# Stored data for newform 490.2.c.d, downloaded from the LMFDB on 25 April 2024. {"label": "490.2.c.d", "space_label": "490.2.c", "level": 490, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510936354619882, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 597103509676199496, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [0, 1]], [11, [-3, 1]], [19, [5, 1]]], "qexp_display": "q+iq^{2}-q^{4}+(2+i)q^{5}-iq^{8}+3q^{9}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 1960, "analytic_conductor": 3.912669699042739, "hecke_ring_index": 1, "level_radical": 70, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [490, 2, [197, 101], [1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 7], "conrey_indexes": [99], "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": "1.929", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.197", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "149.597", "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, 0, 0, 0, 6, -2, 6, 0, 0, 0, 0, 2, 0, 0, -10, -4, 0, 0, 0, 0, 6, 10, 0, 0, 8, 0, 4, 0, 0, -4, 0, -6, 0, 0, 0, 2, -6, 0, 0, -6, 12, -14, 0, 0, 0, -8, 0, 0, 0, 0, 12, 0, 0, 0, -8, 0, -12, 0, 0, -2, 10, 0, 0, 0, 0, 0, -12, 0, 0, -2, 0, 10, 0, 0, -28, 4, 18, 0, 0, 0, -4, 4, 0, 0, 4, -6, 0, 0, 0, -14, -20, 0, 0, 0, 18, -6, 0, 0, 0, -10, 0, 18, 0, 0, -4, -6, 0, 0, 0, 0, -14, -8, 0, 0, 0, 0, -4, 0, 0, -4, 4, 0, 0, 0, 0, 20, 2, 0, 0, -4, 0, 4, 0, 0, 32, 0, 0, 0, 0, 6, 16, 32, 0, 0, 36, 0, -12, 0, 0, 0, 8, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 12, 0, 0, -24, -8, -30, 0, 0, 0, 0, 6, 0, 0, -26, -12, -52, 0, 0, 14, -2, 0, 0, 0, 0, 10, -40, 0, 0, -24, 0, 0, 0, 0, 36, 8, 0, 0, 0, 0, -12, 16, 0, 0, -30, 0, -18, 0, 0, 32, 4, 0, 0, 0, 0, -12, 20, 0, 0, 0, 18, 28, 0, 0, 32, -28, 0, 0, 0, 30, -14, 8, 0, 0, -40, 0, 18, 0, 0, 12, 0, 0, 0, 0, 0, -22, -10, 0, 0, -14, 0, 2, 0, 0, 0, -10, 24, 0, 0, 0, 18, 0, 0, 0, -20, 0, -48, 0, 0, 16, 18, 0, 0, 0, 12, 0, 18, 0, 0, 12, 0, 30, 0, 0, 26, -8, 0, 0, 0, 0, -16, 2, 0, 0, 70, 0, 0, 0, 0, -10, -24, -12, 0, 0, 0, -4, -12, 0, 0, -18, 0, 28, 0, 0, 24, -4, 0, 0, 0, -18, 40, -24, 0, 0, 0, 0, 10, 0, 0, 30, -4, 0, 0, 0, 0, 4, 12, 0, 0, -4, 0, -18, 0, 0, -24, 0, 0, 0, 0, 0, -24, -4, 0, 0, -32, 6, 12, 0, 0, 0, 32, 0, 0, 0, -18, -4, 0, 0, 0, -12, 0, 14, 0, 0, 58, 20, 0, 0, 0, 0, 0, -20, 0, 0, 12, 0, -28, 0, 0, 10, -56, -18, 0, 0, 0, 6, -30, 0, 0, 0, 36, 0, 0, 0, -28, 6, 0, 0, 0, -42, 12, 10, 0, 0, 70, 0, -40, 0, 0, -18, -16, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 4, 0, 0, -56, 6, 0, 0, 0, 0, 8, 16, 0, 0, -10, -24, -18, 0, 0, -12, 0, 0, 0, 0, 0, 14, 64, 0, 0, 8, 0, -16, 0, 0, 0, -28, 0, 0, 0, 0, -30, 0, 0, 0, 72, 0, 10, 0, 0, 4, -24, 0, 0, 0, 0, 0, 48, 0, 0, -50, 36, 4, 