# Stored data for newform 169.2.b.b, downloaded from the LMFDB on 23 April 2024.
{"label": "169.2.b.b", "space_label": "169.2.b", "level": 169, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503668380401833, "dim": 6, "is_polredabs": true, "nf_label": "6.0.153664.1", "trace_hash": 2158640600856562815, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 0, 5, 0, 6, 0, 1]]], "qexp_display": "q+(\\beta _{3}+\\beta _{5})q^{2}+(-1+\\beta _{4})q^{3}+(1-2\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 13, "char_orbit_label": "b", "char_is_real": true, "Nk2": 676, "analytic_conductor": 1.3494717941596386, "hecke_ring_index": 1, "level_radical": 13, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [169, 2, [2], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [13], "conrey_indexes": [168], "field_disc": -153664, "field_disc_factorization": [[-1, 1], [2, 6], [7, 4]], "field_poly": [1, 0, 6, 0, 5, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.610", "prec": 17}, {"__RealLiteral__": 0, "data": "0.451", "prec": 17}, {"__RealLiteral__": 0, "data": "163.390", "prec": 24}, {"__RealLiteral__": 0, "data": "53.009", "prec": 20}, {"__RealLiteral__": 0, "data": "6823.782", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -4, 0, 0], "traces": [0, 6, 0, -4, 0, 0, 0, 0, 0, -6, -10, 0, 0, 0, -10, 0, 4, 4, 0, 0, 0, 0, 6, 10, 0, 10, 0, 2, 0, -2, 2, 0, 0, 0, 0, 8, 14, 0, -24, 0, -6, 0, 16, -26, 0, 0, 0, 0, 2, 8, 0, 2, 0, 2, 0, 12, 8, 0, 0, 0, 0, 8, -2, 0, 22, 0, 10, 0, -42, 12, 0, 0, 0, 0, -16, -30, 0, -16, 0, -10, 0, -2, 28, 0, 0, 0, 0, -36, -30, 0, 24, 0, 0, 0, 10, -6, 0, 0, 0, 0, -14, -10, 0, 6, 0, 18, 0, 4, -28, 0, 0, 0, 0, 54, 16, 0, -28, 0, 44, 0, -10, 14, 0, 0, 0, 0, 10, 44, 0, -6, 0, -34, 0, -34, -20, 0, 0, 0, 0, -28, 42, 0, -22, 0, -4, 0, 44, -10, 0, 0, 0, 0, 36, -32, 0, 24, 0, -18, 0, 50, -14, 0, 0, 0, 0, 6, 14, 0, 32, 0, -30, 0, 14, 48, 0, 0, 0, 0, -18, -30, 0, -56, 0, -38, 0, -18, -8, 0, 0, 0, 0, -10, 4, 0, 70, 0, -14, 0, -48, 32, 0, 0, 0, 0, 28, 28, 0, -38, 0, 26, 0, 12, -42, 0, 0, 0, 0, -18, -20, 0, -14, 0, -8, 0, 28, 18, 0, 0, 0, 0, -26, 34, 0, 38, 0, 48, 0, -26, -44, 0, 0, 0, 0, 42, -70, 0, -42, 0, 80, 0, -62, 0, 0, 0, 0, 0, -56, -50, 0, 10, 0, 44, 0, 16, 62, 0, 0, 0, 0, -32, -8, 0, -16, 0, -8, 0, 28, -30, 0, 0, 0, 0, 26, 4, 0, 18, 0, 42, 0, -34, 8, 0, 0, 0, 0, 32, 52, 0, 30, 0, -28, 0, -36, -54, 0, 0, 0, 0, -70, 38, 0, 18, 0, -76, 0, -22, 126, 0, 0, 0, 0, 2, 2, 0, -56, 