# Stored data for newform 570.2.d.b, downloaded from the LMFDB on 08 May 2024. {"label": "570.2.d.b", "space_label": "570.2.d", "level": 570, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503805819355706, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1682863491277147874, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [0, 1]], [11, [4, 1]], [13, [16, 0, 1]]], "qexp_display": "q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "d", "char_is_real": true, "Nk2": 2280, "analytic_conductor": 4.551472915212982, "hecke_ring_index": 1, "level_radical": 570, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.517", "prec": 17}, "analytic_rank_proved": true, "char_values": [570, 2, [191, 457, 211], [2, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 19], "conrey_indexes": [229], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.873", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.736", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "146.414", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 4, 0], "traces": [0, 2, 0, 0, -2, 4, -2, 0, 0, -2, -2, -8, 0, 0, 0, -2, 2, 0, 0, 2, -4, 0, 0, 0, 2, 6, -8, 0, 0, 4, -4, 0, 0, 0, -12, 0, 2, 0, 0, -8, 2, -24, 0, 0, 8, -4, 0, 0, 0, 14, -8, -12, 0, 0, 2, -16, 0, 0, 0, 20, 2, -12, 0, 0, -2, -8, 8, 0, 0, 0, 0, 24, 0, 0, 8, -8, -2, 0, 0, 16, 4, 2, 0, 0, 0, -12, 12, 0, 0, 16, 2, 0, 0, 0, 0, 4, -2, 0, 0, 8, -6, 24, 0, 0, 8, 0, -28, 0, 0, 28, 8, 8, 0, 0, -2, 0, -4, 0, 0, 0, 4, 10, 0, 0, 0, 4, 0, 0, 0, 12, -16, -40, 0, 0, 8, 2, 12, 0, 0, 24, 0, 0, 0, 0, -2, 8, 16, 0, 0, 0, -6, 32, 0, 0, 0, 0, 8, 0, 0, -28, -2, 0, 0, 0, 24, 8, 24, 0, 0, -6, -24, -2, 0, 0, -4, 0, -8, 0, 0, -12, 4, -20, 0, 0, 0, 8, 0, 0, 0, 0, -2, 12, 0, 0, 20, -16, -14, 0, 0, 8, 8, 8, 0, 0, 12, -48, 4, 0, 0, -8, 0, -16, 0, 0, -40, 12, -2, 0, 0, 16, 16, -48, 0, 0, 0, -6, -20, 0, 0, 20, 0, 0, 0, 0, 8, 0, -20, 0, 0, -20, -2, 52, 0, 0, 12, 28, 24, 0, 0, 24, -22, -48, 0, 0, 20, -24, 2, 0, 0, 0, 8, -4, 0, 0, -8, -28, 0, 0, 0, 4, 4, -56, 0, 0, 12, -24, 0, 0, 0, 0, 0, 24, 0, 0, -24, -2, 32, 0, 0, -38, -4, 20, 0, 0, -14, 40, -8, 0, 0, 0, 8, 0, 0, 0, 2, -24, 12, 0, 0, 4, 0, -36, 0, 0, -12, 0, -16, 0, 0, -16, -4, -40, 0, 0, -2, -32, -20, 0, 0, 0, 16, 16, 0, 0, -24, 8, 0, 0, 0, -20, 12, 0, 0, 0, -12, 0, -4, 0, 0, -68, 0, 8, 0, 0, -20, 48, -16, 0, 0, -68, -2, 2, 0, 0, 0, 16, 12, 0, 0, 24, 16, 0, 0, 0, 48, -22, 0, 0, 0, -24, -4, 20, 0, 0, 2, 0, -20, 0, 0, 8, 8, 0, 0, 0, 20, 32, -8, 0, 0, 0, 6, 56, 0, 0, -24, 4, 0, 0, 0, 68, 24, 12, 0, 0, 0, 24, -8, 0, 0, -16, 0, -28, 0, 0, 28, -48, -24, 0, 0, 32, 24, -24, 0, 0, 0, -4, -28, 0, 0, -32, -8, -14, 0, 0, -8, 32, 20, 0, 0, 64, 8, 96, 0, 0, 24, 0, 2, 0, 0, 12, 0, 48, 0, 0, 4, 0, 28, 0, 0, 0, 0, -12, 0, 0, -16, 6, 0, 0, 0, -76, -4, 32, 0, 0, -10, 20, -2, 0, 0, -20, -14, 72, 0, 0, -8, 16, 0, 0, 0, 8, -4, -24, 0, 0, 0, 