# Stored data for newform 605.2.b.h, downloaded from the LMFDB on 25 April 2024. {"label": "605.2.b.h", "space_label": "605.2.b", "level": 605, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525266144625245, "dim": 12, "is_polredabs": true, "trace_hash": 1612785776712578282, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [3, 0, 29, 0, 11, 0, 1]], [19, [-3888, 0, 1332, 0, -72, 0, 1]]], "qexp_display": "q+\\beta _{9}q^{2}-\\beta _{8}q^{3}+(-2-\\beta _{6})q^{4}+\\beta _{4}q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 2420, "analytic_conductor": 4.830949322287463, "hecke_ring_index": 8, "level_radical": 55, "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": "0.758", "prec": 17}, "analytic_rank_proved": true, "char_values": [605, 2, [122, 486], [1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [5, 11], "conrey_indexes": [364], "field_disc": 34534870610048188416, "field_disc_factorization": [[2, 26], [3, 6], [163, 4]], "field_poly": [1089, 4398, 6697, 3848, -67, -668, 516, -20, -123, 34, 1, -4, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.131", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1045.949", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "154201.242", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, -6, 0], "traces": [0, 12, 0, 0, -20, -6, 0, 0, 0, -20, 0, 0, 0, 0, -32, 20, 36, 0, 0, 0, 26, 0, 0, 0, 0, -10, 20, 0, 0, 0, 0, 8, 0, 0, 12, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 48, 0, 0, -32, -92, 0, 0, 0, 28, 0, 0, 0, 0, -16, -12, 112, 0, 0, 0, 36, 0, 0, 0, 0, -106, -20, 0, 0, 0, 0, -56, 0, 0, -108, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, -116, 0, 0, 0, 0, 0, 0, 72, 0, 0, 96, -68, 0, 0, 0, -56, 0, 0, 0, 0, -40, -36, 168, 0, 0, 0, -70, 0, 0, 0, 0, -88, -28, 0, 0, 0, 0, -56, 0, 0, 52, 0, 200, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, -50, 0, 0, 0, 264, 0, 0, 0, 0, -48, -18, -20, 0, 0, 0, 30, 0, 0, 0, 0, -36, 96, 0, 0, 0, 0, -116, 0, 0, -32, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 52, 0, 0, 112, -14, 0, 0, 0, -68, 0, 0, 0, 0, -36, 20, 208, 0, 0, 0, -52, 0, 0, 0, 0, -58, -96, 0, 0, 0, 0, 104, 0, 0, 40, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 64, 0, 0, -184, -68, 0, 0, 0, -32, 0, 0, 0, 0, 136, -114, -24, 0, 0, 0, 120, 0, 0, 0, 0, 36, -120, 0, 0, 0, 0, 36, 0, 0, -96, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 188, 0, 0, 0, 0, 0, 0, -32, 0, 0, -8, 84, 0, 0, 0, -232, 0, 0, 0, 0, -88, 168, -120, 0, 0, 0, -4, 0, 0, 0, 0, 48, 180, 0, 0, 0, 0, 60, 0, 0, 88, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, -76, 0, 0, -52, 36, 0, 0, 0, 84, 0, 0, 0, 0, 48, 122, -36, 0, 0, 0, 114, 0, 0, 0, 0, 90, 160, 0, 0, 0, 0, 68, 0, 0, -168, 0, -292, 0, 0, 0, 0, 0, 0, 0, 0, -176, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 4, 0, 0, -120, 54, 0, 0, 0, -84, 0, 0, 0, 0, -120, -76, -432, 0, 0, 0, -100, 0, 0, 0, 0, 184, -116, 0, 0, 0, 0, 0, 0, 0, 528, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 174, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, -264, 0, 0, -16, 268, 0, 0, 0, -24, 0, 0, 0, 0, 16, -36, 16, 0, 0, 0, 72, 0, 0, 0, 0, 206, -48, 0, 0, 0, 0, -120, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 156, 0, 0, 0, 0, 0, 0, 120, 0, 0, 28, -36, 0, 0, 0, -80, 0, 0, 0, 0, 152, 214, -136, 0, 0, 0, -360, 0, 0, 0, 0, -84, -100, 0, 0, 0, 0, 272, 0, 0, -360, 0, -220, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, -456, 0, 0, 192, 96, 0, 0, 0, 88, 0, 0, 0, 0, 136, -172, -304, 0, 0, 0, 6, 0, 0, 0, 0, 132, 280, 0, 0, 0, 0, 56, 0, 0, -240, 0, -300, 0, 0, 0, 0, 0, 0, 0, 0, 166, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 76, 0, 0, 104, 168, 0, 0, 0, -24, 0, 0, 0, 0, 316, -120, -280, 0, 0, 0, 90, 0, 0, 0, 0, 56, -216, 0, 0, 0, 0, -80, 0, 0, 456, 0, -456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 16, 0, 0, -72, 210, 0, 0, 0, 396, 0, 0, 0, 0, 100, -252, -64, 0, 0, 0, -4, 0, 0, 0, 0, 174, -288, 0, 0, 0, 0, -296, 0, 0, -184, 0, 176, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, -280, 