0, 0, 0, 0], [4, 0, 4, 0], [1, 0, 1, 0], [0, 0, 0, 0], [-2, 0, 0, -4], [0, 3, -4, 4], [0, 0, 0, 0], [0, -1, -8, -1], [-2, 1, -2, 0], [0, 0, 0, 0], [0, 1, -2, 1], [4, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, -1, 0], [0, 0, 0, 0], [2, 3, 2, 0], [0, 6, 2, 6], [0, 0, 0, 0], [5, 2, 5, 4], [-1, 0, 0, -4], [0, 0, 0, 0], [1, 2, 1, 0], [-2, 7, -2, 0], [0, 0, 0, 0], [-2, 0, 0, -1], [0, -1, -1, 1], [0, 0, 0, 0], [0, 4, -3, 4], [-7, 1, -7, 0], [0, 0, 0, 0], [0, 2, 9, 2], [4, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, -3, 2, -3], [0, 0, 0, 0], [-7, 3, -7, 0], [0, -4, 2, -4], [0, 0, 0, 0], [-4, 4, -4, 1], [4, 0, 0, -5], [0, 0, 0, 0], [8, 1, 8, 0], [-8, -1, -8, 0], [0, 0, 0, 0], [-2, 0, 0, -1], [-1, 2, 0, 1], [0, 0, 0, 0], [0, -3, -9, -3], [-2, 1, -2, 0], [0, 0, 0, 0], [0, -1, -4, -1], [-2, 0, 0, -10], [0, 0, 0, 0], [12, 0, 0, 10], [0, 4, 0, 4], [0, 0, 0, 0], [-1, 0, -1, 0], [0, -6, -4, -6], [0, 0, 0, 0], [-8, -3, -5, -1], [2, 0, 0, -3], [0, 0, 0, 0], [2, 6, 2, 0], [6, -4, 6, 0], [0, 0, 0, 0], [-1, 0, 0, 2], [5, 4, 0, 2], [0, 0, 0, 0], [0, -4, 1, -4]]}