48, 0, 0, 0, -36, 12, 0, 0, 0, 4, 4, -12, 0, 0, -4, 16, -24, 0, 0, 40, 0, 32, 0, 0, 46, -56, -20, 0, 0, -16, -40, -8, 0, 0, -56, -2, 4, 0, 0, -12, 56, 0, 0, 0, 12, 32, 4, 0, 0, 28, 16, -24, 0, 0, 48, 0, 48, 0, 0, 0, -20, -4, 0, 0, -64, -4, 8, 0, 0, 0, 0, 2, 0, 0, -20, -8, 0, 0, 0, -16, 8, 28, 0, 0, 0, -20, 20, 0, 0, -8, 0, 0, 0, 0, 24, 6, -84, 0, 0, -32, 20, -24, 0, 0, 0, 12, 0, 0, 0, 0, 24, 0, 0, 0, 56, 0, 0, 0, 0, -8, -14, 8, 0, 0, 48, 0, 56, 0, 0, -36, 20, 28, 0, 0, -24, 2, 72, 0, 0, 0, 24, -12, 0, 0, -80, -24, 0, 0, 0, -28, -80, -24, 0, 0, 52, -8, -4, 0, 0, -24, 0, -8, 0, 0, 20, 16, 48, 0, 0, -36, 8, 6, 0, 0, 0, 24, 24, 0, 0, 2, 12, 0, 0, 0, -112, 0, -8, 0, 0, -64, 48, 4, 0, 0, 28, 0, 40, 0, 0, 8, 0, 44, 0, 0, -44, -24, -16, 0, 0, 0, 32, 12, 0, 0, -12, -4, 0, 0, 0, 20, 12, -10, 0, 0, -2, 32, 72, 0, 0, 24, -14, 0, 0, 0, -40, -8, -8, 0, 0, 0, 0, 24, 0, 0, 0, -4, -16, 0, 0, -16, 64, 0, 0, 0, 0, 2, -60, 0, 0, -12, 12, 72, 0, 0, -100, 0, 4, 0, 0, -12, 0, -20, 0, 0, -24, 16, -96, 0, 0, 14, -12, 40, 0, 0, 32, -16, 0, 0, 0, -36, -56, -8, 0, 0, 0, -8, -16, 0, 0, -8, 0, 0, 0, 0, -52, -2, -80, 0, 0, -32, -20, -12, 0, 0, 0, 48, -8, 0, 0, -4, 32, 0, 0, 0, -100, 48, 28, 0, 0, -24, -24, 8, 0, 0, -16, 0, -50, 0, 0, 16, -12, 0, 0, 0, -4, -36, 0, 0, 0, 0, -4, 40, 0, 0, 56, -12, 0, 0, 0, 2, -4, -36, 0, 0, -64, -8, 32, 0, 0, 0, 0, -16, 0, 0, 28, -16, 84, 0, 0, 48, -20, -24, 0, 0, 0, -16, -8, 0, 0, 0, -24, 0, 0, 0, 0, 6, -168, 0, 0, 20, -40, -32, 0, 0, -24, 0, -96, 0, 0, 64, 12, -20, 0, 0, -8, 0, 0, 0, 0, 0, 32, 32, 0, 0, 84, 0, 14, 0, 0, 48, 48, -8, 0, 0, 8, 0, 116, 0, 0, 20, 0, -48, 0, 0, 64, -8, -36, 0, 0, 28, 24, 20, 0, 0, 0, 2, -62, 0, 0, -52, -20, 0, 0, 0, -12, 40, 76, 0, 0, 36, -24, -12, 0, 0, -64, -28, -28, 0, 0, -24, 20, -24, 0, 0, 0, -8, 96, 0, 0, 0, 16, -24, 0, 0, -8, 22], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "570.2.d.b", "char_is_minimal": true, "conrey_index": 229, "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], [1, 0], [0, 1], [0, 1], [-1, 0], [2, 1], [-1, 0], [0, 0], [0, -1], [-1, 0], [-1, 2], [-4, 0], [0, -1], [0, 4], [0, 0], [-1, 2], [1, 0], [0, 6], [0, -1], [1, 0], [-2, -1], [0, 0], [0, -4], [0, 0], [1, 0], [3, 4], [-4, 0], [0, -1], [0, 0], [2, 0], [-2, -1], [0, 0], [0, 1], [0, -4], [-6, 0], [0, 0], [1, 0], [0, -4], [0, 1], [-4, 0], [1, -2], [-12, 0], [0, 0], [0, -6], [4, 0], [-2, -1], [0, 0], [0, 0], [0, 1], [7, 0], [-4, 3], [-6, 0], [0, -4], [0, 14], [1, 0], [-8, -4], [0, 0], [0, 1], [0, 2], [10, 0], [1, -2], [-6, 0], [0, 0], [0, 0], [-1, 0], [-4, 8], [4, 0], [0, -4], [0, -6], [0, 0], [0, 0], [12, 0], [0, 1], [0, -8], [4, 0], [-4, 3], [-1, 0], [0, 0], [0, -4], [8, 0], [2, 1], [1, 0], [0, -12], [0, -12], [0, 0], [-6, 12], [6, 0], [0, 2], [0, 4], [8, 0], [1, -2], [0, 0], [0, 0], [0, 0], [0, 0], [2, 1], [-1, 0], [0, -10], [0, 7], [4, 0], [-3, -4]]}