# Stored data for newform 490.2.i.a, downloaded from the LMFDB on 19 April 2024.
{"label": "490.2.i.a", "space_label": "490.2.i", "level": 490, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 549789368810, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1514213592442196089, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [0, 1]], [11, [9, 3, 1]], [19, [25, -5, 1]]], "qexp_display": "q+\\zeta_{12}q^{2}+\\zeta_{12}^{2}q^{4}+(-2+\\zeta_{12}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "i", "char_is_real": false, "Nk2": 1960, "analytic_conductor": 3.912669699042739, "hecke_ring_index": 1, "level_radical": 70, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [490, 6, [197, 101], [3, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 5, 7], "conrey_indexes": [79, 459], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "3.926", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "97.252", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3709.551", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, -4, 0], "traces": [0, 4, 0, 0, 2, -4, 0, 0, 0, -6, 2, -6, 0, 0, 0, 0, -2, 0, 0, 10, -8, 0, 0, 0, 0, -6, -10, 0, 0, 16, 0, -4, 0, 0, -8, 0, -12, 0, 0, 0, -2, -12, 0, 0, 6, -12, 14, 0, 0, 0, -16, 0, 0, 0, 0, 24, 0, 0, 0, 8, 0, 12, 0, 0, -4, -10, 0, 0, 0, 0, 0, -24, 0, 0, 2, 0, 20, 0, 0, 28, -4, -18, 0, 0, 0, -8, -4, 0, 0, -4, -12, 0, 0, 0, 14, 20, 0, 0, 0, 36, 6, 0, 0, 0, -20, 0, 36, 0, 0, 4, 6, 0, 0, 0, 0, 14, 8, 0, 0, 0, 0, 4, 0, 0, 4, 8, 0, 0, 0, 0, -20, -2, 0, 0, -8, 0, -4, 0, 0, 64, 0, 0, 0, 0, -6, -16, 64, 0, 0, -36, 0, 12, 0, 0, 0, 16, 0, 0, 0, 0, -4, 0, 0, 0, -6, 0, -12, 0, 0, -48, 8, 30, 0, 0, 0, 0, 12, 0, 0, 26, 12, -104, 0, 0, -14, 2, 0, 0, 0, 0, 20, 40, 0, 0, 24, 0, 0, 0, 0, -36, -8, 0, 0, 0, 0, 12, -16, 0, 0, -60, 0, -36, 0, 0, -32, -4, 0, 0, 0, 0, 12, -20, 0, 0, 0, 36, -28, 0, 0, -32, -56, 0, 0, 0, -30, 14, -8, 0, 0, -80, 0, -18, 0, 0, 24, 0, 0, 0, 0, 0, 22, -20, 0, 0, 14, 0, -2, 0, 0, 0, -20, -24, 0, 0, 0, 36, 0, 0, 0, 20, 0, 48, 0, 0, 32, -18, 0, 0, 0, 24, 0, 36, 0, 0, -12, 0, 60, 0, 0, -26, 8, 0, 0, 0, 0, -32, -2, 0, 0, -70, 0, 0, 0, 0, 10, 24, 12, 0, 0, 0, 4, 12, 0, 0, -36, 0, 56, 0, 0, -24, 4, 0, 0, 0, 18, -40, 24, 0, 0, 0, 0, -10, 0, 0, -30, -8, 0, 0, 0, 0, -4, -12, 0, 0, -8, 0, 18, 0, 0, -48, 0, 0, 0, 0, 0, 24, -8, 0, 0, 32, -6, -12, 0, 0, 0, 64, 0, 0, 0, 18, -8, 0, 0, 0, 12, 0, -14, 0, 0, 116, -20, 0, 0, 0, 0, 0, -40, 0, 0, -12, 0, -56, 0, 0, -10, 56, 18, 0, 0, 0, 12, 30, 0, 0, 0, 72, 0, 0, 0, 28, -6, 0, 0, 0, -84, -12, -10, 0, 0, 140, 0, -80, 0, 0, 18, 16, 0, 0, 0, 0, -8, -4, 0, 0, 0, 0, -4, 0, 0, 56, 12, 0, 0, 0, 0, -8, -16, 0, 0, -20, 24, 18, 0, 0, -24, 0, 0, 0, 0, 0, -14, 128, 0, 0, -8, 0, 16, 0, 0, 0, -56, 0, 0, 0, 0, -60, 0, 0, 0, -72, 0, -10, 0, 0, 8, 24, 0, 0, 0, 0, 0, 96, 0, 0, 50, -36, 8, 0, 0, 8, 4, 0, 0, 0, 0, 0, 42, 0, 0, 68, 0, 0, 0, 0, 12, -16, 0, 0, 0, 0, 20, -54, 0, 0, -4, 0, 0, 0, 0, 52, -36, -48, 0, 0, 0, -32, -4, 0, 0, 0, 0, 32, 0, 0, 4, -16, 0, 0, 0, 36, 24, 40, 0, 0, 8, 0, 32, 0, 0, -40, 0, 0, 0, 0, 0, -28, -56, 0, 0, -30, 0, -64, 0, 0, 0, -112, 6, 0, 0, 0, -32, 0, 0, 0, 32, -30, -18, 0, 0, -40, -8, 0, 0, 0, 0, 0, -72, 0, 0, -24, 0, 88, 0, 0, -12, 8, 0, 0, 0, 0, 24, -70, 0, 0, 44, 0, 0, 0, 