# Stored data for newform 605.2.j.d, downloaded from the LMFDB on 20 April 2024.
{"label": "605.2.j.d", "space_label": "605.2.j", "level": 605, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511417390957149, "dim": 16, "is_polredabs": true, "trace_hash": 647036208119930326, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [121, 0, -308, 0, 345, 0, -138, 0, 159, 0, -62, 0, 15, 0, -2, 0, 1]], [19, [121, 198, 1433, -879, 280, -9, 3, 3, 1]]], "qexp_display": "q+(\\beta _{1}-\\beta _{12}-\\beta _{13})q^{2}+(-\\beta _{5}-\\beta _{13}+\\cdots)q^{3}+\\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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [605, 10, [122, 486], [5, 6]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [5, 11], "conrey_indexes": [9, 124, 269, 444], "field_disc": 1369296016000000000000, "field_disc_factorization": [[2, 16], [5, 12], [11, 2], [29, 4]], "field_poly": [121, 0, -33, 0, 235, 0, -303, 0, 194, 0, -57, 0, 25, 0, -7, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.350", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1279.485", "prec": 27}, {"__RealLiteral__": 0, "data": "1052.751", "prec": 27}, {"__RealLiteral__": 0, "data": "190640.292", "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, -2, 0], "traces": [0, 16, 0, 0, -4, -2, 18, 0, 0, 2, 0, 0, 0, 0, -12, -16, 16, 0, 0, -6, -8, -8, 0, 0, -6, -16, 40, 0, 0, -2, -26, 8, 0, 0, -16, -22, 10, 0, 0, -30, -12, 52, 0, 0, 0, 12, 62, 0, 0, -10, -28, 42, 0, 0, 40, 0, -20, 0, 0, 2, -32, 40, 0, 0, -8, 40, 0, 0, 0, 26, -34, 36, 0, 0, -48, -20, -56, 0, 0, -38, 34, 68, 0, 0, -12, -58, 22, 0, 0, 24, -78, -20, 0, 0, -14, -48, 86, 0, 0, 0, 12, 94, 0, 0, -40, -12, 54, 0, 0, -20, 0, -36, 0, 0, -88, -24, 34, 0, 0, -54, 64, 0, 0, 0, -24, -74, 50, 0, 0, 8, -20, -148, 0, 0, -42, -24, 62, 0, 0, -64, -10, 76, 0, 0, 44, -14, 46, 0, 0, 50, -28, 70, 0, 0, 0, -20, 70, 0, 0, 38, -62, 8, 0, 0, 36, 0, -36, 0, 0, -32, -8, 38, 0, 0, 74, 16, 0, 0, 0, 24, -6, 8, 0, 0, -44, 30, -16, 0, 0, -26, -20, 46, 0, 0, 26, -70, 50, 0, 0, -112, -56, -2, 0, 0, -74, 34, 86, 0, 0, 0, -56, 40, 0, 0, -106, -58, 24, 0, 0, 84, 0, 0, 0, 0, 22, -50, 18, 0, 0, -50, 16, 0, 0, 0, -50, -28, 80, 0, 0, -24, -70, 64, 0, 0, 46, 10, 86, 0, 0, -36, -6, -66, 0, 0, 180, 4, 0, 0, 0, -26, -40, -10, 0, 0, 0, 80, 2, 0, 0, 100, 18, 78, 0, 0, -184, 0, 88, 0, 0, 8, 48, 62, 0, 0, -48, -124, 0, 0, 0, 78, -36, -30, 0, 0, -30, 42, 112, 0, 0, -110, 16, 32, 0, 0, 74, 2, -132, 0, 0, -136, 2, 4, 0, 0, 98, 4, -34, 0, 0, 0, -68, -16, 0, 0, -56, 60, -78, 0, 0, 180, 0, 192, 0, 0, -46, -104, 66, 0, 0, -28, 124, 0, 0, 0, -150, 52, 0, 0, 0, 74, 36, -40, 0, 0, 186, -90, -84, 0, 0, 8, 22, 82, 0, 0, 20, 76, 10, 0, 0, -110, -2, -112, 0, 0, 0, 64, -76, 0, 0, 36, -12, -58, 0, 0, -192, 0, -180, 0, 0, 188, 180, -92, 0, 0, 160, -36, 0, 0, 0, 78, 106, -130, 0, 0, -36, -54, -8, 0, 0, -84, 106, -126, 0, 0, 14, 28, 100, 0, 0, 20, 4, -70, 0, 0, 44, 100, -72, 0, 0, 0, 64, -58, 0, 0, 8, 114, -80, 0, 0, 200, 0, -100, 0, 0, -26, -14, -236, 0, 0, -50, 16, 0, 0, 0, 50, -50, 36, 0, 0, 146, -68, -100, 0, 0, 92, -62, -112, 0, 0, -30, 160, -46, 0, 0, -124, 86, 4, 0, 0, -34, 10, -40, 0, 0, 0, -16, -196, 0, 0, 168, 100, 62, 0, 0, 0, 0, 0, 0, 0, -50, 56, -88, 0, 0, 66, -188, 0, 0, 0, -58, 116, -84, 0, 0, 56, 186, 92, 0, 0, -24, 50, -214, 0, 0, 88, 42, -174, 0, 0, -28, -14, -74, 0, 0, 162, 18, -78, 0, 0, 0, 8, -32, 0, 0, -182, -40, -60, 0, 0, -196, 0, 32, 0, 0, 112, -48, 68, 0, 0, 70, -64, 0, 0, 0, 70, 108, -116, 0, 0, -28, 26, 220, 0, 0, 58, 100, -84, 0, 