# Stored data for newform 605.2.b.e, downloaded from the LMFDB on 28 December 2025. {"Nk2": 2420, "analytic_conductor": 4.830949322287463, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": 1, "char_values": [605, 2, [122, 486], [1, 2]], "cm_discs": [], "conrey_index": 364, "dim": 4, "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [1, 0, 4, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 0, 4, 0, 1]], [19, [-26, -2, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014467262513757, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "605.2.b.e", "level": 605, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 11], "level_radical": 55, "minimal_twist": "605.2.b.d", "nf_label": "4.0.2304.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{1}q^{2}-\\beta _{3}q^{3}+\\beta _{2}q^{4}+(-\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "605.2.b", "trace_display": [0, 0, 0, 0], "trace_hash": 779145789178412698, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.739", "prec": 17}, {"__RealLiteral__": 0, "data": "0.061", "prec": 17}, {"__RealLiteral__": 0, "data": "68.855", "prec": 20}, {"__RealLiteral__": 0, "data": "16.869", "prec": 20}, {"__RealLiteral__": 0, "data": "1769.053", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.515", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, -4, 0, 0, 4, 12, -12, 0, 0, 8, 4, -12, 0, 0, 0, 0, -28, 0, 0, -8, 12, -12, 0, 0, -12, -4, 0, 0, 0, 0, -12, -28, 0, 0, 4, -24, 16, 0, 0, 16, 0, 12, 0, 0, 12, 12, 40, 0, 0, 16, 24, 0, 0, 0, 20, 12, -12, 0, 0, -24, 24, -36, 0, 0, -8, 24, -8, 0, 0, -24, -8, -48, 0, 0, 12, 16, -36, 0, 0, -4, -36, 12, 0, 0, 0, 0, -36, 0, 0, 12, -24, 44, 0, 0, 16, 0, 0, 0, 0, 4, 8, 48, 0, 0, 24, 12, 0, 0, 0, -12, 0, -12, 0, 0, 36, 36, -36, 0, 0, 60, 4, -16, 0, 0, 4, 12, -40, 0, 0, -28, 48, -24, 0, 0, -48, 4, 4, 0, 0, 0, -12, -36, 0, 0, -4, -36, 12, 0, 0, -12, 0, 28, 0, 0, -20, 0, 40, 0, 0, 0, 24, 0, 0, 0, 48, 12, -28, 0, 0, -20, 24, -28, 0, 0, -24, 40, -36, 0, 0, -12, -36, -36, 0, 0, 8, -24, -24, 0, 0, 24, -12, 12, 0, 0, 0, 12, 4, 0, 0, -20, 12, 20, 0, 0, 24, 0, 24, 0, 0, 48, 4, 8, 0, 0, 44, 36, 0, 0, 0, -48, 44, -12, 0, 0, -12, 20, -8, 0, 0, 12, -36, 0, 0, 0, 28, 28, -36, 0, 0, -12, 24, 36, 0, 0, -24, 0, -48, 0, 0, 0, -40, -36, 0, 0, 72, -12, -32, 0, 0, 44, 0, 12, 0, 0, -16, 24, 0, 0, 0, -36, -32, 0, 0, 0, 36, -48, 36, 0, 0, 4, -12, 0, 0, 0, -24, 24, 24, 0, 0, -76, 12, -8, 0, 0, 12, -16, -36, 0, 0, 24, 0, 24, 0, 0, 0, -12, 16, 0, 0, -60, 0, -24, 0, 0, -84, 0, -52, 0, 0, -8, -36, -36, 0, 0, 8, -24, 0, 0, 0, -36, 12, 52, 0, 0, 40, 0, -12, 0, 0, 12, -36, -24, 0, 0, 108, 8, 36, 0, 0, -36, 0, 40, 0, 0, 12, 48, 36, 0, 0, 0, 28, 40, 0, 0, 8, 12, 0, 0, 0, 40, 0, -24, 0, 0, 24, 24, -40, 0, 0, -8, 24, 0, 0, 0, 60, -4, -60, 0, 0, -72, -60, 48, 0, 0, -56, 12, 20, 0, 0, -64, -56, 108, 0, 0, 84, -36, 8, 0, 0, 4, -48, -12, 0, 0, 0, 60, 48, 0, 0, -12, 48, 36, 0, 0, 16, 0, 40, 0, 0, -24, -24, -24, 0, 0, -48, -48, 0, 0, 0, -104, -36, -28, 0, 0, 40, -48, 132, 0, 0, 96, -40, 52, 0, 0, 12, 48, 72, 0, 0, -8, 4, 48, 0, 0, 24, 48, -72, 0, 0, 0, -24, 40, 0, 0, -12, 40, -48, 0, 0, -120, 0, 4, 0, 0, -112, -36, 4, 0, 0, -12, -72, 0, 0, 0, 60, -8, 24, 0, 0, -4, -24, 24, 0, 0, -92, 36, 60, 0, 0, 84, -12, 76, 0, 0, -12, -84, 24, 0, 0, 12, 4, 24, 0, 