0, -30, 0, 70, -64, 0, 0, 0, 0, 140, -54, 0, 58, 0, -50, 0, 64, 66, 0, 0, 0, 0, -54, -42, 0, -54, 0, -70, 0, -6, -86, 0, 0, 0, 0, 6, 38, 0, 42, 0, -38, 0, 52, 16, 0, 0, 0, 0, 18, 74, 0, -22, 0, -50, 0, 70, -76, 0, 0, 0, 0, -64, 68, 0, -44, 0, 16, 0, 4, -36, 0, 0, 0, 0, 4, -12, 0, 18, 0, 98, 0, -62, 78, 0, 0, 0, 0, 98, 18, 0, -70, 0, 98, 0, -154, 14, 0, 0, 0, 0, 16, -32, 0, 70, 0, 62, 0, -22, 28, 0, 0, 0, 0, -62, -8, 0, -8, 0, 88, 0, 62, -42, 0, 0, 0, 0, 84, 14, 0, -16, 0, -10, 0, 24, 34, 0, 0, 0, 0, -34, 26, 0, 76, 0, 16, 0, -16, -94, 0, 0, 0, 0, -100, -22, 0, -28, 0, -82, 0, -14, 56, 0, 0, 0, 0, -18, -110, 0, 22, 0, -40, 0, 96, -28, 0, 0, 0, 0, 0, -78, 0, 38, 0, -112, 0, 20, 144, 0, 0, 0, 0, -42, -96, 0, -144, 0, -130, 0, -118, -84, 0, 0, 0, 0, -84, -50, 0, 56, 0, 40, 0, -82, 62, 0, 0, 0, 0, 52, 70, 0, 16, 0, 68, 0, 6, -4, 0, 0, 0, 0, -2, 70, 0, 58, 0, 38, 0, 50, 88, 0, 0, 0, 0, 12, 94, 0, 54, 0, 30, 0, -30, -92, 0, 0, 0, 0, 112, -56, 0, -66, 0, 154, 0, 0, -74, 0, 0, 0, 0, 16, -46, 0, 58, 0, 16, 0, 42, 34, 0, 0, 0, 0, -62, 98, 0, -32, 0, 84, 0, 84, 0, 0, 0, 0, 0, 98, -34, 0, -120, 0, -18, 0, -22, 56, 0, 0, 0, 0, -8, 184, 0, 98, 0, -16, 0, -116, -184, 0, 0, 0, 0, -142, 32, 0, -120, 0, -86, 0, 88, 60, 0, 0, 0, 0, 138, 28, 0, -96, 0, -112, 0, 86, -78, 0, 0, 0, 0, 70, -68, 0, 64, 0, -160, 0, 70, 52, 0, 0, 0, 0, -72, -102, 0, -22, 0, -6, 0, -112, -54, 0, 0, 0, 0, 28, -2, 0, 114, 0, -60, 0, 38, 82, 0, 0, 0, 0, 122, 76, 0, 6, 0, 14, 0, 152, -8, 0, 0, 0, 0, -126, 104, 0, 14, 0, -36, 0, -50, -14, 0, 0, 0, 0, -46, 14, 0, 42, 0, 6, 0, -72, 18, 0, 0, 0, 0, 32, -88, 0, -84, 0, 68, 0, -86, 118, 0, 0, 0, 0, -96, -182, 0, 88, 0, 70, 0, -20, -4, 0, 0, 0, 0, 0, -44, 0, 0, 0, 130, 0, 102, -4, 0, 0, 0, 0, 78, 96, 0, -26, 0, 38, 0, -70, 42, 0, 0, 0, 0, 26, 34, 0, 60, 0, 12, 0, -124, -48, 0, 0, 0, 0, -102, 6, 0, -142, 0, 28, 0, -32, 54, 0, 0, 0, 0, -14, -136, 0, 90, 0, 24, 0, 112, -98, 0, 0, 0, 0, 4, -148, 0, 140, 0, -80, 0, 6, 156, 0, 0, 0, 0, -116, 20, 0, -150, 0, -20, 0, -140, -160, 0, 0, 0, 0, 18, 42, 0, 32, 0, -68, 0, -40, -26, 0, 0, 0, 0, 8, 154, 0, -110, 0, -12, 0, 64, -86, 0, 0, 0, 0, 6, -6, 0, -46, 0, 92, 0, 98, 90, 0, 0, 0, 0, 38, 26, 0, 150, 0, 138, 0, -14, -26, 0, 0, 0, 0, 102, -38, 0, -140, 0, 70, 0, -76, -20, 0, 0, 0, 0, 14, -68, 0, 36, 0, 126, 0, 102, 42, 0, 0, 0, 0, -86, -82, 0, -112, 0, -82, 0, 66, -54, 0, 0, 0, 0, 142, 96, 0, -8, 0, 24, 0, -100, 8, 0, 0, 0, 0, -34, 182, 0, 274, 0, -46, 0, -50, -26, 