# Stored data for newform 39.2.e.b, downloaded from the LMFDB on 23 April 2024.
{"label": "39.2.e.b", "space_label": "39.2.e", "level": 39, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538831911, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2601.1", "trace_hash": 889945217941538757, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [16, -4, 5, 1, 1]]], "qexp_display": "q-\\beta _{1}q^{2}-\\beta _{2}q^{3}+(-2+\\beta _{1}+2\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "e", "char_is_real": false, "Nk2": 156, "analytic_conductor": 0.3114165678829935, "hecke_ring_index": 1, "level_radical": 39, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [39, 3, [14, 28], [3, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 13], "conrey_indexes": [16, 22], "field_disc": 2601, "field_disc_factorization": [[3, 2], [17, 2]], "field_poly": [16, 4, 5, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.740", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "50.938", "prec": 20}, {"__RealLiteral__": 0, "data": "5.711", "prec": 17}, {"__RealLiteral__": 0, "data": "1167.079", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, -2, -6, 3], "traces": [0, 4, -1, -2, -5, -6, -1, 3, 18, -2, -7, 4, 10, 2, -20, 3, -3, -1, 2, -6, -1, -6, 2, -4, -9, 6, 25, 4, 16, -1, -7, 2, -9, 4, 18, 4, -5, -11, -28, -1, -10, -1, 10, -5, -20, 3, -2, 0, -3, 1, 24, 2, -28, 22, -1, -6, 22, 12, 25, 14, 2, -16, 8, 3, 14, -3, -4, -5, -11, -4, -4, -28, -9, -24, 3, -3, 2, 12, -26, 30, -21, -2, -9, -20, 16, -7, -12, -1, 18, -18, 14, 27, 20, -1, 34, 26, 18, 13, -25, -8, 18, 11, -9, -22, 9, -8, -31, 0, -5, 30, 14, -11, -60, 9, 14, 6, -46, -1, -48, 10, 5, 14, 50, -1, 6, -30, 10, -15, 23, 10, -29, -20, 10, -8, 6, -6, -13, 7, 4, 7, 10, 0, 28, 2, 6, 27, -11, 1, 38, 9, 24, 12, -10, -1, -20, -20, 5, 32, -16, -11, 5, -12, -1, -11, 22, -6, 22, -4, -44, -50, -10, -6, -4, -24, -50, -21, 6, -28, -26, 18, -1, 14, -10, 32, -18, 25, 8, -4, 34, 3, 76, 10, -7, -6, 4, 27, 46, -2, 2, 1, -24, -5, -3, 48, -11, -7, 14, 8, 75, -24, 2, -27, -53, 56, -34, 16, 18, -7, -50, 12, -4, -26, -6, -16, 22, -3, -94, -6, 2, -32, -14, -6, 21, 104, 1, -68, 52, -15, 22, -52, -21, 15, -14, -2, -57, -27, 18, 48, -8, 10, -1, 12, -32, 8, -16, 14, 17, -13, 6, -16, -26, 2, 56, 6, 18, 18, -4, -18, 8, 18, -7, 31, 54, -3, 10, 6, -10, -23, 112, -1, 18, 30, 34, 15, -70, -52, 52, -20, -9, 25, -29, -26, 