# Stored data for newform 605.2.b.c, downloaded from the LMFDB on 23 April 2024.
{"label": "605.2.b.c", "space_label": "605.2.b", "level": 605, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007268007772765, "dim": 4, "is_polredabs": true, "nf_label": "4.0.1089.1", "trace_hash": 286129829752187021, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 0, 7, 0, 1]], [19, [-4, 1]]], "qexp_display": "q+(-\\beta _{1}-\\beta _{2}+\\beta _{3})q^{2}+(-\\beta _{1}+\\beta _{3})q^{3}+\\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": 2, "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": "0.515", "prec": 17}, "analytic_rank_proved": true, "char_values": [605, 2, [122, 486], [1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [5, 11], "conrey_indexes": [364], "field_disc": 1089, "field_disc_factorization": [[3, 2], [11, 2]], "field_poly": [9, -3, -2, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.677", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "69.881", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1858.439", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, -3, 0], "traces": [0, 4, 0, 0, -6, -3, -8, 0, 0, -2, 10, 0, 0, 0, 12, 1, 14, 0, 0, 16, -12, -12, 0, 0, -4, 1, 0, 0, 0, 12, 6, 2, 0, 0, 16, -18, -30, 0, 0, 0, -28, -12, 0, 0, 0, 18, 8, 0, 0, -20, 18, 28, 0, 0, -20, 0, -60, 0, 0, 18, -18, -20, 0, 0, -2, 0, 0, 0, 0, 14, 24, -6, 0, 0, -12, 15, -24, 0, 0, 28, 6, -8, 0, 0, -48, -2, -12, 0, 0, 6, 28, 0, 0, 0, 44, -12, -36, 0, 0, 0, 48, -24, 0, 0, 0, 42, 56, 0, 0, 40, 0, -54, 0, 0, -32, -1, -84, 0, 0, 24, 36, 0, 0, 0, -36, -36, 60, 0, 0, 12, 0, -12, 0, 0, -48, 19, 8, 0, 0, 4, 60, 44, 0, 0, 26, 24, 24, 0, 0, 0, -2, -20, 0, 0, 0, 15, 0, 0, 0, 32, 12, 12, 0, 0, 84, 0, -44, 0, 0, 52, -12, -8, 0, 0, -24, -6, 0, 0, 0, 6, 6, 62, 0, 0, 4, -15, -4, 0, 0, 36, 40, -66, 0, 0, -36, 0, 30, 0, 0, 32, -24, -18, 0, 0, 24, -24, -36, 0, 0, 0, 36, 40, 0, 0, -44, 18, 56, 0, 0, -24, 0, 0, 0, 0, -12, -50, -28, 0, 0, -70, -6, 0, 0, 0, 0, -22, -60, 0, 0, -36, 20, -44, 0, 0, -36, 15, 24, 0, 0, -44, -44, -54, 0, 0, -60, -54, -90, 0, 0, -84, 0, 60, 0, 0, 0, -40, 48, 0, 0, 0, -18, -8, 0, 0, -76, 0, 12, 0, 0, 32, 12, 48, 0, 0, 108, 4, 0, 0, 0, 12, 96, -30, 0, 0, 40, 3, -72, 0, 0, 0, -6, 48, 0, 0, 56, 48, -8, 0, 0, 36, 38, -24, 0, 0, 132, -24, 24, 0, 0, 0, 18, -44, 0, 0, -54, 0, -12, 0, 0, 0, 0, -22, 0, 0, -44, 39, 24, 0, 0, -82, 36, 0, 0, 0, 60, -27, 40, 0, 0, 16, -96, 0, 0, 0, -36, -45, 24, 0, 0, 72, -52, -12, 0, 0, 0, -36, 40, 0, 0, -60, 42, -48, 0, 0, 0, -44, -44, 0, 0, 14, -48, -72, 0, 0, -68, 0, 120, 0, 0, -18, 0, -28, 0, 0, 40, -54, 0, 0, 0, -48, -46, 0, 0, 0, 36, 39, 168, 0, 0, 64, -96, -34, 0, 0, -4, 22, 0, 0, 0, 0, 36, 80, 0, 0, -104, -30, 12, 0, 0, 0, -24, -12, 0, 0, 72, 36, -60, 0, 0, 40, 0, 10, 0, 0, -84, -21, -24, 0, 0, 30, 24, 0, 0, 0, 100, 0, -16, 0, 0, 4, 18, 60, 0, 0, 108, 17, -8, 0, 0, 60, 0, 66, 0, 0, -56, 4, 96, 0, 0, 24, 60, 0, 0, 0, 0, 21, -44, 0, 0, 12, -50, -72, 0, 0, 0, 0, 40, 0, 0, 80, 54, 88, 0, 0, -36, 18, 0, 0, 0, -102, 4, -96, 0, 0, -16, 54, 48, 0, 0, 4, 0, -6, 0, 0, -48, -102, -116, 0, 0, 78, 24, 24, 0, 0, -12, 22, 108, 0, 0, 0, -78, -68, 0, 0, 72, -30, 0, 0, 0, 76, 0, 48, 0, 0, -72, 123, 192, 0, 0, 0, -96, 0, 0, 0, 0, -13, -84, 0, 0, -132, 24, 40, 0, 0, -168, -15, 34, 0, 0, 144, -36, 0, 0, 