# Stored data for newform 490.2.e.i, downloaded from the LMFDB on 18 April 2024. {"label": "490.2.e.i", "space_label": "490.2.e", "level": 490, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029071930425834, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 1182930327820806687, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4, 8, 14, 4, 1]], [11, [16, -16, 20, 4, 1]], [13, [-4, 4, 1]]], "qexp_display": "q+(1+\\beta _{2})q^{2}+(\\beta _{1}+2\\beta _{2}+\\beta _{3})q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1960, "analytic_conductor": 3.912669699042739, "hecke_ring_index": 1, "level_radical": 70, "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": "0.023", "prec": 17}, "analytic_rank_proved": true, "char_values": [490, 3, [197, 101], [3, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 5, 7], "conrey_indexes": [361, 471], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.048", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "61.178", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1585.965", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [2, -4, -2, 0], "traces": [0, 4, 2, -4, -2, -2, -8, 0, -4, -6, 2, -4, -4, -8, 0, 8, -2, -8, 6, -4, 4, 0, -8, 8, 4, -2, -4, 32, 0, -8, 4, 0, 2, 0, -16, 0, 12, 4, 4, 16, 2, 16, 0, -24, -4, -6, -8, -16, 8, 0, -4, -12, 4, 4, 16, 8, 0, 8, -4, -20, -4, 4, 0, 0, 4, 4, 0, 8, -8, -16, 0, 16, 6, 16, -4, -4, 8, 0, 32, 8, -2, -46, 8, 8, 0, 16, -12, 16, 4, 0, -12, 0, -16, 8, 16, -4, 4, -48, 0, -40, -2, -4, 12, 24, 8, 0, 8, -8, -16, 12, 4, -48, 0, -16, 4, 8, 4, 44, -40, 0, -8, -2, -4, 4, 0, 4, 0, 0, 2, 32, -4, 4, 0, 0, 16, -16, 8, 32, -8, 40, 0, 48, 8, -8, -6, 4, 32, 0, -8, 12, 4, 0, 4, 16, 0, 0, 16, 4, -8, -16, -4, 0, -92, 12, -8, 0, 4, -16, 0, -4, 8, 4, 12, 12, 32, 0, 8, -36, 0, -8, -6, 24, 0, 48, -8, 4, -8, -24, 32, 0, -8, 8, -4, 0, -24, -32, 0, -24, -20, -16, 2, 0, -8, 0, 24, -8, -24, -8, 4, 32, 0, -16, 4, 8, 8, 12, -32, 0, 24, 36, -4, 8, -24, 16, 0, 12, -8, -28, -4, 4, 16, 0, 8, -24, -44, -16, -20, -48, 0, -16, -4, 24, 2, -92, -8, 0, 8, 0, 0, 4, 2, 8, 0, -64, 0, -12, -2, 0, 64, 0, -8, 44, -4, -56, 0, -8, 0, 72, 8, -20, 16, -24, 16, 0, 64, -4, 8, -12, 20, -64, 0, 32, 24, -4, -8, -4, -16, 0, -12, -2, -4, 36, 16, -56, 0, 40, -4, 32, -12, 0, 8, 0, 0, -40, -4, 4, 8, 88, 0, -112, 0, -8, -16, 8, 8, 0, -16, -4, 16, -8, -2, 64, 0, 40, -46, 4, -12, 0, -16, 0, 0, -28, -4, 76, -8, -16, 0, 24, -2, 48, -8, -16, 8, 0, 24, 8, -12, 12, 16, -24, 0, -192, 4, -32, 36, -8, 0, 0, -16, 0, 6, 26, 12, -56, 0, -32, 24, -16, 8, 56, 8, 0, -16, 44, 24, -4, 16, 48, 0, 104, -4, -8, -8, 48, -8, 0, 0, 68, 24, -28, -16, -80, 0, -40, -12, 8, 20, -28, -32, 0, 4, 12, 0, -16, -4, 92, 0, 48, 12, 24, 8, 64, -48, 0, -16, -4, -4, -68, 16, 24, 0, 24, -8, -16, -4, -8, 16, 0, 16, -16, -12, 56, -16, 48, 0, -32, 12, 24, -36, 16, -8, 0, 16, -40, 24, 0, 8, -48, 0, 24, 6, -56, 8, 32, -56, 0, -8, -32, -4, -32, 8, -40, 0, 0, 4, 8, 24, 12, -88, 0, -32, -16, 20, 8, -24, 8, 0, 168, -8, 40, 4, -40, 48, 0, 4, 24, 92, -24, -4, -128, 0, 16, 4, 8, 0, 20, 0, 0, 8, -72, -2, -40, 4, 48, 0, 8, -32, -28, 0, 28, -24, 0, -4, 0, 0, 24, 32, 96, 0, -64, -4, -24, -44, -28, -8, 0, -112, -8, 0, -2, -4, 88, 0, 48, 36, -8, -8, -16, -40, 0, 32, -4, 24, 0, 8, -24, 0, -8, 32, -116, 4, 0, 16, 0, -24, 24, -20, -36, -32, 80, 0, 16, 16, 76, -24, 8, -8, 0, -16, 36, 4, 44, -8, 48, 0, -16, -6, -32, 2, -16, -8, 0, 72, 56, -16, 44, -28, 40, 0, 16, 20, 80, 