0, -164, 26, 0, 0, 0, 160, 170, -8, 0, 0, -8, -78, -264, 0, 0, 0, 24, -112, 0, 0, 162, 50, -166, 0, 0, -132, 0, 112, 0, 0, 34, 144, -70, 0, 0, -44, 36, 0, 0, 0, 202, 36, -112, 0, 0, 70, -4, 140, 0, 0, 132, 12, -84, 0, 0, 62, 96, -82, 0, 0, -24, 58, 60, 0, 0, 62, 182, -134, 0, 0, 0, -300, -10, 0, 0, -230, 58, -102, 0, 0, 52, 0, -128, 0, 0, -84, -28, -172, 0, 0, -128, -60, 0, 0, 0, -326, 84, -42, 0, 0, 58, -8, 264, 0, 0, -80, -84, -84, 0, 0, 210, 88, -82, 0, 0, -52, 62, 60, 0, 0, 90, 12, 44, 0, 0, 0, 196, -312, 0, 0, 210, -36, 10, 0, 0, -92, 0, -156, 0, 0, 172, 60, -124, 0, 0, -18, -144, 0, 0, 0, 206, 152, 4, 0, 0, -92, 140, -76, 0, 0, 50, 94, -100, 0, 0, 86, 26, -2, 0, 0, 180, 108, 72, 0, 0, -190, 36, 0, 0, 0, 0, -28, -162, 0, 0, 128, -28, -6, 0, 0, 24, 0, 256, 0, 0, 10, -16, -118, 0, 0, 38, 0, 0, 0, 0, -10, -46, -84, 0, 0, 162, -54, -92, 0, 0, 210, -186, 18, 0, 0, -172, 112, 186, 0, 0, -140, 72, 40, 0, 0, 168, 124, -212, 0, 0, 0, -308, -102, 0, 0, -130, 34, -182, 0, 0, -60, 0, 180, 0, 0, 12, 10, 100, 0, 0, 178, 132, 0, 0, 0, -246, 38, 18, 0, 0, 28, -46, 276, 0, 0, -152, -64, -24, 0, 0, 88, 38, -104, 0, 0, -340, 0, -154, 0, 0, -16, 78, -150, 0, 0, 0, 68, 130, 0, 0, 108, -10, -4, 0, 0, 176, 0, -80, 0, 0, 30, 174, 136, 0, 0, -66, -232, 0, 0, 0, 110, 2, -96, 0, 0, -72, 138, 144, 0, 0, 140, 112, 10, 0, 0, -2, 30, -172, 0, 0, 592, 32, -82, 0, 0, -16, -114, -32, 0, 0, 0, 136, 30, 0, 0, -50, 20, 40, 0, 0, -92, 0, 140, 0, 0, -66, -62, 74, 0, 0, 54, -36, 0, 0, 0, 30, -72, 110, 0, 0, -74, 32, -160, 0, 0, -14, -26, 0, 0, 0, -162, -72, 54, 0, 0, -92, -34, 10, 0, 0, 358, -200, 4, 0, 0, 0, -40, -70, 0, 0, 0, 148, 42, 0, 0, -128, 0, 76, 0, 0, -54, -76, -110, 0, 0, -10, 96], "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, 3, 1, 5, 0], [1, 1, 55, 10, 1, 10, 0]], "char_orbit_index": 10, "prim_orbit_index": 10, "minimal_twist": "55.2.j.a", "char_is_minimal": false, "conrey_index": 9, "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, 0, 0, 0, 0], [1, 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, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1], [0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, 0, 1, -1, 2, 1, 0, 1, 0, 0, 0, 0], [0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [1, 0, 0, -1, 1, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, -1, -1, 1, 1, -1, -2, -1, -2, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0], [0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [-2, 0, 0, 0, 2, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, 2, 0, 3, 0, 0, 0, 1, -1, 0, 0], [2, 0, 0, 2, -1, 0, -2, -1, 2, 2, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, -3, 0], [0, -2, -3, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, -1, 2], [-1, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0], [-1, 0, 1, 0, 1, -1, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, -1, -1, 1, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, -2, 0], [-1, 0, 0, 3, 1, 0, -2, 0, 0, -1, 0, 2, 0, 0, 0, 0], [-2, 0, 0, -2, 2, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, 2], [2, 0, 0, -2, 3, 0, 1, 2, -3, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0], [-2, 2, 2, -1, 2, 1, 0, -1, 1, 0, -2, -1, 0, 1, 0, 0], [2, 0, 0, -2, -3, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0], [0, 0, -3, 0, 0, 5, 0, 0, 0, 0, 1, 0, -2, 1, -3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, 0, 4, 4, 3, -1, 0, -2, 0, 0, 0, 0], [-1, -1, 1, -1, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1], [1, 0, 0, 1, -1, 0, 0, -2, 3, 