0, 0, 36, 52, 0, 0, -24, 36, -36, 0, 0, 28, 0, -144, 0, 0, 120, -24, -108, 0, 0, -36, 12, 0, 0, 0, -84, -16, 108, 0, 0, 72, -36, -32, 0, 0, -12, -96, 28, 0, 0, -48, 0, 84, 0, 0, -24, 24, 52, 0, 0, 8, 24, 64, 0, 0, 0, 48, 12, 0, 0, 36, 8, -80, 0, 0, -36, 0, -36, 0, 0, -96, 28, -132, 0, 0, -60, -12, 0, 0, 0, 32, -84, 68, 0, 0, -60, -92, 84, 0, 0, 0, 12, 8, 0, 0, -40, 12, 36, 0, 0, 24, -44, 24, 0, 0, 60, 24, -8, 0, 0, 0, -12, 108, 0, 0, 16, 84, -24, 0, 0, -24, 0, 56, 0, 0, -28, -24, -72, 0, 0, 12, -96, 0, 0, 0, -12, 72, 0, 0, 0, 60, -24, 100, 0, 0, -48, -64, -36, 0, 0, 120, 8, 20, 0, 0, 16, -108, 48, 0, 0, -20, 72, -96, 0, 0, 0, -84, 20, 0, 0, -52, 24, -32, 0, 0, 24, 0, 24, 0, 0, 180, 36, 36, 0, 0, -72, 0, 0, 0, 0, -8, 24, -72, 0, 0, -132, -32, 60, 0, 0, -128, -24, 96, 0, 0, -68, 12, 132, 0, 0, 12, 0, 56, 0, 0, 144, -36, -60, 0, 0, 0, 32, 24, 0, 0, 12, 16, -52, 0, 0, 16, 0, -52, 0, 0, -108, -28, -36, 0, 0, 36, -36, 0, 0, 0, -76, -96, -36, 0, 0, 4, -32, 24, 0, 0, 96, 36, 0, 0, 0, 80, 24, 36, 0, 0, 12, 60, 48, 0, 0, -72, 52, 28, 0, 0, 0, 36, 32, 0, 0, 0, 0, -96, 0, 0, -12, 0, -12, 0, 0, -64, -84, -144, 0, 0, 4, 4, 0, 0, 0, 72, 36, 76, 0, 0, 84, 0, -52, 0, 0, 0, -8, -72, 0, 0, 12, -48, -16, 0, 0, 68, -84, 24, 0, 0, 0, 40, 108, 0, 0, 0, 48, 108, 0, 0, -136, 84, 24, 0, 0, -68, 0, 24, 0, 0, 72, 0, -64, 0, 0, -12, 36, 0, 0, 0, -48, 24, 84, 0, 0, -48, -12, 8, 0, 0, -8, -72, 4, 0, 0, 36, 0, -24, 0, 0, -60, 52, -48, 0, 0, 28, -12, -12, 0, 0, 0, -48, -48, 0, 0, 120, -12, 112, 0, 0, 68, 0, -24, 0, 0, -84, 36, 108, 0, 0, -36, -60, 0, 0, 0, 0, -96, 56, 0, 0, 128, 12, 60, 0, 0, 84, 4, 84, 0, 0, -84, 72, 12, 0, 0, -56, -12, -72, 0, 0, -36, -12, -16, 0, 0, 0, 12, -20, 0, 0, -12, -56, 0, 0, 0, -180, 0, -52, 0, 0, -36, 0, 84, 0, 0, 24, -28], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, -1], [0, 0, 1, 0], [0, -1, 1, 1], [1, 0, 0, 0], [0, 1, 0, -2], [0, 0, 0, 1], [1, 0, -1, 0], [1, -2, -1, 1], [0, 0, 0, 0], [0, 1, 0, -2], [0, 3, 0, -3], [0, 0, 1, 0], [1, 1, 1, -2], [-1, 0, 2, 0], [0, 0, 0, 2], [0, 3, 0, -1], [1, 0, -3, 0], [3, 1, 0, 1], [-3, 0, -2, 0], [0, 0, 0, 0], [0, 3, 0, 1], [2, 0, 1, 0], [1, 2, 0, 2], [-3, 0, 3, 0], [0, -1, 0, -2], [0, 0, 0, -3], [0, 0, 4, 0], [0, -1, 1, 1], [-7, 0, -1, 0], [0, -5, 0, 4], [0, 0, 0, 0], [-2, 0, 0, 0], [3, 0, 1, -3], [-3, 0, 1, 0], [0, 4, 0, -2], [0, 7, 0, -3], [-3, 0, -3, 0], [-1, -1, -1, 2], [0, 0, -1, 0], [0, 1, 0, -2], [0, 5, 0, 2], [0, 0, 0, 0], [-3, -2, 1, 0], [-7, 0, 3, 0], [0, 4, 0, -7], [0, 2, 0, -3], [1, 0, -3, 0], [-6, 1, 2, 0], [4, 0, 2, 0], [0, -3, 0, -3], [0, -7, 0, 3], [4, 0, -1, 0], [0, 0, 0, 0], [3, 0, 2, 0], [0, -3, 0, 5], [0, -8, 0, 4], [3, 0, -1, 0], [3, 0, 1, -3], [10, 0, 1, 0], [0, -5, 0, -1], [0, 1, 0, 1], [4, 0, -1, 0], [6, -3, 0, -3], [0, 0, 0, 0], [0, -8, 0, 1], [0, -2, 0, 4], [5, 0, 1, 0], [3, 1, 0, 1], [-3, 0, -3, 0], [0, 1, 0, -1], [0, 2, 0, 2], [-6, 0, 4, 0], [6, 0, 2, -1], [-9, 0, 1, 0], [0, 0, 0, 0], [0, 3, 0, -3], [-2, 0, 2, 0], [6, 3, -1, 1], [-2, 0, -5, 0], [0, 2, 0, -1], [0, -7, 0, 7], [-6, 0, -3, 0], [-2, -2, -2, 4], [-12, 0, 5, 0], [0, 4, 0, -8], [0, 0, 0, 0], [3, 0, -2, 0], [4, -5, -2, 1], [-9, 0, -3, 0], [0, -7, 0, 5], [0, -1, 0, 9], [-1, 0, 4, 0], [-9, -4, 1, -2], [3, 0, 4, 0], [0, -1, 0, 5], [0, 7, 0, -3], [0, 0, 0, 0], [0, -6, 1, 6]]}