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, -2, 0, 0, 0, 0, -52, 36, -24, 0, 0, 0, 32, 4, 0, 0, 0, 0, -32, 0, 0, -4, -8, 0, 0, 0, -36, -24, -40, 0, 0, 4, 0, -32, 0, 0, -20, 0, 0, 0, 0, 0, 28, -28, 0, 0, 30, 0, 64, 0, 0, 0, -56, -6, 0, 0, 0, -16, 0, 0, 0, -32, 30, 18, 0, 0, -20, 8, 0, 0, 0, 0, 0, -36, 0, 0, 24, 0, 44, 0, 0, 12, -8, 0, 0, 0, 0, 12, 70, 0, 0, -44, 0, 0, 0, 0, 38, -8, 0, 0, 0, 0, -14, 44, 0, 0, -4, 0, -36, 0, 0, 4, -14, 0, 0, 0, -36, 2, -10, 0, 0, 0, 0, 20, 0, 0, -24, 30, 0, 0, 0, 0, 4, -6, 0, 0, 72, 0, -32, 0, 0, -12, 0, -6, 0, 0, 0, -8, -36, 0, 0, -20, 0, 24, 0, 0, 0, 8, 0, 0, 0, 30, 16, 0, 0, 0, -90, 0, 88, 0, 0, 24, 64, 0, 0, 0, 0, 0, 52, 0, 0, -6, 0, -48, 0, 0, -24, 12, -84, 0, 0, 0, 30, 26, 0, 0, 52, 12, 0, 0, 0, 52, 24, 0, 0, 0, 54, 64, 8, 0, 0, 26, 0, -14, 0, 0, 58, 2, 0, 0, 0, 0, 72, 52, 0, 0, 0, 0, 56, 0, 0, 40, -24, 0, 0, 0, 0, -10, -2, 0, 0, 40, -12, -42, 0, 0, -58, 0, 0, 0, 0, 12, 12, 24, 0, 0, 30, 0, -36, 0, 0, 0, -18, 0, 0, 0, 0, 28, 0, 0, 0, -28, 0, -36, 0, 0, -28, -8, 12, 0, 0, 0, 0, 20, 0, 0, 10, -18, 66, 0, 0, -6, -24, 0, 0, 0, 0, 12, -36, 0, 0, -16, 0, 0, 0, 0, -52, 24, 0, 0, 0, 0, 30, 30, 0, 0, -68, 0, -26, 0, 0, 18, -48, -42, 0, 0, 0, -12, -14, 0, 0, 0, -60, -32, 0, 0, -24, -4, 0, 0, 0, 0, -18, -56, 0, 0, -84, 0, 20, 0, 0, 70, 0, 0, 0, 0, 0, 12, 30, 0, 0, -20, 0, 60, 0, 0, 0, -4, 54, 0, 0, 0, -52, 0, 0, 0, 16, -18, 36, 0, 0, -28, -104, 0, 0, 0, 0, 0, 4, 0, 0, 20, 0, -32, 0, 0, -40, 28, 0, 0, 0, 0, -8, -34, 0, 0, 42, 0, 0, 0, 0, 68, -12, -30, 0, 0, 0, 14, 56, 0, 0, -8, 0, 12, 0, 0, -160, 40, 0, 0, 0, 54, -80, 40, 0, 0, 0, 0, -54, 0, 0, -18, -20, 0, 0, 0, 0, -48, 66, 0, 0, 64, 0, -12, 0, 0, 12, 0, -12, 0, 0, 0, 10, -16, 0, 0, 28, -18, -16, 0, 0, 0, 72, 0, 0, 0, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "70.2.i.b", "char_is_minimal": true, "conrey_index": 99, "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, 0], [-1, 0], [2, 1], [0, 0], [0, 0], [0, -1], [3, 0], [-1, 2], [3, 0], [0, 0], [0, -5], [0, 0], [0, 0], [1, 0], [0, 2], [0, 3], [-5, 0], [-2, -1], [0, 0], [0, 3], [0, 7], [0, 0], [3, 4], [5, 0], [0, 0], [0, 0], [4, 0], [0, 0], [2, 0], [0, 1], [0, 0], [-2, 0], [0, 0], [-3, 0], [0, 1], [0, -5], [0, 0], [1, -2], [-3, 0], [0, 0], [0, -2], [-3, 0], [6, 3], [-7, 0], [0, 7], [0, 0], [0, 0], [-4, 3], [0, 0], [0, 5], [0, -9], [0, 0], [6, 3], [0, 0], [0, 0], [0, 4], [-4, 0], [0, 0], [-6, 0], [0, 2], [0, 0], [-1, 0], [5, -10], [0, 0], [0, 2], [0, -2], [0, 0], [0, 0], [-6, 0], [0, -3], [0, -16], [-1, 0], [0, 0], [5, 0], [0, 0], [0, 0], [-14, 0], [2, 1], [9, 0], [0, -3], [0, -6], [0, 0], [-2, 4], [2, 0], [0, 0], [0, -3], [2, 0], [-3, 6], [0, 0], [0, -7], [0, 0], [-7, 0], [-10, -5], [0, 0], [0, 12], [0, 0], [9, 0], [-3, -4]]}