# Stored data for newform 1386.2.k.l, downloaded from the LMFDB on 23 April 2024.
{"label": "1386.2.k.l", "space_label": "1386.2.k", "level": 1386, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49540283129398634, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 38990948649153585, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4, 2, 1]], [13, [-2, 1]], [17, [1, -1, 1]], [23, [1, 1, 1]]], "qexp_display": "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{4}-2\\zeta_{6}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": 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": [1386, 3, [155, 199, 1135], [3, 1, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 7, 11], "conrey_indexes": [793, 991], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "2.009", "prec": 17}, {"__RealLiteral__": 0, "data": "0.125", "prec": 17}, {"__RealLiteral__": 0, "data": "12.047", "prec": 20}, {"__RealLiteral__": 0, "data": "1.182", "prec": 17}, {"__RealLiteral__": 0, "data": "109.471", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 0, -2, 4], "traces": [0, 2, 1, 0, -1, -2, 0, 4, -2, 0, 2, 1, 0, 4, -1, 0, -1, 1, 0, 3, 4, 0, 2, -1, 0, 1, 2, 0, -5, 2, 0, 2, 1, 0, 2, 2, 0, 5, -3, 0, 2, 20, 0, 2, 1, 0, 1, 7, 0, 2, 2, 0, -2, 12, 0, -4, -4, 0, 1, -3, 0, 14, 4, 0, 2, -4, 0, -12, 1, 0, 10, -10, 0, 8, -5, 0, -6, 5, 0, 0, -2, 0, 10, 12, 0, -4, 1, 0, -1, -6, 0, 8, 2, 0, -7, 6, 0, 14, -11, 0, 1, -9, 0, 6, -4, 0, 24, -2, 0, 20, -2, 0, 1, -20, 0, -2, -1, 0, -6, 5, 0, -1, -14, 0, 2, -24, 0, -2, 1, 0, 4, 0, 0, -3, -24, 0, -1, 6, 0, -26, 8, 0, -5, 2, 0, -2, 16, 0, -10, -11, 0, 15, -3, 0, 4, -8, 0, -1, 0, 0, -4, 1, 0, -10, -10, 0, 6, -4, 0, -18, -2, 0, -1, 14, 0, 5, -2, 0, 6, -7, 0, -20, -2, 0, 1, 10, 0, -1, -14, 0, 12, -8, 0, -8, 7, 0, -13, -54, 0, 2, -1, 0, -18, 4, 0, -20, -6, 0, -2, 6, 0, 8, 12, 0, 2, -2, 0, 10, 40, 0, 2, 2, 0, -52, 5, 0, -10, -10, 0, 10, -4, 0, -2, -21, 0, 14, -3, 0, 4, 44, 0, 12, 1, 0, -28, 22, 0, 6, -2, 0, -12, 42, 0, -2, -1, 0, -1, -6, 0, -5, 8, 0, 0, -6, 0, -48, -15, 0, -12, 12, 0, -16, -2, 0, 12, -1, 0, 24, -13, 0, -2, -14, 0, 0, 5, 0, 4, 40, 0, 16, 2, 0, 8, -18, 0, 12, -5, 0, 11, -2, 0, 4, 30, 0, 3, 28, 0, -8, -1, 0, -4, 13, 0, -7, -2, 0, 0, 6, 0, 1, -2, 0, 5, 6, 0, 2, 10, 0, -20, -7, 0, 2, -6, 0, -2, 48, 0, 0, -9, 0, 2, -2, 0, -20, -2, 0, -14, -32, 0, -32, 4, 0, -1, -6, 0, 10, 12, 0, -14, 10, 0, 10, -10, 0, -10, -32, 