0, -120, 0, -32, 0, 0, 8, 78, 4, 0, 0, 0, -84, 132, 0, 0, 48, -100, 16, 0, 0, -168, 0, 48, 0, 0, 96, 16, 0, 0, 0, 204, -36, 0, 0, 0, -22, -6, 2, 0, 0, 0, 49, -60, 0, 0, 108, -12, 14, 0, 0, -172, 24, -48, 0, 0, -96, 52, -90, 0, 0, 48, -42, 64, 0, 0, 0, 0, 60, 0, 0, -80, 42, -108, 0, 0, 108, 0, 38, 0, 0, 44, -72, 72, 0, 0, -42, -30, 0, 0, 0, -144, 21, -78, 0, 0, 12, -72, 76, 0, 0, -120, 59, 24, 0, 0, 0, 2, 122, 0, 0, -68, -102, 120, 0, 0, -80, 108, 96, 0, 0, 0, -66, 92, 0, 0, -130, -114, -80, 0, 0, -48, 0, 156, 0, 0, 18, 30, 144, 0, 0, -192, -96, 0, 0, 0, 64, 48, -24, 0, 0, -168, -5, 36, 0, 0, -20, 6, 0, 0, 0, 64, -66, 72, 0, 0, 0, 72, 98, 0, 0, 0, 114, -120, 0, 0, 0, -112, -108, 0, 0, 132, -32, -64, 0, 0, -44, 0, 104, 0, 0, -60, -49, 48, 0, 0, -48, 0, 0, 0, 0, -70, -99, 24, 0, 0, 28, 4, -108, 0, 0, 120, -24, -48, 0, 0, -88, 48, -36, 0, 0, 60, -42, 0, 0, 0, -108, 46, -68, 0, 0, 0, 18, 32, 0, 0, 0, 36, 72, 0, 0, 180, 0, 120, 0, 0, -22, 0, -60, 0, 0, -8, 88, 0, 0, 0, 6, -48, 52, 0, 0, 72, -39, 44, 0, 0, -48, 4, 54, 0, 0, 72, 72, 44, 0, 0, -10, -60, -96, 0, 0, -24, -38, 180, 0, 0, 0, -48, 0, 0, 0, 32, 0, -96, 0, 0, -56, 0, 30, 0, 0, 0, 21, -136, 0, 0, -24, -18, 0, 0, 0, 0, -87, 36, 0, 0, 72, 42, -64, 0, 0, -80, 3, 40, 0, 0, 12, 0, -168, 0, 0, -72, 28, 72, 0, 0, -44, -36, 192, 0, 0, 0, 39, -120, 0, 0, 120, -30, -80, 0, 0, 32, 0, 0, 0, 0, 126, 132, 96, 0, 0, 96, 6, 0, 0, 0, 0, 72, -70, 0, 0, 104, 33, 120, 0, 0, 84, 16, -90, 0, 0, 132, -48, -24, 0, 0, 112, -6, 90, 0, 0, 72, 0, -4, 0, 0, 0, 60, -20, 0, 0, -120, -38, 48, 0, 0, -12, 0, -16, 0, 0, -216, -24, 0, 0, 0, 30, 44], "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": "55.2.b.a", "char_is_minimal": true, "conrey_index": 364, "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, -1, -1, 1], [0, -1, 0, 1], [-1, 1, 0, 1], [-1, 0, 1, -1], [-2, 0, 0, 0], [0, 0, 2, 0], [0, 1, 3, -1], [-1, -1, 0, -1], [2, -1, -1, -1], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [2, -2, 0, -2], [0, 1, -1, -2], [3, -1, 0, -1], [0, 2, 0, -2], [0, -1, -3, 1], [4, 0, 0, 0], [-3, -3, -4, 3], [-4, -2, 0, -2], [0, 0, 0, 0], [0, 1, 0, -1], [-2, -2, 0, -2], [1, 3, 1, 0], [0, 0, 0, 0], [0, -1, -2, 1], [0, -6, -6, 6], [2, -2, 0, -2], [2, 0, -2, 2], [0, -1, 0, -1], [0, -3, -1, 3], [0, 0, 0, 0], [4, 0, 0, 0], [-4, 4, 0, -2], [-7, 1, 0, 1], [0, -3, 2, 3], [0, -4, -4, 4], [0, 0, 0, 0], [-6, 5, 1, -1], [-2, 2, 0, 2], [0, 0, -4, 0], [0, 0, -2, 0], [0, 0, 0, 0], [5, 3, 2, -1], [2, 0, 0, 0], [0, 4, 2, -4], [0, -2, -2, 2], [-5, 0, 0, 0], [4, 1, 5, -3], [8, 2, 0, 2], [0, 0, 0, 0], [0, 4, 4, -4], [-4, 2, 0, 2], [0, 0, 0, 0], [-14, 2, 0, 2], [0, -4, 0, 4], [0, -6, -10, 6], [4, -1, 0, -1], [-4, 4, 0, -2], [-6, -2, 0, -2], [0, -2, -4, 2], [0, 6, 2, -6], [-1, -1, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, -4, 3], [0, 0, -4, 0], [4, 1, 0, 1], [6, 6, 8, -6], [0, 3, 0, 3], [0, 7, 5, -7], [0, 0, 4, 0], [-4, -2, 0, -2], [4, -2, 3, 3], [-4, 4, 0, 4], [0, 0, 0, 0], [0, 0, 0, 0], [8, 2, 0, 2], [1, 3, 6, -5], [-3, -2, 0, -2], [0, 6, 10, -6], [0, -4, -2, 4], [-12, 0, 0, 0], [0, -2, 2, 4], [-2, 2, 0, 2], [0, 0, -4, 0], [0, 0, 0, 0], [2, 1, 0, 1], [6, -5, -1, 1], [0, 0, 0, 0], [0, 0, -2, 0], [0, 1, -2, -1], [10, -2, 0, -2], [-4, 0, 4, -4], [-10, -2, 0, -2], [0, -3, -2, 3], [0, 5, 5, -5], [0, 0, 0, 0], [11, -5, -6, 1]]}