# Stored data for newform 1400.2.bh.e, downloaded from the LMFDB on 19 April 2024. {"label": "1400.2.bh.e", "space_label": "1400.2.bh", "level": 1400, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18016666285770104, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1517900522139996896, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [16, 0, -4, 0, 1]], [11, [1, -1, 1]]], "qexp_display": "q+2\\zeta_{12}q^{3}+(-2\\zeta_{12}-\\zeta_{12}^{3})q^{7}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "bh", "char_is_real": false, "Nk2": 5600, "analytic_conductor": 11.179056282979253, "hecke_ring_index": 1, "level_radical": 70, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.517", "prec": 17}, "analytic_rank_proved": true, "char_values": [1400, 6, [351, 701, 1177, 801], [6, 6, 3, 4]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 4, "level_primes": [2, 5, 7], "conrey_indexes": [249, 849], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "3.857", "prec": 17}, {"__RealLiteral__": 0, "data": "1.364", "prec": 17}, {"__RealLiteral__": 0, "data": "95.169", "prec": 20}, {"__RealLiteral__": 0, "data": "41.514", "prec": 20}, {"__RealLiteral__": 0, "data": "3571.993", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -10, 0, -4, 0, 0, 0, 0, 0, 0, 0, 24, 0, -8, 0, 0, 0, 0, 0, 0, 0, 12, 0, -20, 0, 0, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 24, 0, 0, 0, 0, 0, 0, 0, 56, 0, -16, 0, 0, 0, 0, 0, 0, 0, 28, 0, 22, 0, 0, 0, 0, 0, 0, 0, 12, 0, -24, 0, 0, 0, 0, 0, 0, 0, 4, 0, -24, 0, 0, 0, 0, 0, 0, 0, -8, 0, 40, 0, 0, 0, 0, 0, 0, 0, 4, 0, 20, 0, 0, 0, 0, 0, 0, 0, -24, 0, -14, 0, 0, 0, 0, 0, 0, 0, -16, 0, 72, 0, 0, 0, 0, 0, 0, 0, 20, 0, 20, 0, 0, 0, 0, 0, 0, 0, -44, 0, -70, 0, 0, 0, 0, 0, 0, 0, 16, 0, 10, 0, 0, 0, 0, 0, 0, 0, 18, 0, 8, 0, 0, 0, 0, 0, 0, 0, -32, 0, -24, 0, 0, 0, 0, 0, 0, 0, -8, 0, -16, 0, 0, 0, 0, 0, 0, 0, -20, 0, -52, 0, 0, 0, 0, 0, 0, 0, -48, 0, -12, 0, 0, 0, 0, 0, 0, 0, -56, 0, -20, 0, 0, 0, 0, 0, 0, 0, -24, 0, -46, 0, 0, 0, 0, 0, 0, 0, 16, 0, 116, 0, 0, 0, 0, 0, 0, 0, -50, 0, 12, 0, 0, 0, 0, 0, 0, 0, -24, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, -12, 0, 0, 0, 0, 0, 0, 0, -26, 0, 24, 0, 0, 0, 0, 0, 0, 0, -42, 0, 48, 0, 0, 0, 0, 0, 0, 0, 160, 0, 8, 0, 0, 0, 0, 0, 0, 0, 12, 0, -96, 0, 0, 0, 0, 0, 0, 0, -90, 0, 54, 0, 0, 0, 