# Stored data for newform 605.2.j.f, downloaded from the LMFDB on 19 April 2024.
{"label": "605.2.j.f", "space_label": "605.2.j", "level": 605, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518616645698141, "dim": 16, "is_polredabs": true, "nf_label": "16.0.6879707136000000000000.7", "trace_hash": 574682781625024395, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 0, -4, 0, 15, 0, -56, 0, 209, 0, -56, 0, 15, 0, -4, 0, 1]], [19, [456976, 35152, 20280, 2912, 1004, -112, 30, -2, 1]]], "qexp_display": "q+\\beta _{12}q^{2}-\\beta _{3}q^{3}-\\beta _{10}q^{4}+(-\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 10, "char_parity": 1, "char_degree": 4, "char_conductor": 55, "char_orbit_label": "j", "char_is_real": false, "Nk2": 2420, "analytic_conductor": 4.830949322287463, "hecke_ring_index": 1, "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, 10, [122, 486], [5, 6]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 8, "level_primes": [5, 11], "conrey_indexes": [9, 124, 269, 444], "field_disc": 6879707136000000000000, "field_disc_factorization": [[2, 32], [3, 8], [5, 12]], "field_poly": [1, 0, -4, 0, 15, 0, -56, 0, 209, 0, -56, 0, 15, 0, -4, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "14.441", "prec": 20}, {"__RealLiteral__": 0, "data": "11.604", "prec": 20}, {"__RealLiteral__": 0, "data": "2877.051", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "925140.069", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c10", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 0, 0, 4, 0, 0, -4, -16, 0, 0, 0, 0, -4, 4, 0, 0, 4, -12, 48, 0, 0, 8, -4, 12, 0, 0, 0, 0, 28, 0, 0, -32, 12, 12, 0, 0, -12, -4, 0, 0, 0, 0, -48, -28, 0, 0, -4, -24, 16, 0, 0, -64, 0, 48, 0, 0, -12, -12, 40, 0, 0, -16, -96, 0, 0, 0, -20, -12, 12, 0, 0, -24, -24, 144, 0, 0, -8, -24, 8, 0, 0, -24, -8, 48, 0, 0, 48, 16, 36, 0, 0, -4, -36, 12, 0, 0, 0, 0, -36, 0, 0, -12, -24, 44, 0, 0, -64, 0, 0, 0, 0, -4, -8, 48, 0, 0, -24, -48, 0, 0, 0, 12, 0, 12, 0, 0, 36, -36, 144, 0, 0, 60, -4, 16, 0, 0, 4, 12, 40, 0, 0, -112, 48, 24, 0, 0, -48, 4, 4, 0, 0, 0, -48, -36, 0, 0, 4, -36, 12, 0, 0, 48, 0, 112, 0, 0, 20, 0, 40, 0, 0, 0, -96, 0, 0, 0, -48, -12, 28, 0, 0, -20, -24, 112, 0, 0, -24, -40, 36, 0, 0, -12, -36, 36, 0, 0, 32, -24, 24, 0, 0, 24, -12, 12, 0, 0, 0, 48, 4, 0, 0, 20, 12, 20, 0, 0, -96, 0, 96, 0, 0, -48, -4, 8, 0, 0, -44, -144, 0, 0, 0, 48, -44, 12, 0, 0, -12, -20, 32, 0, 0, 12, 36, 0, 0, 0, 28, 28, 36, 0, 0, -48, 24, -36, 0, 0, -24, 0, -48, 0, 0, 0, -160, -36, 0, 0, -72, -12, -32, 0, 0, -176, 0, 48, 0, 0, 16, -24, 0, 0, 0, 36, 128, 0, 0, 0, -36, 48, -36, 0, 0, 4, 12, 0, 0, 0, -24, -24, -24, 0, 0, -76, 12, 8, 0, 0, 48, -16, 36, 0, 0, 24, 0, 24, 0, 0, 0, -48, 16, 0, 0, 60, 0, -24, 0, 0, 336, 0, -208, 0, 0, 8, 36, -36, 0, 0, -8, 96, 0, 0, 0, 36, -12, -52, 0, 0, 40, 0, 48, 0, 0, 12, 36, 24, 0, 0, 108, 