0, 32, -1, 0, 20, 60, 0, -26, 1, 0, -7, 4, 0, -16, 6, 0, 8, 25, 0, -8, -16, 0, -7, -30, 0, -2, -2, 0, -27, 0, 0, 27, 4, 0, -2, -24, 0, 4, -9, 0, -1, 10, 0, -16, 20, 0, -12, -15, 0, -12, 2, 0, 3, -58, 0, -34, 4, 0, -12, -1, 0, -14, 4, 0, 2, -16, 0, -38, 8, 0, 20, 3, 0, -31, 4, 0, 4, 15, 0, -12, -26, 0, 4, 24, 0, 10, 10, 0, -20, 4, 0, -32, -10, 0, -2, -66, 0, 32, -1, 0, 21, 27, 0, -60, 28, 0, 3, 1, 0, 6, -1, 0, 22, -26, 0, 10, 24, 0, 2, -14, 0, 34, -14, 0, 26, 12, 0, 1, -6, 0, -4, -20, 0, -8, 12, 0, 21, 84, 0, 36, -1, 0, 1, -20, 0, 40, -2, 0, 6, 12, 0, 14, -25, 0, 4, 14, 0, 4, 0, 0, -12, -2, 0, 22, -24, 0, -12, 40, 0, -4, 12, 0, 24, 13, 0, 16, 16, 0, -1, -80, 0, 78, 6, 0, 1, 3, 0, 0, 48, 0, 13, -35, 0, 4, -10, 0, -7, -38, 0, 20, 0, 0, 10, -15, 0, -7, 2, 0, -10, -2, 0, -14, -16, 0, 4, 24, 0, -12, -8, 0, -9, -24, 0, 12, 6, 0, 5, 15, 0, -8, 22, 0, 2, 0, 0, 16, -1, 0, 15, -2, 0, 28, 6, 0, 56, 14, 0, 14, -4, 0, -5, -72, 0, -26, 4, 0, 26, 6, 0, 19, 7, 0, -1, 10, 0, 36, 0, 0, -6, 2, 0, 4, 2, 0, 2, -12, 0, -64, 4, 0, 3, 48, 0, 3, 4, 0, 20, 14, 0, 0, -10, 0, -35, -88, 0, -5, -2, 0, -12, 30, 0, -1, 2, 0, 24, 28, 0, 44, 0, 0, 9, 7, 0, 28, 4, 0, 2, -39, 0, -24, -37, 0, -1, 24, 0, 18, -28, 0, -64, 26, 0, 10, -16, 0, -1, -18, 0, -15, 1, 0, -12, -45, 0, -9, -10, 0, 6, -4, 0, -8, -7, 0, -10, 23, 0, -6, 20, 0, 10, 1, 0, 28, -8, 0, -16, 1, 0, 10, 64, 0, -2, 12, 0, -36, 10, 0, 48, -72, 0, -22, 26, 0, 2, 2, 0, 32, 7, 0, 2, -60, 0, 94, -8, 0, -6, 18, 0, 100, 16, 0, -25, -6, 0, -40, 2, 0, -8, 36, 0, -2, -14, 0, -60, 30, 0, -5, -1, 0, 11, 4, 0, 31, 27, 0, 0, -40, 0, 28, -27, 0, 2, -44, 0, 14, -1, 0, 24, -8, 0, -10, 8, 0, 9, 18, 0, -56, -5, 0, 5, -20, 0, 3, -32, 0, 40, -30, 0, -44, -6, 0, -12, -68, 0, -7, 12, 0, 4, 13, 0, 4, -3, 0, -29, 48, 0, -56, -17, 0, -4, 18, 0, 1, -24, 0, 1, 5, 0, 28, -70, 0, 2, -47, 0, 26, 4, 0, -32, 44, 0, 28, -19, 0, -2, 0, 0, -24, -20, 0, 6, -48, 0, 14, 31, 0, 2, -24, 0, 80, 2, 0, -15, 44, 0, -4, -24, 0, 26, -21, 0, 28, -1, 0, 12, 2, 0, -12, 20, 0, 20, 20, 0, 40, -10, 0, 20, 90, 0, 6, 32, 0, -20, 0, 0, -57, 2, 0, -33, -20, 0, 10, 16, 0, 1, 36, 0, -33, 42, 0, -27, -2, 0, 36, -48, 0, 14, 35, 0, -10, 6, 0, 2, -53, 0, 16, 3, 0, -5, 52, 0, -16, -22, 0, -52, 30, 0, 27, -10, 0, 12, 32, 0, -2, 1, 0, 14, 4, 0, -52, 68, 0, 14, 28, 0, -12, 4, 0, 6, 39, 0, 54, 2, 0, -12, -1, 0, -16, -2, 0, 5, -8, 0, 42, 8, 0, 24, 10, 0, 3, -21, 0, 42, 