0, 0, 0, 0, -80, 0, 8, 0, 0, 0, 0, 0, 0, 0, -56, 0, -48, 0, 0, 0, 0, 0, 0, 0, 60, 0, -12, 0, 0, 0, 0, 0, 0, 0, -10, 0, 22, 0, 0, 0, 0, 0, 0, 0, 84, 0, 68, 0, 0, 0, 0, 0, 0, 0, -32, 0, -56, 0, 0, 0, 0, 0, 0, 0, -80, 0, -26, 0, 0, 0, 0, 0, 0, 0, -12, 0, -48, 0, 0, 0, 0, 0, 0, 0, 20, 0, 120, 0, 0, 0, 0, 0, 0, 0, -12, 0, 32, 0, 0, 0, 0, 0, 0, 0, -20, 0, -26, 0, 0, 0, 0, 0, 0, 0, -52, 0, -10, 0, 0, 0, 0, 0, 0, 0, -16, 0, 56, 0, 0, 0, 0, 0, 0, 0, 8, 0, 20, 0, 0, 0, 0, 0, 0, 0, -32, 0, -30, 0, 0, 0, 0, 0, 0, 0, 32, 0, -80, 0, 0, 0, 0, 0, 0, 0, 56, 0, 20, 0, 0, 0, 0, 0, 0, 0, -36, 0, 24, 0, 0, 0, 0, 0, 0, 0, 152, 0, 30, 0, 0, 0, 0, 0, 0, 0, 52, 0, 32, 0, 0, 0, 0, 0, 0, 0, 22, 0, 80, 0, 0, 0, 0, 0, 0, 0, -24, 0, -60, 0, 0, 0, 0, 0, 0, 0, 72, 0, -16, 0, 0, 0, 0, 0, 0, 0, -22, 0, -56, 0, 0, 0, 0, 0, 0, 0, 80, 0, -32, 0, 0, 0, 0, 0, 0, 0, 80, 0, -108, 0, 0, 0, 0, 0, 0, 0, 68, 0, -56, 0, 0, 0, 0, 0, 0, 0, -24, 0, -54, 0, 0, 0, 0, 0, 0, 0, 70, 0, -56, 0, 0, 0, 0, 0, 0, 0, -40, 0, 160, 0, 0, 0, 0, 0, 0, 0, -8, 0, -70, 0, 0, 0, 0, 0, 0, 0, -16, 0, 80, 0, 0, 0, 0, 0, 0, 0, 64, 0, 72, 0, 0, 0, 0, 0, 0, 0, 64, 0, 48, 0, 0, 0, 0, 0, 0, 0, -48, 0, -32, 0, 0, 0, 0, 0, 0, 0, -66, 0, -16, 0, 0, 0, 0, 0, 0, 0, 16, 0, 168, 0, 0, 0, 0, 0, 0, 0, -36, 0, -28, 0, 0, 0, 0, 0, 0, 0, -72, 0, -200, 0, 0, 0, 0, 0, 0, 0, -52, 0, 24, 0, 0, 0, 0, 0, 0, 0, -82, 0, -120, 0, 0, 0, 0, 0, 0, 0, 120, 0, -36, 0, 0, 0, 0, 0, 0, 0, 28, 0, 6, 0, 0, 0, 0, 0, 0, 0, 164, 0, -96, 0, 0, 0, 0, 0, 0, 0, 50, 0, -8, 0, 0, 0, 0, 0, 0, 0, -32, 0, 160, 0, 0, 0, 0, 0, 0, 0, -72, 0, -12, 0, 0, 0, 0, 0, 0, 0, 110, 0, -20, 0, 0, 0, 0, 0, 0, 0, -30, 0, -60, 0, 0, 0, 0, 0, 0, 0, 76, 0, 8, 0, 0, 0, 0, 0, 0, 0, 56, 0, 28, 0, 0, 0, 0, 0, 0, 0, 88, 0, 70, 0, 0, 0, 0, 0, 0, 0, 80, 0, 20, 0, 0, 0, 0, 0, 0, 0, 56, 0, -24, 0, 0, 0, 0, 0, 0, 0, -84, 0, -28, 0, 0, 0, 0, 0, 0, 0, -136, 0, -22, 0, 0, 0, 0, 0, 0, 0, -48, 0, 44, 0, 0, 0, 0, 0, 0, 0, -48, 0, 168, 0, 0, 0, 0, 0, 0, 0, -36, 0, -24, 0, 0, 0, 0, 0, 0, 0, -62, 0, 130, 0, 0, 0, 0, 0, 0, 0, 128, 0, -48, 0, 0, 0, 0, 0, 0, 0, -72, 0, -16, 0, 0, 0, 0, 0, 0, 0, 24, 0, 30, 0, 0, 0, 0, 0, 0, 0, -40, 0, -14, 0, 0, 0, 0, 0, 0, 0, 24, 0, -16, 0, 0, 0, 0, 0, 0, 0, 84, 0, -88, 0, 0, 0, 0, 0, 0, 0, -40, 0, 6, 0, 0, 0, 0, 0, 0, 0, -28, 0, -104, 0, 0, 0, 0, 0, 0, 0, 72, 0, 64, 0, 0, 0, 0, 0, 