8, -36, 0, 0, -144, 0, -40, 0, 0, 12, 48, 36, 0, 0, 0, 112, 40, 0, 0, -8, 12, 0, 0, 0, -160, 0, -96, 0, 0, -24, -24, -40, 0, 0, 8, -96, 0, 0, 0, -60, 4, 60, 0, 0, -72, 60, -192, 0, 0, -56, -12, -20, 0, 0, -64, -56, -108, 0, 0, 336, -36, -8, 0, 0, 4, -48, -12, 0, 0, 0, 240, 48, 0, 0, 12, 48, 36, 0, 0, -64, 0, 160, 0, 0, 24, 24, -24, 0, 0, 48, 192, 0, 0, 0, 104, 36, 28, 0, 0, 40, 48, -528, 0, 0, 96, 40, -52, 0, 0, 12, 48, -72, 0, 0, -32, 4, -48, 0, 0, 24, 48, -72, 0, 0, 0, -96, 40, 0, 0, 12, 40, -48, 0, 0, 480, 0, 16, 0, 0, 112, 36, 4, 0, 0, 12, 288, 0, 0, 0, -60, 8, -24, 0, 0, -4, 24, -96, 0, 0, -92, -36, -60, 0, 0, 84, -12, -76, 0, 0, -48, -84, -24, 0, 0, 12, 4, 24, 0, 0, 0, 144, 52, 0, 0, 24, 36, -36, 0, 0, -112, 0, -576, 0, 0, -120, 24, -108, 0, 0, 36, -48, 0, 0, 0, 84, 16, -108, 0, 0, 72, 36, 128, 0, 0, -12, 96, -28, 0, 0, -48, 0, -84, 0, 0, -96, 24, -52, 0, 0, 8, 24, 64, 0, 0, 0, 192, 12, 0, 0, -36, 8, -80, 0, 0, 144, 0, -144, 0, 0, 96, -28, -132, 0, 0, 60, 48, 0, 0, 0, -32, 84, -68, 0, 0, -60, 92, -336, 0, 0, 0, -12, -8, 0, 0, -40, 12, -36, 0, 0, 96, -44, -24, 0, 0, 60, 24, -8, 0, 0, 0, -48, 108, 0, 0, -16, 84, -24, 0, 0, 96, 0, 224, 0, 0, 28, 24, -72, 0, 0, -12, 384, 0, 0, 0, 12, -72, 0, 0, 0, 60, 24, -400, 0, 0, -48, 64, 36, 0, 0, 120, 8, -20, 0, 0, 64, -108, -48, 0, 0, -20, 72, -96, 0, 0, 0, -336, 20, 0, 0, 52, 24, -32, 0, 0, -96, 0, 96, 0, 0, -180, -36, 36, 0, 0, 72, 0, 0, 0, 0, 8, -24, 72, 0, 0, -132, 32, -240, 0, 0, -128, 24, -96, 0, 0, -68, 12, -132, 0, 0, 48, 0, -56, 0, 0, 144, -36, -60, 0, 0, 0, 128, 24, 0, 0, -12, 16, -52, 0, 0, -64, 0, -208, 0, 0, 108, 28, -36, 0, 0, -36, 144, 0, 0, 0, 76, 96, 36, 0, 0, 4, 32, -96, 0, 0, 96, -36, 0, 0, 0, 80, 24, -36, 0, 0, 48, 60, -48, 0, 0, -72, 52, 28, 0, 0, 0, 144, 32, 0, 0, 0, 0, -96, 0, 0, 48, 0, -48, 0, 0, 64, 84, -144, 0, 0, -4, -16, 0, 0, 0, -72, -36, -76, 0, 0, 84, 0, 208, 0, 0, 0, 8, 72, 0, 0, 12, -48, 16, 0, 0, 272, -84, -24, 0, 0, 0, 40, 108, 0, 0, 0, 192, 108, 0, 0, 136, 84, 24, 0, 0, 272, 0, 96, 0, 0, -72, 0, -64, 0, 0, 12, -144, 0, 0, 0, 48, -24, -84, 0, 0, -48, 12, -32, 0, 0, -8, 72, -4, 0, 0, 36, 0, 24, 0, 0, -240, 52, 48, 0, 0, 28, -12, -12, 0, 0, 0, -192, -48, 0, 0, -120, -12, 112, 0, 0, -272, 0, -96, 0, 0, 84, -36, 108, 0, 0, 36, 240, 0, 0, 0, 0, 96, -56, 0, 0, 128, -12, -240, 0, 0, 84, -4, -84, 0, 0, -84, 72, -12, 0, 0, -224, -12, 72, 0, 0, -36, -12, -16, 0, 0, 0, 48, -20, 0, 0, 12, -56, 0, 0, 0, 720, 0, -208, 0, 0, 36, 0, 84, 0, 0, -24, 112], "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, 3, 11, 3, 1, 5, 0], [1, 3, 55, 10, 1, 10, 0]], "char_orbit_index": 10, "prim_orbit_index": 10, "minimal_twist": "605.2.b.d", "char_is_minimal": false, "conrey_index": 9, "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, 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, 0, 0, 0, 0, 0, 0, 0, 1, 