72, 0, -64, 18, 0, 1, 4, 0, 2, 2, 0, 20, 0, 0, 100, 32, 0, -1, 10, 0, 0, 12, 0, 24, -22, 0, 14, 7, 0, -20, 28, 0, 4, -4, 0, 28, 11, 0, -6, -4, 0, 0, -100, 0, -110, -6, 0, 2, -8, 0, 75, 44, 0, 24, 58, 0, -96, 3, 0, 20, 7, 0, -22, -8, 0, 24, 5, 0, 1, 12, 0, 2, 24, 0, 7, -16, 0, 32, -16, 0, -6, 1, 0, -40, 28, 0, -106, 39, 0, -6, 29, 0, -5, 2, 0, -3, -25, 0, -8, 0, 0, 24, 60, 0, 9, 26, 0, -70, 52, 0, -4, 2, 0, -8, -18, 0, 30, 7, 0, -76, 11, 0, -44, -20, 0, 0, 12, 0, 40, 5, 0, 15, 12, 0, 10, -14, 0, -2, 20, 0, 20, -50, 0, -1, 62, 0, -19, -28, 0, -32, -12, 0, -42, 2, 0, -6, -64, 0, -42, 12, 0, -16, -8, 0, -26, 9, 0, -12, 14, 0, -4, 6, 0, -6, 26, 0, -36, 10, 0, -15, 8, 0, 20, 2, 0, 11, 6, 0, -44, 4, 0, 0, -20, 0, 16, 8, 0, -5, -48, 0, -5, -15, 0, -4, -14, 0, -17, -28, 0, 3, 12, 0, -24, 28, 0, -14, -48, 0, 13, 28, 0, 4, 38, 0, -70, -4, 0, -36, 12, 0, -46, -52, 0, 8, -8, 0, -10, 13, 0, 30, 2, 0, 10, -19, 0, 14, -35, 0, -42, 1, 0, 5, -18, 0, 28, 18, 0, 0, 2, 0, -40, -12, 0, -2, 20, 0, -72, -22, 0, 1, -24, 0, -38, 4, 0, -24, 24, 0, -12, -32, 0, -1, -108, 0, -8, -3, 0, 96, 50, 0, 28, -3, 0, 2, -64, 0, -68, 10, 0, -14, 4, 0, 1, 0, 0, 10, -18, 0, 24, -28, 0, -44, 12, 0, -7, -10, 0, -4, -12, 0, 4, -6, 0, 24, -2, 0, 2, 1, 0, 4, 8, 0, 12, -24, 0, 14, 0, 0, -48, 22, 0, 0, -15, 0, -40, 18, 0, -7, -32, 0, 6, -7, 0, 2, -66, 0, 7, 4, 0, -78, 24, 0, 12, -12, 0, -17, 136, 0, -12, 1, 0, 48, -108, 0, -48, -18, 0, -14, -96, 0, 48, -32, 0, -26, -4, 0, 10, 20, 0, 16, -1, 0, 98, -5, 0, -9, 14, 0, 14, -30, 0, 2, -54, 0, 6, -6, 0, -36, 0, 0, 40, 9, 0, -20, 2, 0, 56, -6, 0, -2, -12, 0, -88, -4, 0, 7, -16, 0, 20, -20, 0, -23, 3, 0, 0, -30, 0, 10, 32, 0, 23, 20, 0, 2, -14, 0, -71, 14, 0, 2, 28, 0, -29, 16, 0, 2, 12, 0, 18, -10, 0, 32, -40, 0, -46, -1, 0, -12, 3, 0, 16, -72, 0, -10, -39, 0, 36, -12, 0, -36, 30, 0, 69, -44, 0, 52, -18, 0, -4, 1, 0, 10, -24, 0, 0, -32, 0, 14, 2, 0, -6, -2, 0, -30, 112, 0, -12, 47, 0, 8, 50, 0, 26, -12, 0, -18, -51, 0, 28, 80, 0, 8, -13, 0, -76, -50, 0, -12, 8, 0, 12, -20, 0, 10, 24, 0, 66, 8, 0, 72, 10, 0, -5, 2, 0, -7, 42, 0, -52, -30, 0, -30, -54, 0, -104, -10, 0, 1, -14, 0, 104, 13, 0, 2, -25, 0, -2, 62, 0, 54, 18, 0, -45, 0, 0, 10, 60, 0, 12, -28, 0, -54, -50, 0, 5, -2, 0, -22, -4, 0, 132, 7, 0, 1, 31, 0, -10, 48, 0, 8, -13, 0, -124, -8, 0, 4, 46, 0, -6, 18, 0, 36, -36, 0, -74, -28, 0, -4, -48, 0, 23, -5, 0, -40, 21, 0, 5, -3, 