0, 0, 432, -52, 0, 0, 0, -216, 0, 0, 0, 0, 228, 72, -240, 0, 0, 0, -300, 0, 0, 0, 0, -132, -64, 0, 0, 0, 0, 180, 0, 0, 408, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 32, 0, 0, -116, 244, 0, 0, 0, 432, 0, 0, 0, 0, -136, 24, -48, 0, 0, 0, 64, 0, 0, 0, 0, 66, 168, 0, 0, 0, 0, 272, 0, 0, 208, 0, -264, 0, 0, 0, 0, 0, 0, 0, 0, -228, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 100, 0, 0, 244, 0, 0, 0, 0, -72, 0, 0, 0, 0, -240, -64, 96, 0, 0, 0, -46, 0, 0, 0, 0, 74, 432, 0, 0, 0, 0, 192, 0, 0, -332, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 84, 0, 0, -312, -92, 0, 0, 0, -512, 0, 0, 0, 0, 24, 300, 416, 0, 0, 0, -96, 0, 0, 0, 0, 100, -52, 0, 0, 0, 0, -240, 0, 0, -48, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 294, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, -16, 0, 0, -352, 72, 0, 0, 0, 96, 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, 11, 2, -1, 2, 0], [1, 1, 55, 4, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "605.2.b.h", "char_is_minimal": true, "conrey_index": 364, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [-2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0], [-3, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0], [-4, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0], [3, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, -1], [1, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 1, 0], [0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, 2, 0, -1, 0, 1, 0, -2, 0, 0, 0], [0, -2, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 1], [0, 3, 0, -1, 0, 1, 0, -2, 0, 0, 0, 0], [-1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 1], [1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 1, 0], [0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, -3, 0, 1, 0, 0, 0, 3, -1, 0], [3, 0, -2, 0, 2, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0], [9, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, -3], [0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0], [0, -1, 0, 1, 0, 0, 0, 0, 0, 4, 2, 0], [0, 1, 0, 3, 0, 1, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 2, 0, -1, 0, 0, 0, -3, 0, 0, -1], [0, -1, 0, 4, 0, -1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 4], [-1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, -1, 0, 0, 0, 2, 2, 0], [0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1], [0, 1, 0, 5, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0], [0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, -2], [-1, 0, -2, 0, 2, 0, -1, 0, 0, 0, 0, 0], [-9, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, 4], [0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 1, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0], [4, 0, -2, 0, 2, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 1, 0, 0, 0, 2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0], [3, 0, -4, 0, 4, 0, 1, 0, 0, 0, 0, 0], [-3, 0, 2, 0, -2, 0, 0, 0, -3, 0, 0, -1], [11, 0, -2, 0, 2, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 1, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0], [0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [6, 0, -4, 0, 2, 0, 0, 0, 1, 0, 0, 2], [0, 5, 0, -6, 0, 1, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 3], [0, -4, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0], [-8, 0, 0, 0, 3, 0, -2, 0, -2, 0, 0, -2], [0, 0, -2, 0, 2, 0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4, 0, -1, 1, 0], [0, 5, 0, 3, 0, -1, 0, -2, 0, 0, 0, 0], [0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0], [-10, 0, 5, 0, -5, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, -5, 0, 1, 0, 0, 0, 0, 3, 0], [3, 0, 2, 0, -2, 0, -3, 0, 0, 0, 0, 0], [0, 0, 3, 0, 3, 0, 0, 0, -1, 0, 0, -5], [0, 0, -1, 0, -1, 0, 0, 0, -3, 0, 0, -3], [0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 3, 0, 0, 0, 1, 0, -5, 0, 0, 0, 0], [0, 0, 0, 9, 0, -2, 0, 1, 0, 0, 0, 0], [0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -4, 0, 3, 0, 0, 0, 1, 0, 0, -3]]}