0, 0, 0, 0, -126, 40, 0, 38, 0, -90, 0, -82, 196, 0, 0, 0, 0, 66, 58, 0, 16], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "169.2.a.b", "char_is_minimal": false, "conrey_index": 168, "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, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1], [-1, 0, 0, 0, 1, 0], [1, 0, -2, 0, -1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 0, -1, 0, 0], [0, -1, 0, 2, 0, 0], [0, 2, 0, -1, 0, -2], [0, 0, -1, 0, -2, 0], [-1, 0, -1, 0, -1, 0], [0, 1, 0, 0, 0, -3], [-1, 0, 1, 0, 2, 0], [0, 0, 0, 0, 0, 0], [-1, 0, -2, 0, 0, 0], [0, 1, 0, -1, 0, 0], [1, 0, -1, 0, 0, 0], [-1, 0, 3, 0, 2, 0], [0, 1, 0, -2, 0, -4], [0, -2, 0, 3, 0, 3], [0, 3, 0, -3, 0, -2], [0, -2, 0, -1, 0, 1], [-1, 0, 3, 0, 3, 0], [1, 0, 0, 0, 2, 0], [0, -1, 0, -1, 0, 3], [2, 0, 1, 0, -2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 2, 0, -1, 0], [0, 0, 0, -1, 0, -5], [0, 0, 2, 0, -3, 0], [0, 0, 1, 0, 0, 0], [0, -5, 0, 2, 0, 4], [0, 5, 0, -3, 0, -5], [0, -3, 0, -1, 0, 4], [0, -3, 0, 5, 0, 7], [2, 0, -3, 0, 1, 0], [1, 0, 4, 0, 0, 0], [0, -2, 0, 1, 0, 5], [-1, 0, -6, 0, -3, 0], [0, 0, 0, 0, 0, 0], [-2, 0, 3, 0, 0, 0], [0, -4, 0, -2, 0, 3], [3, 0, 0, 0, -1, 0], [-3, 0, -1, 0, -3, 0], [0, -1, 0, 5, 0, 2], [0, -2, 0, 0, 0, -3], [0, 0, 0, 1, 0, 3], [0, -1, 0, 2, 0, -5], [0, 0, 0, 0, 1, 0], [1, 0, 1, 0, 0, 0], [0, -1, 0, 4, 0, 2], [2, 0, -2, 0, -3, 0], [0, 0, 0, 0, 0, 0], [-3, 0, 3, 0, 7, 0], [0, -2, 0, 4, 0, 3], [1, 0, 1, 0, 2, 0], [-1, 0, 2, 0, 5, 0], [0, 0, 0, -1, 0, -2], [0, -2, 0, 4, 0, 1], [0, 4, 0, -4, 0, -9], [0, 1, 0, 0, 0, 2], [0, 0, 5, 0, -1, 0], [3, 0, -6, 0, -4, 0], [0, 5, 0, -3, 0, -4], [0, 0, 6, 0, 5, 0], [0, 0, 0, 0, 0, 0], [4, 0, -3, 0, -4, 0], [0, 6, 0, -1, 0, -2], [-4, 0, -6, 0, -3, 0], [3, 0, -2, 0, -1, 0], [0, 3, 0, -4, 0, -3], [0, 3, 0, -3, 0, 7], [0, -2, 0, 5, 0, 1], [0, 6, 0, -9, 0, -2], [1, 0, -6, 0, -5, 0], [-7, 0, 2, 0, 4, 0], [0, 2, 0, -7, 0, -10], [-6, 0, 5, 0, 5, 0], [0, 0, 0, 0, 0, 0], [4, 0, -9, 0, -8, 0], [0, 3, 0, -2, 0, 0], [-4, 0, 4, 0, 7, 0], [6, 0, -1, 0, -3, 0], [0, 9, 0, -7, 0, -3], [0, -4, 0, 1, 0, 4], [0, -3, 0, 4, 0, 4], [0, 1, 0, -5, 0, -8], [-8, 0, 3, 0, 3, 0], [-6, 0, -1, 0, 4, 0], [0, -7, 0, 7, 0, 1], [2, 0, 3, 0, 3, 0], [0, 0, 0, 0, 0, 0], [1, 0, -4, 0, 1, 0], [0, 2, 0, 3, 0, -7], [-1, 0, 3, 0, 5, 0], [1, 0, -5, 0, -1, 0], [0, -2, 0, -2, 0, 7], [0, -1, 0, -6, 0, -4], [0, -1, 0, 3, 0, 3], [0, 2, 0, 4, 0, 1], [1, 0, -4, 0, -6, 0]]}