0, -38, 8, 0, 0, 0, 0, 14, -44, 0, 0, -8, 0, -72, 0, 0, -4, 14, 0, 0, 0, 36, -2, 10, 0, 0, 0, 0, -20, 0, 0, 24, 60, 0, 0, 0, 0, -4, 6, 0, 0, 144, 0, 32, 0, 0, -24, 0, -12, 0, 0, 0, 8, -72, 0, 0, 20, 0, -24, 0, 0, 0, 16, 0, 0, 0, -30, 32, 0, 0, 0, 90, 0, -88, 0, 0, 48, -64, 0, 0, 0, 0, 0, 104, 0, 0, 6, 0, -96, 0, 0, 24, -12, 84, 0, 0, 0, 60, -26, 0, 0, -52, 24, 0, 0, 0, -52, -24, 0, 0, 0, 108, -64, -8, 0, 0, 52, 0, -28, 0, 0, -58, -2, 0, 0, 0, 0, -72, -52, 0, 0, 0, 0, -56, 0, 0, -40, -48, 0, 0, 0, 0, 10, 2, 0, 0, 80, 12, 42, 0, 0, -116, 0, 0, 0, 0, -12, -12, 48, 0, 0, -30, 0, 36, 0, 0, 0, -36, 0, 0, 0, 0, 56, 0, 0, 0, 28, 0, 36, 0, 0, -56, 8, -12, 0, 0, 0, 0, 40, 0, 0, -10, 18, 132, 0, 0, 6, 24, 0, 0, 0, 0, 24, 36, 0, 0, 16, 0, 0, 0, 0, 52, -24, 0, 0, 0, 0, -30, -30, 0, 0, -136, 0, -52, 0, 0, -18, 48, -84, 0, 0, 0, 12, 14, 0, 0, 0, -120, 32, 0, 0, 24, -8, 0, 0, 0, 0, 18, 56, 0, 0, -168, 0, -20, 0, 0, 140, 0, 0, 0, 0, 0, -12, 60, 0, 0, 20, 0, -60, 0, 0, 0, -8, -54, 0, 0, 0, -104, 0, 0, 0, -16, 18, -36, 0, 0, -56, 104, 0, 0, 0, 0, 0, 8, 0, 0, -20, 0, -64, 0, 0, 40, -28, 0, 0, 0, 0, -16, 34, 0, 0, -42, 0, 0, 0, 0, -68, 12, 30, 0, 0, 0, -14, -56, 0, 0, -16, 0, 24, 0, 0, 160, -40, 0, 0, 0, -54, 80, -40, 0, 0, 0, 0, 54, 0, 0, 18, -40, 0, 0, 0, 0, 48, -66, 0, 0, 128, 0, 12, 0, 0, 24, 0, -24, 0, 0, 0, -10, -32, 0, 0, -28, 18, 16, 0, 0, 0, 144, 0, 0, 0, 0, 44], "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, 7, 3, 1, 3, 0], [1, 1, 35, 10, 1, 6, 0]], "char_orbit_index": 9, "prim_orbit_index": 10, "minimal_twist": "70.2.i.b", "char_is_minimal": false, "conrey_index": 79, "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], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [-2, 1, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [-3, 0, 3, 0], [0, -2, 1, 2], [0, 0, -3, 0], [0, 0, 0, 0], [0, 0, 0, 5], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 1, 0], [0, -2, 0, 2], [0, -3, 0, 3], [5, 0, -5, 0], [-2, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, -3], [0, 7, 0, 0], [0, 0, 0, 0], [0, -4, -3, 4], [-5, 0, 5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4, 0, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, -1, 0, 1], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 0, 0], [0, 1, 0, 0], [0, 5, 0, -5], [0, 0, 0, 0], [-1, -2, 1, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [3, 0, -3, 0], [0, -3, -6, 3], [0, 0, 7, 0], [0, 7, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, -3], [0, 0, 0, 0], [0, -5, 0, 5], [0, 9, 0, -9], [0, 0, 0, 0], [6, 0, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [6, 0, -6, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-1, 0, 0, 0], [-5, -10, 5, 0], [0, 0, 0, 0], [0, -2, 0, 2], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, -3, 0, 0], [0, 16, 0, -16], [0, 0, 1, 0], [0, 0, 0, 0], [5, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [14, 0, -14, 0], [0, -1, -2, 1], [0, 0, -9, 0], [0, -3, 0, 0], [0, 0, 0, 6], [0, 0, 0, 0], [-2, 0, 0, -4], [-2, 0, 2, 0], [0, 0, 0, 0], [0, 3, 0, -3], [-2, 0, 2, 0], [-3, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 7], [0, 0, 0, 0], [0, 0, 7, 0], [0, 5, 10, -5], [0, 0, 0, 0], [0, 0, 0, -12], [0, 0, 0, 0], [9, 0, 0, 0], [3, -4, -3, 0]]}