13, -45, 50, -4, -41, 4, -26, -2, -36, -1, -54, 11, -84, 7, -9, 82, -32, 11, -12, -60, 21, -30, 43, 4, -46, -18, -31, 2, -38, 0, 20, 14, 10, 3, 96, -15, -13, -34, -28, 27, 42, 22, 32, 16, 30, -8, 38, -18, -9, 2, 14, -6, -14, 6, -44, -14, 23, 7, 72, 2, -36, -23, 24, 42, 124, 10, 26, 12, 5, -14, -29, -28, -94, 70, -25, -3, -6, 2, -47, 42, -12, -32, 18, 15, -68, -77, -20, -35, 14, -15, 24, -4, 23, 16, -71, -5, 24, 62, 22, 4, -21, 10, 50, -28, 10, -13, -188, -8, 72, -33, -12, 1, -38, 3, -46, 22, 26, 12, 5, -14, 36, -38, -2, -4, -30, -14, -28, 52, 10, 92, 12, 0, 150, 24, -14, 41, 68, 2, 52, 14, -3, -34, 24, 27, -80, 24, -11, 15, -10, -2, 9, -40, -19, 10, -8, -18, 2, 0, -48, 2, 65, -6, -28, 2, 20, 16, -26, -1, 4, 53, -20, -82, 75, 10, -26, -104, 23, 2, -34, -16, 80, -20, -16, -60, -84, -11, -38, -4, -10, -31, 70, 6, 35, -28, 2, -6, -89, 22, 29, 56, -11, -50, -14, 12, 24, 42, 22, -48, 29, -4, -216, 40, 22, -25, -8, 25, 92, 7, 5, -1, -78, -6, 87, 16, -4, 0, 38, 48, -5, -94, 25, -10, 76, 42, 54, 8, -12, 38, -13, 14, 40, 25, 52, -34, -14, 18, 84, -2, -1, -20, -44, -7, -13, 40, -46, -42, 9, -16, -48, 108, -18, 31, 74, 25, -42, 57, -16, 23, -12, 2, 35, 22, -68, 29, -18, -6, -126, -32, -38, 28, -10, -20, 22, -6, -7, -94, 4, -6, -50, -32, -2, 22, -74, -24, 62, -54, -23, -20, -64, -2, 9, 54, 2, 2, 31, -2, -52, -84, 12, 43, 8, 10, -66, -21, 6, 32, -10, -24, 78, 0, 22, 12, 22, -7, 88, 1, 14, 10, 8, -4, -2, -88, -78, 32, -18, 12, 11, -6, 2, 33, 152, -27, 81, 14, 106, 77, 100, -28, -43, -7, 68, -7, 32, -32, -10, 54, -9, 56, 12, 14, -70, -38, -50, -72, -27, 12, 136, -12, 2, -36, -112, 1, -124, 12, 3, -2, -48, -16, -26, -64, 22, 30, -15, 6, 37, 20, 47, -11, -23, 12, -16, 2, -4, -19, -24, 16, -36, 11, 28, 49, -26, -6, -156, -70, 21, 18, 46, -52, -78, 28, 25, 100, 14, 34, -37, 16, 52, -18, 196, -15, -98, -2, -44, -54, -124, 26, -54, 22, 42, -25, 95, -30, -43, -78, 7, 2, 164, 4, 59, 6, -57, 148, -78, -27, 36, 10, -9, -4, -6, 6, -212, 50, 4, -5, -70, 10, 22, -68, -1, -14, 102, -24, 38, 84, 16, -60, 8, -16, 66, 6, 32, 65, 8, -7, 208, 58, -34, 36, -4, -13, 166, 32, 6, 54, 50, 8, 61, -28, 1, -112, -18, -1, -75, -150, 56, -43, -92, 6, -44, -56, -36, -59, -140, -9, 96, 42, 8, 34, 12, 36, -25, -24, -4, -16, 4, -36, 41, -21, -7, 2, -94, 31, 12, -26, -27, -32, -114, -24, 18, 20, -5, -16, -116, 6, -104, 40, -10, 6, 18, 46, 7, 50, -56, 40, -4, 2, -8, -2, -36, -19, 11, -15, 