# Stored data for newform 1805.2.b.b, downloaded from the LMFDB on 08 May 2024. {"label": "1805.2.b.b", "space_label": "1805.2.b", "level": 1805, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503668380403469, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1150432967790823770, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 0, 1]], [29, [9, 1]]], "qexp_display": "q+iq^{2}-2q^{4}+(-1-i)q^{5}-2iq^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 7220, "analytic_conductor": 14.41299756484111, "hecke_ring_index": 2, "level_radical": 95, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [1805, 2, [362, 1446], [1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [5, 19], "conrey_indexes": [1084], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.898", "prec": 17}, {"__RealLiteral__": 0, "data": "0.099", "prec": 17}, {"__RealLiteral__": 0, "data": "14.218", "prec": 20}, {"__RealLiteral__": 0, "data": "0.932", "prec": 17}, {"__RealLiteral__": 0, "data": "132.502", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, -2, 0], "traces": [0, 2, 0, 0, -4, -2, 0, 0, 0, 6, 8, -2, 0, 0, 16, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, -6, -8, 0, 0, -18, 0, -14, 0, 0, 8, -16, -12, 0, 0, 0, 0, 4, 0, 0, 4, -6, 24, 0, 0, -18, -16, 0, 0, 0, 0, 2, 0, 0, 0, -18, 0, -14, 0, 0, 16, 8, 0, 0, 0, 0, -16, 2, 0, 0, -8, 0, 0, 0, 0, -2, 8, 18, 0, 0, 0, -8, 8, 0, 0, 22, 24, 16, 0, 0, -24, 0, 0, 0, 0, -6, 12, 30, 0, 0, 0, 0, 16, 0, 0, -30, -8, 0, 0, 0, 0, -24, 36, 0, 0, -16, 0, -20, 0, 0, 28, 22, 48, 0, 0, 0, 8, 24, 0, 0, 40, 0, 0, 0, 0, -40, 32, 0, 0, 0, -24, 18, 40, 0, 0, 2, 0, 18, 0, 0, -16, 14, 0, 0, 0, 0, -32, -48, 0, 0, -8, 0, -24, 0, 0, 18, -8, 0, 0, 0, 0, 32, 8, 0, 0, -30, 12, -12, 0, 0, 0, 8, 0, 0, 0, 0, 0, -6, 0, 0, 24, 0, 36, 0, 0, -26, 0, 0, 0, 0, 0, -4, 64, 0, 0, 0, 0, 10, 0, 0, 40, -8, 0, 0, 0, 0, -4, 8, 0, 0, -64, -18, -48, 0, 0, -34, -24, 0, 0, 0, -24, 24, 36, 0, 0, 38, 0, 2, 0, 0, 28, 18, 0, 0, 0, 0, -8, 26, 0, 0, 24, 0, 32, 0, 0, 16, -16, -54, 0, 0, 0, -16, 0, 0, 0, -6, 0, 6, 0, 0, -48, 6, 0, 0, 0, -42, 0, 20, 0, 0, -4, 0, 8, 0, 0, 26, -72, 0, 0, 0, 0, 18, 0, 0, 0, 24, 0, -16, 0, 0, 0, 14, 24, 0, 0, 0, -56, 0, 0, 0, -16, -48, 4, 0, 0, 18, -16, 0, 0, 0, -36, -16, 16, 0, 0, 48, 0, 40, 0, 0, 48, -40, 0, 0, 0, 0, 16, 14, 0, 0, 0, 0, -96, 0, 0, -28, -48, 0, 0, 0, 0, -2, -44, 0, 0, 40, 0, 0, 