# Stored data for newform 570.2.i.a, downloaded from the LMFDB on 23 April 2024.
{"label": "570.2.i.a", "space_label": "570.2.i", "level": 570, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 549789368890, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 299028360242493663, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [1, 1]], [11, [3, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}+(-1+\\zeta_{6})q^{3}-\\zeta_{6}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": 1, "level_radical": 570, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [570, 3, [191, 457, 211], [3, 3, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5, 19], "conrey_indexes": [121, 391], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "1.975", "prec": 17}, {"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "12.016", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "113.793", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, -1, 1, -2], "traces": [0, 2, -1, -1, -1, 1, -1, -2, 2, -1, 1, -6, 2, -2, 1, 1, -1, 6, 2, -7, -2, 1, 3, -9, -1, -1, 4, 2, 1, 0, -2, -8, -1, 3, 6, -1, -1, 10, -1, 4, 1, 3, 1, 10, 3, -2, 18, 0, -1, -12, 2, 6, -2, -3, -1, -3, -2, -1, 0, 12, 1, 10, 4, 1, 2, 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-8, -21, 30, -1, 29, -26, 30, -50, -9, 0, 4, 6, 22, 6, -45, 0, -38, 20, 7, 12, -24, 6, -17, -10, -3, 60, -78, -1, -21, -32, 38, -4, 42, 0, 20, -2, 16, -63, 2, 4, -35, -14, -9, -3, 78, -12, -26, 12, 24, -36, -36, -5, 11, 15, 3, -2, 0, 36, 15, 1, -18, -3, 0, 2, -36, -9, -10, -12, 32, 10, 10, -12, -6, -2, 60, 8, 108, -38, -10, 10, 9, 6, 16, -18, 16, -30, 0, 6, -5, -11, 1, 0, -27, 8, 42, 12, 0, 0, 18, -2, 4, 20, 16, 0, 24, -26, -54, 12, -1, -30, -18, -14, -16, -7, 30, -6, 0, -3, 6, -12, 0, 24, -12, 1, -30, 20, -6, 10, -10, 9, -44, -4, -48, -16, -12, -1, -4, -11, -2, -20, -48, 22, 45, 12, 4, -3, -9, 3, -3, 0, 0, -2, -180, -3, 52, 4, -5, 0, 20, -36, 49, 25, 10, -2], "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.a", "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], [1, 0], [-1, 1], [-1, 1], [0, -1], [1, -1], [0, -1], [-1, 0], [1, 0], [0, -1], [0, 1], [-3, 0], [1, 0], [0, -2], [1, -1], [0, 1], [-1, 1], [6, -6], [1, 0], [-5, 3], [-1, 0], [1, -1], [3, -3], [0, -9], [-1, 1], [0, -1], [2, 0], [1, 0], [0, 1], [0, 0], [-1, 0], [-4, 0], [0, -1], [3, -3], [0, 6], [-1, 1], [-1, 1], [5, 0], [2, -5], [2, 0], [1, -1], [3, -3], [0, 1], [10, -10], [0, 3], [-1, 0], [9, 0], [0, 0], [0, -1], [-6, 0], [1, 0], [0, 6], [-2, 2], [0, -3], [-1, 1], [-3, 3], [-1, 0], [2, -5], [0, 0], [12, -12], [1, -1], [0, 10], [4, -4], [0, 1], [1, 0], [-2, 0], [0, 3], [0, 10], [-6, 0], [9, 0], [0, -1], [0, 0], [0, -1], [4, -4], [-5, 5], [1, 0], [3, 2], [3, 0], [-2, 2], [-14, 14], [0, 1], [-1, 1], [0, 3], [-18, 0], [-1, 0], [0, -6], [0, 10], [0, 0], [-3, 0], [0, -15], [1, -1], [0, 2], [-9, 9], [4, -4], [0, 0], [-2, 5], [1, 0], [-8, 8], [6, -6], [0, 3], [-1, 1]]}