84, 75, -68, -21, -93, 15, -24, -22, -70, -8, 114, 26, -34, 134, -2, 90, 6, 10, -10, 56, -9, 70, 102, 25, -26, 30, 58, -28, 220, 13, 28, -14, -26, -43, -18, 90, 42, 47, -25, -6, 71, 8, -92, -74, -41, -62, -46, 4, 80, -68, 13, -10, 52, -2, 68, -26, 18, -31, -36, -1, 83, 30, -54, -56, 2, -22, -2, 56, 42, -20, 93, -14, 6, -66, 18, -56, 10, -41, -138, -14, 64, -42, 46, 11, -42, -5, -12, -108, -130, 30, 26, -28, -30, -22, 8, 15, 34, 56, 43, -2, -144, 4, -12, 28, 92, -12, -144, 9, 62, 4, 62, -32, 14, -4, 32, -2, 19, -106, -126, 0, -5, -59, 20, -20, 63, 14, -108, -40, -5, 49, -28, -78, 150, -77, -48, 36, 50, -15, -6, -28, -13, 54, 21, 68, -50, 20, 14, 10, 4, -54, 140, 92, -84, 0, 80, -11, -118], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "39.2.e.b", "char_is_minimal": true, "conrey_index": 16, "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, 0, 0], [0, 0, -1, 0], [-2, 1, 2, 1], [-2, 0, 0, -1], [0, 1, 0, 1], [1, -1, -1, -1], [4, 0, 0, -1], [-1, 0, 1, 0], [0, 1, -4, 0], [0, 0, 2, 0], [2, 0, 0, -1], [1, 2, -1, 1], [-4, 0, 0, 2], [0, -1, 2, 0], [0, -3, 0, 0], [0, 1, 0, 1], [0, 0, 0, -1], [-4, -2, 4, -2], [0, 1, 0, 1], [-1, 0, 0, 1], [0, -2, 0, -2], [0, 0, -2, 0], [0, -1, -4, 0], [3, 0, 0, 3], [8, -1, -4, -1], [1, 0, 0, 0], [0, 4, 6, 0], [0, 3, -2, 0], [-4, -1, 4, -1], [1, 0, 0, 1], [-4, 1, 4, 1], [2, 0, -2, 0], [4, 0, 0, -1], [2, 0, -2, 0], [0, -1, -2, 0], [0, 1, -6, 0], [-8, 0, 0, -2], [-1, -1, 0, -2], [-4, 0, 0, -3], [0, -1, 0, 0], [0, 2, 4, 0], [-3, -1, 3, -1], [-4, 0, 0, 2], [2, 1, -2, 1], [0, 2, 0, 2], [2, 0, 0, 4], [0, 3, 0, 3], [0, -3, 2, 0], [0, 0, 12, 0], [0, 0, 0, -1], [-4, -2, -2, 3], [4, 0, 0, -3], [0, -1, 0, 0], [0, 2, -4, 0], [8, -6, -8, -6], [4, 0, 0, 2], [12, -1, -12, -1], [6, -2, -6, -2], [0, 0, 0, -1], [-7, 2, 7, 2], [0, 0, 4, 0], [0, 1, 1, 0], [4, 0, 0, 1], [-6, -3, 10, -2], [0, 0, 0, 2], [0, 1, -3, 0], [0, -3, -4, 0], [-2, 0, 2, 0], [0, 0, 0, 2], [-14, 0, 14, 0], [-4, 1, 4, 1], [-7, 0, 0, -2], [4, 5, -4, 5], [0, 3, -3, 0], [0, 2, 0, 0], [2, 0, 0, -2], [-4, 0, -4, 1], [7, 0, 0, -1], [0, 3, -12, 0], [0, 0, -1, 0], [-4, 1, 4, 1], [-4, 0, 0, 2], [6, -4, -6, -4], [-4, -1, 4, -1], [-4, 0, 0, -2], [-2, -3, 2, -3], [0, 2, 8, 0], [0, -2, -8, 0], [4, 0, 0, 1], [4, 1, 3, -2], [4, 0, 0, -2], [0, 1, -1, 0], [0, 2, 16, 0], [16, 6, -16, 6], [4, 0, 0, -1], [7, 1, -7, 1], [-12, 1, 12, 1], [-2, 0, 0, 0], [6, -6, -6, -6]]}