0, 0, -32, -40, 0, 0, 0, 12, 8, -32, 0, 0, -8, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 16, 64, 0, 0, 66, 0, -24, 0, 0, 72, 2, 12, 0, 0, 0, 24, 6, 0, 0, -60, -18, -144, 0, 0, 10, 16, 0, 0, 0, 72, 24, 32, 0, 0, -18, 0, -30, 0, 0, 0, 16, 0, 0, 0, 0, -8, 42, 0, 0, -112, 0, 60, 0, 0, 26, 0, -54, 0, 0, 0, -22, -8, 0, 0, -62, -48, -4, 0, 0, -56, -16, 0, 0, 0, 0, 48, -50, 0, 0, 72, 0, -32, 0, 0, -80, 24, 0, 0, 0, 0, 0, 32, 0, 0, -30, 0, -8, 0, 0, 40, -24, 0, 0, 0, 0, -72, 26, 0, 0, 0, 6, 56, 0, 0, -56, -44, 0, 0, 0, 0, -30, -24, 0, 0, -36, 0, -80, 0, 0, 24, -64, 0, 0, 0, 0, 0, 30, 0, 0, -48, 0, 0, 0, 0, -26, -16, -54, 0, 0, 0, -40, 0, 0, 0, 18, 0, 46, 0, 0, -32, 30, 0, 0, 0, -42, 16, 0, 0, 0, 112, 0, 80, 0, 0, 8, 64, 0, 0, 0, 0, 48, 56, 0, 0, -30, 0, 26, 0, 0, 32, 48, 48, 0, 0, 0, -36, 48, 0, 0, 0, 24, 16, 0, 0, 0, -72, 0, 0, 0, 0, 16, -4, 0, 0, 24, 0, 34, 0, 0, -36, 20, 0, 0, 0, 0, -56, -24, 0, 0, -64, 0, 0, 0, 0, -8, -28, 0, 0, 0, 0, -14, 120, 0, 0, 8, -48, 2, 0, 0, 8, -24, 0, 0, 0, 6, 0, 42, 0, 0, 96, 0, 0, 0, 0, 18, 24, 0, 0, 0, 0, -24, -16, 0, 0, -40, 0, -30, 0, 0, 0, 0, -24, 0, 0, 0, -40, 14, 0, 0, -136, 0, -36, 0, 0, -48, 0, 0, 0, 0, 0, 48, -32, 0, 0, 16, 0, 6, 0, 0, 48, 40, 0, 0, 0, 0, -64, 12, 0, 0, -16, 0, -32, 0, 0, -50, 8, -6, 0, 0, 0, -8, 60, 0, 0, 42, 24, -128, 0, 0, 24, 54, 0, 0, 0, 54, -40, -8, 0, 0, 64, 0, -96, 0, 0, 58, -16, 0, 0, 0, 0, -2, -48, 0, 0, -80, 0, 82, 0, 0, 72, -18, 0, 0, 0, 0, 0, -36, 0, 0, 12, -24, 24, 0, 0, -10, 16, 0, 0, 0, 24, 42, 0, 0, 0, 0, 0, -2, 0, 0, 72, 16, 0, 0, 0, 0, -8, 96, 0, 0, 32, 0, 52, 0, 0, 24, 64, 66, 0, 0, 0, 48, 56, 0, 0, 86, 72, 18, 0, 0, 8, -16, 0, 0, 0, 48, 8, 42, 0, 0, 0, 0, -144, 0, 0, -4, 24, 0, 0, 0, 0, -48, 0, 0, 0, -96, 0, 104, 0, 0, -20, -18, -72, 0, 0, 0, -24, 24, 0, 0, -112, 0, 0, 0, 0, -2, 16, 0, 0, 0, 0, 96, -16, 0, 0, 2, 0, 40, 0, 0, 0, 16, 0, 0, 0, 0, -8, 74, 0, 0, -16, 0, 16, 0, 0, -48, 88, -18, 0, 0, 0, 30, 0, 0, 0, 126, 36, -16, 0, 0, 0, 12, 0, 0, 0, 90, 64, 82, 0, 0, -136, 0, 68, 0, 0, -32, 0, 0, 0, 0, 0, -16, -16, 0, 0, -102, 0, 0, 0, 0, -40, 8, 0, 0, 0, 0, -48, 70, 0, 0, 72, 0, -8, 0, 0, 40, 0, 0, 0, 0, 48, 6, -76, 0, 0, 96, 0, 36, 0, 0, -4, -64, 0, 0, 0, 0, -24, 72, 0, 0, 152, 0, 56, 0, 0, -22, -36, -90, 0, 0, 0, -72, -72, 0, 0, -24, -24, 88, 0, 0, 16, 26, 0, 0, 0, 0, 0, -16, 0, 0, -52, 0, -104, 0, 0, -90, 120, 0, 0, 0, 0, 