0, 0, 148, 0, -40, 0, 0, 0, 0, 0, 0, 0, -24, 0, 32, 0, 0, 0, 0, 0, 0, 0, 24, 0, 108, 0, 0, 0, 0, 0, 0, 0, -80, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -48, 0, 126, 0, 0, 0, 0, 0, 0, 0, -20, 0, -100, 0, 0, 0, 0, 0, 0, 0, -10, 0, 76, 0, 0, 0, 0, 0, 0, 0, 44, 0, 24, 0, 0, 0, 0, 0, 0, 0, 112, 0, -160, 0, 0, 0, 0, 0, 0, 0, 98, 0, 72, 0, 0, 0, 0, 0, 0, 0, 16, 0, -40, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 96, 0, 0, 0, 0, 0, 0, 0, -40, 0, 102, 0, 0, 0, 0, 0, 0, 0, 14, 0, -64, 0, 0, 0, 0, 0, 0, 0, -120, 0, -144, 0, 0, 0, 0, 0, 0, 0, 8, 0, 78, 0, 0, 0, 0, 0, 0, 0, 48, 0, -190, 0, 0, 0, 0, 0, 0, 0, -308, 0, 20, 0, 0, 0, 0, 0, 0, 0, -48, 0, -88, 0, 0, 0, 0, 0, 0, 0, -160, 0, 48, 0, 0, 0, 0, 0, 0, 0, 50, 0, -8, 0, 0, 0, 0, 0, 0, 0, -160, 0, -72, 0, 0, 0, 0, 0, 0, 0, -72, 0, 40, 0, 0, 0, 0, 0, 0, 0, -48, 0, 192, 0, 0, 0, 0, 0, 0, 0, -276, 0, -50, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, -140, 0, 0, 0, 0, 0, 0, 0, 140, 0, 74, 0, 0, 0, 0, 0, 0, 0, -256, 0, 84, 0, 0, 0, 0, 0, 0, 0, -120, 0, -20, 0, 0, 0, 0, 0, 0, 0, 40, 0, -40, 0, 0, 0, 0, 0, 0, 0, 40, 0, 38, 0, 0, 0, 0, 0, 0, 0, -24, 0, 176, 0, 0, 0, 0, 0, 0, 0, 216, 0, 32, 0, 0, 0, 0, 0, 0, 0, -36, 0, 72, 0, 0, 0, 0, 0, 0, 0, -80, 0, 80, 0, 0, 0, 0, 0, 0, 0, -66, 0, -16, 0, 0, 0, 0, 0, 0, 0, 24, 0, -24, 0, 0, 0, 0, 0, 0, 0, -16, 0, -88, 0, 0, 0, 0, 0, 0, 0, -116, 0, -28, 0, 0, 0, 0, 0, 0, 0, -14, 0, -120, 0, 0, 0, 0, 0, 0, 0, -18, 0, -32, 0, 0, 0, 0, 0, 0, 0, 240, 0, -24, 0, 0, 0, 0, 0, 0, 0, -48, 0, 62, 0, 0, 0, 0, 0, 0, 0, 132, 0, 16, 0, 0, 0, 0, 0, 0, 0, -116, 0, 140, 0, 0, 0, 0, 0, 0, 0, -64, 0, 168, 0, 0, 0, 0, 0, 0, 0, -88, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 22, 0, 0, 0, 0, 0, 0, 0, -220, 0, -112, 0, 0, 0, 0, 0, 0, 0, -52, 0, 36, 0, 0, 0, 0, 0, 0, 0, -12, 0, -128, 0, 0, 0, 0, 0, 0, 0, 224, 0, -78, 0, 0, 0, 0, 0, 0, 0, 88, 0, 64, 0, 0, 0, 0, 0, 0, 0, 16, 0, 60, 0, 0, 0, 0, 0, 0, 0, -60, 0, 90, 0, 0, 0, 0, 0, 0, 0, 132, 0, 36, 0, 0, 0, 0, 0, 0, 0, -6, 0, 44, 0, 0, 0, 0, 0, 0, 0, 4, 0, -20, 0, 0, 0, 0, 0, 0, 0, 40, 0, -80, 0, 0, 0, 0, 0, 0, 0, -24, 0, -204, 0, 0, 0, 0, 0, 0, 0, 224, 0, -20, 0, 0, 0, 0, 0, 0, 0, 116, 0, 84, 0, 0, 0, 0, 0, 0, 0, -336, 0, -64, 0, 0, 0, 0, 0, 0, 0, -24, 0, 60, 0, 0, 0, 0, 0, 0, 0, 2, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 