4, -32, 64, 0, -24, -56, 0, 16, 4, 32, 0, 80, 0, -2, 40, 24, -8, 0, 8, 16, -8, 36, 44, -8, 0, -88, -56, -44, 0, 0, -16, 0, -32, -2, -8, -8, 4, 0, 0, -16, -8, -48, 4, 0, 32, 0, -16, 72, 2, 4, 32, 104, 0, -64, 20, -16, 46, -48, 8, 0, -24, -20, 0, 4, -8, -128, 0, -120, 0, 20, 28, 40, -8, 0, 152, 0, 8, 16, -8, -144, 0, -192, 12, -16, 2, -28, 96, 0, -16, -68, 16, -56, 4, -64, 0, -96, 12, 40, -8, -12, -24, 0, 24, -20, -16, -52, -12, 160, 0, -24, -96, -8, -4, -24, -64, 0, 72, -28, 8, 56, 0, -32, 0, 16, -8, 0, 0, -32, 12, 0, 52, 52, -12, 4, -28, -48, 0, 276, -16, 40, -24, -68, -32, 0, 16, 48, -56, -12, 4, -16, 0, 128, -8, 12, -44, 36, 48, 0, -8, 56, -16, -4, 24, 0, 0, -8, 52, 16, 4, -8, -16, 0, -16, -8, -48, 32, -4, 16, 0, -56, 0, 4, -68, 0, 48, 0, -56, -36, 16, -64, -40, -192, 0, -8, -20, 28, 12, -112, 16, 0, 40, 56, 28, -16, -16, -88, 0, 144, 2, -144, -12, 24, 0, 0, -32, -64, 4, -40, 46, 136, 0, 96, 24, 12, -12, 16, 48, 0, 16, -12, -64, 16, -24, 0, 0, -112, -8, 44, 4, 16, -8, 0, -136, 8, -16, 64, 12, -112, 0, -68, 12, -32, 8, 2, -32, 0, -8, 4, 8, 16, 8, -184, 0, -8, 8, 24, 16, -28, -24, 0, 112, -24, 16, 12, 24, -56, 0, 0, -16, 16, -12, 24, 48, 0, -72, 4, -16, 40, -4, 64, 0, -144, 8, -36, 40, 48, 48, 0, 0, 4, -8, -40, -24, 16, 0, 32, 12, -16, -6, 40, -112, 0, 16, -12, -32, 56, -28, 280, 0, 32, -4, -32, 32, -24, -8, 0, -64, -48, -8, -68, -20, 64, 0, -8, 0, 104, -4, -8, 16, 0, 48, -16, -12, -24, -44, 64, 0, 72, -16, 100, 16, 72, 40, 0, 16, 4, 24, -40, 4, 64, 0, 24, 84, 8, 8, -16, 80, 0, 8, 46, 40, -88, 24, 0, 0, -48, 2, -16, -24, -4, 184, 0, -48, 16, 4, 48, -64, -144, 0, 120, 8, 64, -4, 12, 16, 0, 0, -32, -20, -16, 0, 224, 0, 32, 4, -20, 72, 160, -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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "490.2.a.l", "char_is_minimal": false, "conrey_index": 361, "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, 0, 1, 0], [0, 1, 2, 1], [0, 0, 1, 0], [-1, 0, -1, 0], [-2, 0, 0, 1], [0, 0, 0, 0], [-1, 0, 0, 0], [-3, -4, -3, 0], [0, 0, -1, 0], [0, -2, 2, -2], [-2, -1, -2, 0], [-2, 0, 0, 2], [0, 0, 0, 0], [2, 0, 0, -1], [-1, 0, -1, 0], [0, -1, 4, -1], [0, -4, -3, -4], [-2, 1, -2, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, -2], [4, -2, 4, 0], [0, -1, -2, -1], [0, 0, 1, 0], [-2, -2, -2, 0], [8, 0, 0, -8], [0, 0, 0, 0], [-2, 0, 0, 2], [2, 1, 2, 0], [0, -2, 0, -2], [0, 0, -1, 0], [0, 2, 0, 0], [-4, 0, 0, -1], [0, 0, 0, 0], [3, 0, 0, -4], [2, 4, 2, 0], [0, 1, -2, 1], [0, -6, -8, -6], [1, 0, 1, 0], [4, 0, 0, 5], [0, 0, 0, 0], [-6, 0, 0, 2], [-2, 2, -2, 0], [0, 4, 3, 4], [0, -2, 4, -2], [-8, 2, -8, 0], [2, 0, 0, -1], [0, 0, 0, 0], [-1, 0, 0, 0], [-6, -2, -6, 0], [0, -2, -2, -2], [0, 6, -2, 6], [8, 8, 8, 0], [2, 0, 0, 2], [0, 0, 0, 0], [2, 0, 0, 0], [-2, -2, -2, 0], [0, -1, 10, -1], [0, 1, 2, 1], [2, -8, 2, 0], [0, 0, 0, -2], [0, 0, 0, 0], [1, 0, 0, 0], [2, 2, 2, 0], [0, 2, 0, 2], [0, 4, -4, 4], [-4, 1, -4, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [4, 0, 0, 6], [3, 4, 3, 0], [0, -1, -8, -1], [0, 4, 2, 4], [-2, -1, -2, 0], [2, 0, 0, 1], [0, 0, 0, 0], [8, 0, 0, -6], [4, 2, 4, 0], [0, 0, 1, 0], [0, 12, 23, 12], [4, -5, 4, 0], [2, 0, 0, 3], [0, 0, 0, 0], [4, 0, 0, 1], [-6, -2, -6, 0], [0, -6, -8, -6], [0, 2, -2, 2], [0, -9, 0, 0], [-3, 0, 0, 4], [0, 0, 0, 0], [-4, 0, 0, -2], [4, 4, 4, 0], [0, 2, -8, 2], [0, -1, 2, -1], [2, 1, 2, 0], [-12, 0, 0, -3], [0, 0, 0, 0], [-10, 0, 0, -2], [-1, 0, -1, 0]]}