0, 0, 1, 0, 0, 0, 0], [0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, -1, -2], [0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, 1, 0], [-2, 0, 0, -5, -2, 0, 5, 5, -2, -3, 0, -5, 0, 0, 0, 0], [0, 0, -2, 0, -1, 2, 2, 0, 1, 3, 2, 0, -1, 2, -2, 0], [5, 0, 0, -2, -5, 0, 0, 3, -2, 0, 0, -2, 0, 0, 0, 0], [0, -3, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, -1, 2, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 0, 0, 0, 3, 0, 0, 1, 1, 0, -1, -3, -2, 0, 0], [4, 0, 0, 3, 1, 0, -1, 0, 0, 4, 0, 1, 0, 0, 0, 0], [0, -5, -3, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 4, 0, -1], [0, -1, -3, 0, 0, 2, 0, 0, 0, 0, 2, 0, -4, 0, -2, 1], [-4, 0, 0, 1, 4, 0, -1, 1, -4, -5, 0, -1, 0, 0, 0, 0], [-2, -4, 0, -2, 0, -3, 2, 0, -2, 0, 0, 0, 4, 0, 2, 0], [-3, 0, 0, 3, 4, 0, -2, -3, -4, -9, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, -2, 0, 2], [0, 8, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -5, -5, 1, -1], [5, 0, 0, 0, -2, 0, 2, 2, 4, 2, 0, 2, 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, -1, 0, 3, 0, 0, 0, 0], [0, -5, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1], [0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1], [3, 0, 0, -3, 0, 0, -2, 3, 0, 2, 0, 0, 0, 0, 0, 0], [-5, -1, 0, 0, 2, 0, 0, 3, -5, -5, -1, -3, 1, 0, 1, 0], [4, 0, 0, 0, -3, 0, 0, 4, 4, -1, 0, -4, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1], [0, -1, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1], [-4, 0, 0, 2, 1, 0, 3, 0, 0, -4, 0, -3, 0, 0, 0, 0], [3, 2, 2, 0, 3, -3, -3, -3, -1, 2, -1, 4, 1, -3, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -1, 0, 0, 2, 0, 0, 0, 0, -3, 0, -1, -1, -1, 3], [0, 1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2], [3, 0, 0, -1, -3, 0, 0, 4, -2, 0, 0, -1, 0, 0, 0, 0], [-1, -1, -1, 1, -1, 0, -3, -1, 1, 2, 0, 0, 2, 2, 0, 1], [9, 0, 0, -6, -9, 0, 6, 3, 9, 6, 0, -3, 0, 0, 0, 0], [0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, -2, 0, 1, 0], [0, 5, 4, 0, 0, 1, 0, 0, 0, 0, 1, 0, -5, -1, -1, -5], [-3, 0, 0, -2, 3, 0, 0, 4, -2, 0, 0, -2, 0, 0, 0, 0], [-4, -3, 3, 2, 4, -1, 0, 0, 0, -4, 0, 0, 4, 4, 2, -2], [-4, 0, 0, 0, -1, 0, 1, 1, 0, -1, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 5, 0, 0, -12, 0, 0, 0, 0, 0, 0, 7, -1, 5, 0], [-1, 0, 0, -5, -1, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0], [2, 1, 2, 3, -2, 1, 0, 0, -1, 0, -2, 3, 0, 1, 0, -2], [-2, 0, 0, 2, 5, 0, 2, -2, -5, -8, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, -5, 0, 0, 0, 0, 3, 0, -3, 0, 2, 0], [0, 2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, -2, 0, 1, 0], [-2, 0, 0, 2, 0, 0, -1, -2, 0, -1, 0, 0, 0, 0, 0, 0], [-5, 3, -2, 3, 5, 0, 0, 2, -1, 0, 2, 3, 0, 0, 0, -1], [3, 0, 0, 3, -8, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, -3, 0, 0, 0, 0, 3, 0, 2, 2, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 6, 0, -6, -6, -2, 4, 0, 2, 0, 0, 0, 0], [-7, 0, 1, 1, -4, 1, 2, 0, 0, -7, 0, -2, -1, -1, 1, -1], [0, 0, 0, -4, 0, 0, 0, 2, 1, 0, 0, -4, 0, 0, 0, 0], [0, -2, -3, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1, 0, -1, 2], [0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, -1, 0, -3, 0], [-1, 0, 0, 9, 1, 0, -9, -7, -1, 6, 0, 7, 0, 0, 0, 0], [-2, 0, 2, 2, -1, -2, -3, -2, 1, 4, -2, 0, 2, 1, 2, 0], [6, 0, 0, 3, -6, 0, 0, -6, 4, 0, 0, 3, 0, 0, 0, 0], [0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -1, 1], [0, 1, 1, 0, 0, -4, 0, 0, 0, 0, 2, 0, 3, 1, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 2, 0, 0, 2, 0, -2, -2, 3, 5, 2, 3, 0, 0, 0, -2]]}