24, 0, -52, 0, 0, 0, 0, 0, 0, 0, 150, 0, -16, 0, 0, 0, 0, 0, 0, 0, 90, 0, -40, 0, 0, 0, 0, 0, 0, 0, -88, 0, -160, 0, 0, 0, 0, 0, 0, 0, 108, 0, 48, 0, 0, 0, 0, 0, 0, 0, 144, 0, -56, 0, 0, 0, 0, 0, 0, 0, -96, 0, -72, 0, 0, 0, 0, 0, 0, 0, -132, 0, -16, 0, 0, 0, 0, 0, 0, 0, 120, 0, 118, 0, 0, 0, 0, 0, 0, 0, -32, 0, 134, 0, 0, 0, 0, 0, 0, 0, 96, 0, -264, 0, 0, 0, 0, 0, 0, 0, 64, 0, 32, 0, 0, 0, 0, 0, 0, 0, 164, 0, 16, 0, 0, 0, 0, 0, 0, 0, 28, 0, 168, 0, 0, 0, 0, 0, 0, 0, 8, 0, -144, 0, 0, 0, 0, 0, 0, 0, 96, 0, -60, 0, 0, 0, 0, 0, 0, 0, -124, 0, -10, 0, 0, 0, 0, 0, 0, 0, 260, 0, -192, 0, 0, 0, 0, 0, 0, 0, -26, 0, -100, 0, 0, 0, 0, 0, 0, 0, -56, 0, 132, 0, 0, 0, 0, 0, 0, 0, 240, 0, 80, 0, 0, 0, 0, 0, 0, 0, 136, 0, 300, 0, 0, 0, 0, 0, 0, 0, -4, 0, 92, 0, 0, 0, 0, 0, 0, 0, -120, 0, -28, 0, 0, 0, 0, 0, 0, 0, 360, 0, -220, 0, 0, 0, 0, 0, 0, 0, -18, 0, -96, 0, 0, 0, 0, 0, 0, 0, 82, 0, -44, 0, 0, 0, 0, 0, 0, 0, -24, 0, 4, 0, 0, 0, 0, 0, 0, 0, -40, 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, 5, 2, 1, 2, 0], [1, 1, 35, 10, 1, 6, 0], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 34, "prim_orbit_index": 10, "minimal_twist": "280.2.q.c", "char_is_minimal": false, "conrey_index": 249, "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, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -1], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, -5, 0], [0, 0, 0, 0], [2, 0, -6, 0], [0, 0, 0, 0], [0, 7, 0, -7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 4, 0], [0, 0, 0, 0], [0, 2, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 5, 0, -5], [0, 0, 0, 0], [6, 0, -6, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 9, 0, -9], [0, 0, 0, 0], [-5, 0, 8, 0], [0, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 0], [0, -11, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -10], [0, 0, 0, 0], [8, 0, -8, 0], [0, 0, 0, 0], [0, 0, 12, 0], [0, 0, 0, 0], [0, 1, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, 0], [14, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, 2], [0, 0, 0, 0], [0, 0, 14, 0], [0, 0, 0, 0], [11, 0, -11, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 12, 0, 0], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 0, 0], [-9, 0, 6, 0], [0, 0, 0, 0], [0, -8, 0, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0]]}