0, -16, -56, 0, -22, 20, 0, 30, -24, 0, 70, -88, 0, 6, 7, 0, -4, 3, 0, -34, 4, 0, -68, -14, 0, 24, -15, 0, -16, 2, 0, 2, -76, 0, 0, -4, 0, -6, 88, 0, 12, 29, 0, 24, -16, 0, 118, -28, 0, 17, 0, 0, 60, -8, 0, -18, 18, 0, 148, 5, 0, -12, 60, 0, -42, 2, 0, 10, 0, 0, -4, 14, 0, -56, 108, 0, -3, -2, 0, -94, 74, 0, 9, -26, 0, 2, 44, 0, -94, -16, 0, -44, 1, 0, -6, 56, 0, 19, 34, 0, 128, -10, 0, 0, -35, 0, -25, -48, 0, -40, 32, 0, 26, 3, 0, 12, 12, 0, -54, -14, 0, 62, 84, 0, 13, -2, 0, -12, 20, 0, 24, 40, 0, -2, 14, 0, -4, -30, 0, -44, -5, 0, 56, 1, 0, -12, 12, 0, 22, 52, 0, -42, -45, 0, -8, 14, 0, -5, -20, 0, 20, -12, 0, 4, 6, 0, 44, 12, 0, 10, -40, 0, -52, 10, 0, -20, -78, 0, -55, 80, 0, 10, 0, 0, -4, 16, 0, 45, -48, 0, -8, 12, 0, 64, 6, 0, -32, -10, 0, 0, -128, 0, -2, 57, 0, 4, -30, 0, 21, 33, 0, -10, 96, 0, -84, 5, 0, -16, -20, 0, -96, 2, 0, -36, -9, 0, 56, -39, 0, 21, -52, 0, 47, -54, 0, -4, -27, 0, -22, 18, 0, 12, 98, 0, -72, -14, 0, 70, 60, 0, -4, 10, 0, 3, 90, 0, 56, 1, 0, 53, 16, 0, 16, 32, 0, -3, -72, 0, 28, -4, 0, 26, 79, 0, -6, -32, 0, -44, -18, 0, 50, -26, 0, 24, -54, 0, -10, -27, 0, -20, 1, 0, 70, -12, 0, 16, 28, 0, 8, -1, 0, -1, -22, 0, 120, 28, 0, -4, -12, 0, 120, 13, 0, 34, -26, 0, 60, 28, 0, 56, 2, 0, -18, -6, 0, -22, 120, 0, 30, -6, 0, 78, -28, 0, 7, -54, 0, 1, -52, 0, 0, -6, 0, 1, -50, 0, 0, -32, 0, 2, 54, 0, 66, 25, 0, -4, -10, 0, -44, 84, 0, 16, 53, 0, -11, 12], "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": "1386.2.k.h", "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], [1, 0], [0, 1], [0, 0], [-1, 1], [0, -2], [0, 0], [1, 2], [-1, 0], [0, 0], [2, -2], [1, -1], [0, 0], [2, 0], [-2, 3], [0, 0], [0, -1], [1, -1], [0, 0], [0, 3], [2, 0], [0, 0], [1, 0], [0, -1], [0, 0], [1, -1], [0, 2], [0, 0], [-3, 1], [1, 0], [0, 0], [2, -2], [1, -1], [0, 0], [1, 0], [4, -6], [0, 0], [0, 5], [-3, 3], [0, 0], [0, 2], [10, 0], [0, 0], [1, 0], [0, 1], [0, 0], [1, -1], [0, 7], [0, 0], [-3, 8], [1, 0], [0, 0], [-2, 2], [12, -12], [0, 0], [-2, 0], [-1, -2], [0, 0], [0, 1], [-3, 3], [0, 0], [0, 14], [2, 0], [0, 0], [1, 0], [0, -4], [0, 0], [-12, 12], [0, 1], [0, 0], [6, -2], [-5, 0], [0, 0], [8, -8], [-5, 5], [0, 0], [-3, 0], [3, -1], [0, 0], [0, 0], [-2, 2], [0, 0], [0, 10], [6, 0], [0, 0], [-2, 0], [0, 1], [0, 0], [-1, 1], [0, -6], [0, 0], [2, 4], [1, 0], [0, 0], [-7, 7], [6, -6], [0, 0], [7, 0], [-8, 5], [0, 0], [0, 1]]}