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, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 1, 0, -2, 0, -1, 0, -2, 0, 1, 0, 2, 1, 0, 0, 2], [0, 0, 0, -1, 0, 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, 0], [-1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, -1, 0, 2, 0, 1, 0, 2, -1, -1, -1, -2, -1, 0, 0, -2], [0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, -1, 0, -3, 0, -1, 0, -2, 0, 1, -2, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, -3, 0], [0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1], [3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 7, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, -3], [3, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 3, -1, 0], [0, -4, 0, 2, 0, 4, 0, 2, 0, 2, 0, -2, 2, 0, 0, -2], [0, 0, 0, 0, 0, -7, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 3, 3, 0], [0, -1, 0, 2, 0, 1, 0, 2, -1, -1, -1, -2, -1, 0, 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, 0, 0, 1, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -7, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 3, 0, 2, 0, 3, 0, -1, 0, -3, -1, 0, 0, -3], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 1, -3, 0], [0, 0, 2, 0, 0, 1, 2, 0, 0, 0, -2, 0, 0, 6, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -3], [-4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 5], [0, -8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, -1, -3, 0, 0, 1, 0, 0, 3, 1, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -10, -1, 0], [0, -5, 0, -1, 0, 5, 0, -1, 0, 6, 0, 1, 6, 0, 0, 1], [0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4], [-5, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, -5, -1, 0], [0, -1, 0, -1, 0, 1, 0, -1, -3, 2, 0, 1, 2, 0, 0, 1], [0, 0, 3, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, -3, -3, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, -2, 0, 2, 0, -4, 0, -2, -4, 0, 0, -2], [-6, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, -6, 4, 0], [0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 1], [9, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 3, 0, 1, 6, 0, 0, 0, 6, 0, 0, 0, 0, -6, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -7, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -3, 0, 0, 0, 0, 0], [-2, 2, 0, -4, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, -2, 0], [0, 0, 0, 0, 12, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 1], [9, 0, 0, 0, -9, 0, 0, 0, -9, 0, 0, 0, 0, 9, 3, 0], [0, 7, 0, -5, 0, -7, 0, -5, 0, -2, 0, 5, -2, 0, 0, 5], [0, 0, 0, 0, 0, 1, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 1, -4, 0], [0, -4, 0, -2, 0, 4, 0, -2, -9, 6, 1, 2, 6, 0, 0, 2], [3, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 3, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -3, 0, 0, 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, -6, 0, 0, 0, 0]]}