# Stored data for newform 570.2.i.f, downloaded from the LMFDB on 28 March 2024. {"label": "570.2.i.f", "space_label": "570.2.i", "level": 570, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518547926221370, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 487583871706301770, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [-5, -2, 1]], [11, [3, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+(1-\\beta _{1})q^{3}-\\beta _{1}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "i", "char_is_real": false, "Nk2": 2280, "analytic_conductor": 4.551472915212982, "hecke_ring_index": 3, "level_radical": 570, "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": "0.017", "prec": 17}, "analytic_rank_proved": true, "char_values": [570, 3, [191, 457, 211], [3, 3, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 19], "conrey_indexes": [121, 391], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "4.133", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "63.322", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1615.967", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 2, -2, 4], "traces": [0, 4, -2, 2, -2, -2, 2, 4, 4, -2, -2, -12, -4, 0, -2, 2, -2, 8, 4, -2, 4, 2, 6, 2, 2, -2, 0, -4, -2, -4, -4, 16, -2, -6, 8, -2, -2, -20, -2, 0, -2, 6, 2, 4, 6, 4, -4, 12, 2, 0, 4, -8, 0, 10, 2, 6, 4, 2, 8, 12, 2, -20, -8, -2, 4, 0, -6, 0, -16, 4, -2, -8, -2, -16, 10, -4, 4, -12, 0, -4, -2, -2, 6, 8, -4, 8, 4, -8, -12, 6, -2, 24, 2, 8, -24, -2, -4, 32, 0, 6, -2, 12, 16, -4, 0, 2, -20, -40, 2, 12, 6, -10, -2, -48, -4, -4, -4, 0, 12, 20, 2, -8, 40, -6, -8, 4, 4, -14, -2, -4, 0, 6, 12, 34, 0, 2, 8, 24, -2, 0, 4, 24, -8, 0, 4, 8, -16, 0, 10, -32, 2, -48, -2, -16, 6, -8, 0, -22, -4, 20, 4, -22, -2, 8, -12, -6, -4, -10, 2, -22, -16, 4, -8, 14, 4, -2, 6, -12, -12, -44, -2, 0, -48, -40, 2, 10, 8, -24, 12, -4, 4, 24, 2, 28, 32, 0, 0, 36, -12, -8, -2, 0, -24, 32, -8, 6, 2, 2, 0, 6, -4, 38, 10, 8, 20, 4, -4, 64, 12, 16, -12, 48, -10, 2, -2, -2, 24, -16, 2, -24, 2, -6, -4, 36, 0, -24, -24, 4, 20, -80, -4, 16, 4, 2, -20, 0, 12, 0, 16, 4, -2, 24, -2, -6, 28, 16, -2, -12, 8, 28, 0, -4, 6, -30, -6, -20, -38, 12, 0, 24, 2, 20, 8, 48, -48, 6, -2, -32, 0, -8, -2, -14, -12, -4, 16, -4, 0, 42, -2, -10, -4, -32, 32, -36, 0, 12, -20, 12, -32, 48, 2, -44, 24, 24, -2, 40, 8, -4, 6, -2, -8, 0, 0, -24, -22, 4, 8, -14, -10, 12, -2, -20, 44, 44, 4, 0, -4, -12, 6, 36, 12, 44, -4, 10, 20, 0, 2, 4, -22, -24, 8, -48, -2, 20, 4, -2, 14, -4, 4, 8, 4, 0, 6, -112, 24, -8, 6, -20, 22, -48, 4, 34, 0, -4, 24, -16, 20, -32, -4, -12, 10, -2, -16, 4, -24, 2, 12, -72, 2, 32, -2, -28, -12, -12, 2, 6, 28, -8, -64, 12, 0, -32, 0, -6, -18, -4, 6, 26, 16, 38, 4, -12, 0, 48, 12, -2, -64, 60, -8, -30, -12, 48, 2, 12, 2, -4, 0, 0, 6, 68, 2, 52, 38, 12, 10, -16, -16, -8, 20, 0, -8, -36, 2, 8, -32, 4, -24, -4, -32, 8, 6, 0, -24, -28, 20, -12, 2, 32, 4, 84, -2, -18, 24, -24, 8, -48, 2, 40, 12, -8, 2, 36, -6, -92, 8, 8, 36, -112, 0, -36, 12, 22, 12, -12, -8, 4, -40, 10, 40, 24, 2, 48, -32, -44, 4, 32, -4, -44, -20, 4, 0, 50, -6, 40, -72, -12, -8, -44, 4, -26, -2, -20, -48, -34, -2, -24, 12, 22, -14, -4, -8, -4, 4, 2, 24, 2, -4, -36, -14, -14, 0, 24, -4, 28, -12, -4, -30, 56, -6, -4, 10, -24, 4, 144, -6, 20, 0, -22, 24, 0, -4, -48, 20, 0, -16, 12, -24, 36, 24, -20, -12, 8, 4, 20, 16, -10, 0, 22, 16, -192, -2, 24, 28, 0, -12, 24, -4, -2, -8, -20, 2, -72, 0, 12, 42, 2, -2, -24, 20, -28, -4, -88, 64, -30, -16, 0, 18, 16, 0, 64, -24, 