144, 0, 0, 0, 90, 0, -44, 0, 0, -64, -12, 0, 0, 0, 0, -64, 42, 0, 0, 24, -72, -32, 0, 0, 40, -32, 0, 0, 0, 108, 0, 64, 0, 0, 12, 0, 22, 0, 0, -56, -10, 0, 0, 0, 0, 32, -12, 0, 0, 0, 0, -16, 0, 0, -68, -40, -48, 0, 0, 0, 16, 12, 0, 0, -24, 0, 72, 0, 0, -12, 112, 0, 0, 0, -60, -120, 78, 0, 0, -88, 0, 0, 0, 0, 32, -12, 0, 0, 0, 0, -8, -16, 0, 0, -42, 0, -30, 0, 0, -56, 8, 84, 0, 0, 0, 64, 0, 0, 0, -40, 66, -96, 0, 0, -28, 48, 0, 0, 0, 144, 56, -8, 0, 0, -40, 0, -32, 0, 0, 0, 34, 0, 0, 0, 0, -72, -114, 0, 0, -24, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 32, -16, 0, 0, -96, 24, -22, 0, 0, 96, -48, 0, 0, 0, 72, -36, -46, 0, 0, 32, 0, -128, 0, 0, -36, -64, 0, 0, 0, 0, -38, -48, 0, 0, 30, 0, -60, 0, 0, 32, -2, 120, 0, 0, 0, -80, 192, 0, 0, 56, 0, 0, 0, 0, -48, -28, 0, 0, 0, 0, 54, 96, 0, 0, -76, 0, -66, 0, 0, -72, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 176, 0, 0, -28, 96, -120, 0, 0, 0, -26, 0, 0, 0, -72, 96, 24, 0, 0, 8, 24, 0, 0, 0, 0, -24, -28, 0, 0, 72, 0, -36, 0, 0, -86, -32, 0, 0, 0, 0, -24, -184, 0, 0, 30, 0, 88, 0, 0, 24, -16, -72, 0, 0, 0, 32, 50, 0, 0, 0, 54, 40, 0, 0, 16, 96, 0, 0, 0, 120, 0, -96, 0, 0, -64, 0, 20, 0, 0, -80, 32, 0, 0, 0, 0, 0, 42, 0, 0, -216, 0, 0, 0, 0, 64, 80, 6, 0, 0, 0, 6, -80, 0, 0, 0, 0, -128, 0, 0, 0, -6, 0, 0, 0, 54, 32, -84, 0, 0, -28, 0, 120, 0, 0, 66, 48, 0, 0, 0, 0, -22, -32, 0, 0, -144, 0, 34, 0, 0, 0, -112, -48, 0, 0, 0, -160, 40, 0, 0, 16, 42, 56, 0, 0, -112, 0, 0, 0, 0, 0, -20, 0, 0, 0, 22, 0, 24, 0, 0, 240, -56, 0, 0, 0, 0, 4, 162, 0, 0, -88, 0, -168, 0, 0, -116, -8, 0, 0, 0, 0, -32, -80, 0, 0, -32, -96, -24, 0, 0, 0, -26, 0, 0, 0, -144, 144, -34, 0, 0, -32, 0, -64, 0, 0, 34, 80, 0, 0, 0, 0, -16, -24, 0, 0, -48, 0, -98, 0, 0, -40, 54, -24, 0, 0, 0, 0, 52, 0, 0, 64, 0, 200, 0, 0, -62, 8, 0, 0, 0, -72, -24, 0, 0, 0, 42, 0, 0, 0, 0, 96, 16, 0, 0, 0, 0, 72, -122, 0, 0, -104, 0, -116, 0, 0, 126, 0, 54, 0, 0, 0, 42, -240, 0, 0, 40, -24, 48, 0, 0, 72, 64, 0, 0, 0, 0, -32, -120, 0, 0, 0, 0, 136, 0, 0, -140, 112, 0, 0, 0, 0, 0, -132, 0, 0, -104, 0, 16, 0, 0, 48, -120, 0, 0, 0, 0, 16, -56, 0, 0, -88, 96, 0, 0, 0, 2, -4, 0, 0, 0, 24, -8, 56, 0, 0, 112, 0, 8, 0, 0, -96, -18, 0, 0, 0, 0, -48, 30, 0, 0, -12, 0, -40, 0, 0, 108, -192, -90, 0, 0, 0, 0, -120, 0, 0, 54, 36, 38, 0, 0, 0, -8, 0, 0, 0, -36, -16, 64, 0, 0, 0, 0, -20, 0, 0, -2, 0, 0, 0, 0, 0, -48, -120, 