# Stored data for newform 140.2.s.b, downloaded from the LMFDB on 20 April 2024.
{"label": "140.2.s.b", "space_label": "140.2.s", "level": 140, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504836611506316, "dim": 32, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [784, 0, -2156, 0, 4445, 0, -3353, 0, 1780, 0, -535, 0, 116, 0, -13, 0, 1]]], "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 140, "char_orbit_label": "s", "char_is_real": false, "Nk2": 560, "analytic_conductor": 1.1179056282979254, "level_radical": 70, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [140, 6, [71, 57, 101], [3, 3, 5]], "inner_twist_count": 8, "level_primes": [2, 5, 7], "conrey_indexes": [19, 59], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, -6, 0], "traces": [32, 0, 0, 6, -6, 0, 0, 0, 4, -12, 0, 0, 0, 22, 0, 18, 0, 0, 0, 0, -52, 0, 0, -48, -26, -18, 0, 0, 0, -26, 0, 0, 0, 0, 0, -28, 0, 0, 0, 42, 0, 0, 0, -26, 36, -22, 0, 0, 0, 36, 0, 0, 0, 48, 0, -16, 0, 0, 0, 4, 36, 0, 0, 36, -4, -24, 0, 0, 0, 26, 0, 0, 0, 14, 0, 0, 0, 0, 0, 72, 72, 0, 0, 56, 20, 8, 0, 0, -108, 0, 0, 0, 0, 30, 0, 60, 0, 0, 0, -26, -36, 0, 0, 0, -44, 60, 0, 0, 44, -60, 0, 0, 0, 4, 0, 4, 0, 0, 0, -112, 64, 0, 0, -132, 0, -30, 0, 0, 0, -32, 0, 0, 0, -200, 0, 36, 0, 0, 0, -40, -120, 0, 0, -42, -120, 0, 0, 0, 20, -18, 0, 0, 0, -104, 0, -40, 0, 0, 0, 0, 96, 0, 0, 102, 70, 108, 0, 0, 72, 26, 0, 0, 0, 0, 0, -172, 0, 0, 0, 24, 0, 0, 0, -34, 30, -56, 0, 0, 32, 208, 0, 0, 0, 228, 0, -34, 0, 0, 0, 28, 60, 0, 0, 392, -12, -120, 0, 0, 0, 86, 0, 0, 0, 4, 0, 0, 0, 0, 0, 24, -144, 0, 0, 86, 16, 20, 0, 0, 84, 0, 0, 0, 0, 66, 0, 132, 0, 0, 0, 40, -168, 0, 0, 0, 206, 96, 0, 0, -96, -186, 0, 0, 0, 22, 0, 58, 0, 0, 0, -244, 8, 0, 0, -276, 0, 134, 0, 0, 60, -30, 0, 0, 0, -400, 0, -36, 0, 0, 0, -12, 72, 0, 0, -72, 18, 0, 0, 0, -68, -132, 0, 0, 0, -92, 0, 102, 0, 0, 0, 0, -248, 0, 0, -186, -46, -144, 0, 0, -104, -34, 0, 0, 0, 0, 0, -128, 0, 0, 0, 84, 0, 0, 0, 26, -120, 92, 0, 0, -136, 292, 0, 0, 0, 78, 0, 12, 0, 0, 0, 72, 84, 0, 0, 264, -78, -102, 0, 0, 0, 64, 0, 0, 0, 56, 0, 0, 0, 0, 0, 114, 96, 0, 0, 38, -20, 44, 0, 0, 108, 0, 0, 0, 0, 252, 0, 90, 0, 0, 0, -4, 288, 0, 0, 0, -120, 256, 0, 0, -52, -252, 0, 0, 0, 78, 0, 130, 0, 0, 0, -180, 112, 0, 0, -216, 0, -4, 0, 0, 276, -42, 0, 0, 0, -164, 0, 54, 0, 0, 0, -116, -48, 0, 0, -14, 258, 0, 0, 0, -120, 0, 0, 0, 0, -132, 0, 52, 0, 0, 0, 0, 148, 0, 0, -372, 10, -336, 0, 0, -8, -116, 0, 0, 0, 0, 0, -96, 0, 0, 0, 