18, 10, 36, -6, 20, 64, -16, 48, -36, -4, 76, -44, 0, 24, 4, -12, 108, 4, 64, -20, -48, 8, 26, -4, 12, -12, 8, -2, 4, 16, -2, 0, -6, 0, -2, 48, -6, 44, -16, -2, 28, -4, -38, 28, 28, -10, 48, -24, 16, -2, 52, -20, -16, -22, 8, -16, 20, -2, -36, 0, 32, -4, -132, 24, 6, 6, 32, -72, -6, -6, 8, -22, 24, 8, -38, -20, 76, -10, -2, 0, 60, -4, -64, 4, 2, 44, 12, -24, 20, 8, -8, 24, -120, -2, -48, -10, -12, 4, 24, -2, -116, -28, 6, -4, 0, -8, -60, -4, -36, -2, -28, 0, 82, -12, -12, 56, 36, -12, -36, 16, 8, 6, -40, 40, 0, 22, -40, -48, 40, -2, -124, -68, 32, 0, -4, -4, -36, 24, 4, 32, 32, 20, 68, 64, 0, 2, 0, 6, -22, -20, 72, 4, 10, 8, -32, -2, -4, 48, -112, 2, -8, -24, 48, -72, 24, 2, -50, -16, -12, -2, 76, 14, 48, -12, 8, -12, 0, -4, 48, 6, -24, -56, 46, 4, -8, 32, 14, -24, 114, 0, 24, 16, 4, 0, -22, 12, -8, -18, 30, 8, -72, 6, -24, 26, -10, -8, 36, -4, 144, -2, 6, -12, 48, 0, 44, -96, -24, 12, -16, 4, 22, 32, -20, -30, -4, 16, -140, 60, 24, 6, -44, -24, 38, -4, 12, 12, 8, -4, 112, -4, -16, 0, 24, 0, 20, -12, -16, -34, -60, 2, -58, 52, -28, -76, -22, 12, -8, -20, 4, 8, -58, 8, -28, 16, -2, -40, 48, 0, -22, 4, -42, 72, 116, 2, 14, -16, -20, -32, 12, 4, 72, 12, -64, 74, 4, 16, -18, 8, -18, 6, 60, 0, -40, -24, 24, 56, 68, -10, -50, 6, 6, -4, -24, -64, 22, -2, -48, -42, 56, 4, 56, -18, 44, -48, 0, -24, 36, 8, 12, 24, -40, -4, -24, -20, 20, 12, 6, -8, -72, -4, 4, 36, -144, 12, 10, 46, 2, -4, -74, -16, 72, -72, 0, 56, -24, 0, 8, 72, -48, 12, 36, -44, -132, 12, 2, -12, 44, 4, 48, -2, -28, 20, 24, 10, -12, 40, 24, -48, 24, 2, 36, -96, 20, 16, 28, 22, -16, -8, 16, -64, -36, 2, -72, 22, 0, 40, 72, 4, -18, 0, -24, 50, -30, -6, -18, -20, 72, 72, 200, 6, -28, -8, 22, -44, 16, -8, -10, -26, 20, 4], "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, 19, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "570.2.i.f", "char_is_minimal": true, "conrey_index": 121, "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], [-1, 1, 0, 0], [1, -1, 0, 0], [0, -1, 0, 0], [-1, 1, 0, 0], [0, 1, 0, 0], [1, 0, 0, -1], [1, 0, 0, 0], [0, -1, 0, 0], [0, -1, 0, 0], [-3, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -2, 0], [-1, 1, -1, 1], [0, 1, 0, 0], [-1, 1, 0, 0], [4, -4, 1, -1], [1, 0, 0, 0], [-1, 1, -1, -1], [1, 0, 0, 0], [1, -1, 1, -1], [3, -3, 0, 0], [0, 1, 2, 0], [1, -1, 0, 0], [0, -1, 0, 0], [0, 0, 0, 2], [-1, 0, 0, 0], [0, -1, 1, 0], [0, -2, -3, 0], [-1, 0, 0, 0], [4, 0, 0, -2], [0, -1, 0, 0], [-3, 3, 0, 0], [0, 4, -1, 0], [-1, 1, -1, 1], [-1, 1, 0, 0], [-5, 0, 0, -2], [0, -1, -1, 2], [0, 0, 0, -2], [-1, 1, 0, 0], [3, -3, 3, -3], [0, 1, -1, 0], [2, -2, -4, 4], [0, 3, 0, 0], [1, 0, 0, 0], [-1, 0, 0, -2], [0, 6, -2, 0], [0, 1, 0, 0], [0, 0, 0, -2], [1, 0, 0, 0], [0, -4, 1, 0], [0, 0, 2, -2], [0, 5, 1, 0], [1, -1, 0, 0], [3, -3, 0, 0], [1, 0, 0, -1], [0, 1, 1, -2], [2, 0, 0, 3], [6, -6, 0, 0], [1, -1, 0, 0], [0, -10, -1, 0], [-4, 4, -2, 2], [0, -1, 1, 0], [1, 0, 0, 0], [0, 0, 0, 2], [0, -3, 0, 0], [0, 0, 3, 0], [-4, 0, 0, 1], [1, 0, 0, 2], [0, -1, 1, 0], [-4, 4, -3, 3], [0, -1, 0, 0], [-8, 8, 1, -1], [5, -5, -2, 2], [-1, 0, 0, 0], [1, 0, 2, -1], [-3, 0, 0, 3], [0, 0, -2, 2], [-2, 2, 2, -2], [0, -1, 0, 0], [-1, 1, 0, 0], [0, 3, -3, 0], [2, 0, 0, 4], [-1, 0, 0, 1], [0, 4, -1, 0], [0, 2, 4, 0], [-2, 0, 0, -3], [-3, 0, 0, 0], [0, 3, 1, 0], [-1, 1, 0, 0], [0, 12, -2, 0], [1, -1, -2, 2], [4, -4, 2, -2], [-6, 0, 0, 2], [0, -1, -1, 2], [-1, 0, 0, 0], [16, -16, -1, 1], [0, 0, -2, 2], [0, 3, 0, 0], [-1, 1, 0, 0]]}