0, 0, -24, 0, 24, 0, 0, -24, -40, 0, 0, 0, 0, -48, -18, 0, 0, 0, 24, -72, 0, 0, 22, -48, 0, 0, 0, 0, 80, 36, 0, 0, -120, 0, -74, 0, 0, 60, 136, 0, 0, 0, 0, 72, 0, 0, 0, -160, 0, -64, 0, 0, -58, -32, 0, 0, 0, 0, -14, -64, 0, 0, 118, 0, 162, 0, 0, 72, 32, 0, 0, 0, -18, 0, -66, 0, 0, -84, 0, 80, 0, 0, 0, 96, 0, 0, 0, 0, -48, 0, 0, 0, -24, 0, 52, 0, 0, 120, 28, 72, 0, 0, 0, 176, -64, 0, 0, 232, 0, -52, 0, 0, 114, 32, 0, 0, 0, 108, 32, -32, 0, 0, 126, 0, 48, 0, 0, 64, -6, 0, 0, 0, 0, 44, -48, 0, 0, 0, 0, 0, 0, 0, 92, -120, -78, 0, 0, 0, -40, 124, 0, 0, -48, 0, -76, 0, 0, 8, 0, 0, 0, 0, 0, -48, -78, 0, 0, -48, 0, 0, 0, 0, -40, 32, 0, 0, 0, 0, 80, 24, 0, 0, 126, 0, 102, 0, 0, 192, -64, 0, 0, 0, 0, 96, 0, 0, 0, 100, -12, -8, 0, 0, 78, 24, 0, 0, 0, 192, 32, -144, 0, 0, -18, 0, -124, 0, 0, 0, 48, 0, 0, 0, 0, 8, -64, 0, 0, 224, 0, 160, 0, 0, 34, 0, 0, 0, 0, 0, -72, 48, 0, 0, 10, 0, 98, 0, 0, 168, -58, 0, 0, 0, 30, 0, -70, 0, 0, 64, 0, -96, 0, 0, 72, -24, 0, 0, 0, 0, -24, 60, 0, 0, 0, 0, 48, 0, 0, 16, -32, 120, 0, 0, 0, -64, 94, 0, 0, -88, -24, 80, 0, 0, -224, 48, 0, 0, 0, 0, -66, -320, 0, 0, 130, 0, 128, 0, 0, 176, 24, 0, 0, 0, 0, 0, 16, 0, 0, -52, 0, 144, 0, 0, 30, -72, 0, 0, 0, 0, 6, 0, 0, 0, -120, -12, -112, 0, 0, -112, -32, 0, 0, 0, 24, -104, 12, 0, 0, -104, 0, 112, 0, 0, 134, -88], "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]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "95.2.i.a", "char_is_minimal": true, "conrey_index": 1084, "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], [-2, 0], [-1, -1], [0, 0], [0, -2], [0, 0], [3, 0], [4, -1], [-1, 0], [0, 0], [0, 1], [8, 0], [0, 0], [-4, 0], [0, -1], [0, 3], [0, 0], [2, 2], [0, 0], [0, -1], [0, -3], [0, 0], [-3, 2], [-4, 0], [0, 0], [0, 4], [-9, 0], [0, 0], [-7, 0], [0, -4], [0, 0], [4, 0], [-8, 2], [-6, 0], [0, 1], [0, 0], [0, 0], [0, 0], [2, 0], [0, 0], [0, -1], [2, 0], [-3, -3], [12, 0], [0, 3], [0, 0], [-9, 0], [-8, -3], [0, 0], [0, -2], [0, -2], [0, 0], [1, 1], [0, 0], [0, 0], [0, -9], [-9, 0], [0, 0], [-7, 0], [0, -7], [0, -6], [8, 0], [4, -1], [0, 0], [0, -5], [0, 2], [0, 0], [-8, -8], [1, 0], [0, 0], [0, -5], [-4, 0], [0, 0], [0, 0], [0, 2], [0, 0], [-1, 0], [4, 4], [9, 0], [0, 2], [0, 3], [0, 0], [-4, 1], [4, 0], [0, 0], [0, 0], [11, 0], [12, -3], [8, 0], [0, 6], [0, 0], [-12, 0], [0, 0], [0, 0], [0, -3], [0, -9], [-3, 0], [6, -4]]}