306, 0, 0, 0, -120, 258, 44, 0, 0, 268, 60, 0, 0, 0, 384, 0, -288, 0, 0, 0, -16, -228, 0, 0, 448, -48, -36, 0, 0, 0, 76, 0, 0, 0, 114, 0, 0, 0, 0, 0, 180, -136, 0, 0, 190, 12, -154, 0, 0, -12, 0, 0, 0, 0, 300, 0, 108, 0, 0, 0, 104, -432, 0, 0, 0, 114, 104, 0, 0, 144, -150, 0, 0, 0, 44, 0, -52, 0, 0, 0, -336, -148, 0, 0, -444, 0, -124, 0, 0, -528, -70, 0, 0, 0, -608, 0, 192, 0, 0, 0, -38, -248, 0, 0, -64, -228, 0, 0, 0, 0, -126, 0, 0, 0, -126, 0, -50, 0, 0, 0, 0, 16, 0, 0, -36, -100, -18, 0, 0, 136, 34, 0, 0, 0, 0, 0, -96, 0, 0, 0, 228, 0, 0, 0, -48, -324, -144, 0, 0, -40, 436, 0, 0, 0, 384, 0, -66, 0, 0, 0, 56, 396, 0, 0, 544, 22, 84, 0, 0, 0, -4, 0, 0, 0, 96, 0, 0, 0, 0, 0, 114, 256, 0, 0, 116, -32, 52, 0, 0, -84, 0, 0, 0, 0, 60, 0, 126, 0, 0, 0, 60, 468, 0, 0, 0, -294, 180, 0, 0, 112, -30, 0, 0, 0, 100, 0, -128, 0, 0, 0, -288, -44, 0, 0, -294, 0, 142, 0, 0, -108, -30, 0, 0, 0, -544, 0, 240, 0, 0, 0, -172, 608, 0, 0, -74, 42, 0, 0, 0, 260, -240, 0, 0, 0, -72, 0, 82, 0, 0, 0, 0, 300, 0, 0, -384, 136, 72, 0, 0, -80, -26, 0, 0, 0, 0, 0, -148, 0, 0, 0, 114, 0, 0, 0, 20, 318, -140, 0, 0, 60, 400, 0, 0, 0, 276, 0, 120, 0, 0, 0, 94, -216, 0, 0, 672, 196, -66, 0, 0, 0, -10, 0, 0, 0, 116, 0, 0, 0, 0, 0, -12, -256, 0, 0, 174, 164, 80, 0, 0, -300, 0, 0, 0, 0, 168, 0, 12, 0, 0, 0, -136, -336, 0, 0, 0, 146, 224, 0, 0, -296, -300, 0, 0, 0, -2, 0, -108, 0, 0, 0, -144, -268, 0, 0, -336, 0, 132, 0, 0, -12, 48, 0, 0, 0, -864, 0, -198, 0, 0, 0, -196, -432, 0, 0, -110, -186, 0, 0, 0, 180, 30, 0, 0, 0, -388, 0, -164, 0, 0, 0, 0, -408, 0, 0, -36, -226, -408, 0, 0, -232, -4, 0, 0, 0, 0, 0, -392, 0, 0, 0, 324, 0, 0, 0, -104, -258, -60, 0, 0, -184, 356, 0, 0, 0, 444, 0, 166, 0, 0, 0, 30, 228, 0, 0, 648, 200, -240, 0, 0, 0, 254, 0, 0, 0, 208, 0, 0, 0, 0, 0, -24, 320, 0, 0, 336, -420, -294, 0, 0, 456, 0, 0, 0, 0, -204, 0, -30, 0, 0, 0, 102, 492, 0, 0, 0, -230, -16, 0, 0, 144, -18, 0, 0, 0, -26, 0, 136, 0, 0, 0, -512, 52, 0, 0, -174, 0, 308, 0, 0, 732, -48, 0, 0, 0, -288, 0, -84, 0, 0, 0, 124, 432, 0, 0, -156, 360, 0, 0, 0, -232, -54, 0, 0, 0, -52, 0, -8, 0, 0, 0, 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, 4, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 20, 4, -1, 2, 0], [1, 1, 28, 6, 1, 6, 0], [1, 1, 35, 9, -1, 6, 0], [1, 1, 140, 19, 1, 6, 0]], "char_orbit_index": 19, "prim_orbit_index": 19, "minimal_twist": "140.2.s.b", "char_is_minimal": true, "conrey_index": 19, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}