# Stored data for newform 400.2.q.b, downloaded from the LMFDB on 25 April 2024.
{"label": "400.2.q.b", "space_label": "400.2.q", "level": 400, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504699172553104, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 65225281847140864, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [2, -2, 1]]], "qexp_display": "q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+2q^{6}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 80, "char_orbit_label": "q", "char_is_real": false, "Nk2": 1600, "analytic_conductor": 3.1940160808512155, "hecke_ring_index": 1, "level_radical": 10, "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": "0.260", "prec": 17}, "analytic_rank_proved": true, "char_values": [400, 4, [351, 101, 177], [4, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [149, 349], "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": "2.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.199", "prec": 17}, {"__RealLiteral__": 0, "data": "12.560", "prec": 20}, {"__RealLiteral__": 0, "data": "2.571", "prec": 17}, {"__RealLiteral__": 0, "data": "110.667", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c4", "trace_display": [2, 2, 0, 4], "traces": [0, 2, 2, 2, 0, 0, 4, 4, -4, 0, 0, 2, 4, 2, 4, 0, -8, 0, -2, -6, 0, 4, 4, 12, 0, 0, 4, 8, 0, -6, 0, -16, -8, 0, -4, 0, -4, -6, 0, 0, 0, 0, 8, 10, 4, 0, 12, 0, -8, -6, 0, 4, 4, -10, 0, 0, -8, -12, 0, 6, 0, -18, -16, 0, 0, 0, 4, -10, -8, 12, 0, 0, -4, -8, 0, 0, 12, 4, 4, 0, 0, 10, 0, 2, 8, 0, 0, -12, 0, 0, 0, 4, 0, -16, 16, 0, -16, 0, -6, 2, 0, 22, 0, 12, 0, 0, 0, 14, -16, -6, 0, -12, -16, 0, -12, 0, 12, 2, 12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 16, 20, 0, 22, 8, -12, -20, 0, -8, -16, 24, 6, 0, -16, -20, 0, 0, 0, -8, -6, 12, -14, 0, 0, 24, -4, 8, 0, 8, 30, 0, -20, 0, 24, 10, 2, 0, 0, 4, 4, 0, 0, 0, 6, -20, 2, -12, 0, -8, 0, -8, 34, 0, -18, 8, -36, -24, 0, -32, 4, 32, 16, 0, -16, -16, 0, -4, 0, 0, 34, 0, 0, 0, 0, 44, -12, -8, 0, 12, 0, -8, -12, 0, -18, 20, 20, 0, 0, -32, -32, 0, -8, 0, 4, -12, 0, -16, 0, 12, 30, 0, -14, 0, 0, 24, -8, 0, 0, 12, 0, -8, 0, 0, -36, -18, -14, 36, 0, 0, -12, 32, 0, 0, 42, -8, 12, 16, 0, 32, 0, 20, -12, 0, 6, 0, 12, 8, 0, 0, 8, -20, -6, 0, -16, 0, 0, -16, 0, 24, -6, 12, 0, 0, 0, 0, -30, -40, 0, 4, 0, 8, 26, 0, 4, 0, 30, -12, 0, 24, 16, -28, 12, 0, 20, -20, 0, 24, 0, -4, -10, 8, 12, 0, 0, 8, 32, 60, 0, 0, -10, -20, -12, 0, 28, 24, 12, 0, 0, 4, -12, 0, 0, 0, 2, 4, 6, 4, 0, -16, 0, -22, -12, 0, -16, 12, -40, -40, 0, 4, -26, 0, -6, 0, 16, -16, 0, 12, 0, -16, 8, 0, 0, 0, 0, -36, 18, 8, 0, -36, 0, -48, 0, 0, -20, -32, -10, 0, 0, 32, -12, 0, 6, 0, -16, -16, 0, 0, 0, -28, -10, -8, 26, 0, 0, 12, 44, 0, 0, -4, -10, -28, -24, 0, -36, -20, -16, 44, 0, 0, -12, -16, 0, 0, -16, 0, 12, -12, 0, -16, 0, -12, -6, 0, -18, 0, 16, 40, 0, 0, -36, -28, -4, 0, 64, -32, 0, -32, 0, 12, -36, -16, 0, 0, 0, 0, -30, 0, 0, -48, 0, 0, -60, 0, 0, 24, 20, 60, 0, 24, 64, -28, -16, 0, 22, 8, 0, 24, 0, -8, -10, -4, -20, 0, 0, 0, 20, 0, 0, -16, 10, 0, 80, 0, -12, -36, 24, -36, 0, -28, 4, 72, 0, 0, -38, 0, 12, -12, 0, 64, 0, 4, -46, 0, 4, 84, 12, -8, 0, 24, 22, 32, -46, 0, -16, 32, 0, -44, 0, 0, -16, 0, 0, 0, 0, 12, 50, -44, 0, 12, 0, 0, 26, 0, 6, 24, 0, 0, 0, 0, 68, 0, -6, 0, -18, -16, 0, 16, 0, 8, -10, 0, 18, 0, 0, 0, 0, 0, 0, 12, -50, 16, 20, 0, 8, -40, -38, 32, 0, 0, 20, -40, 0, 0, 2, 8, -16, 0, 0, 16, 0, 26, 28, 0, 4, 0, -20, 16, 0, 0, 14, -12, 48, 0, 68, 24, 0, 16, 0, -28, 28, 24, 0, 0, 0, 0, -10, -40, 0, 44, 0, 0, -24, 0, -16, 0, -50, -20, 0, 0, 24, 24, -34, 0, 48, 60, 0, 0, 0, 32, -12, 60, 12, 0, 0, 0, -36, -20, 0, 0, -6, -12, -20, 0, -36, 28, 42, 0, 0, 24, 84, -20, 0, 0, -32, 4, -38, -12, 0, 0, 0, 32, 34, 0, -18, 4, 8, 0, 0, 12, -36, 0, 48, 0, -36, -32, 0, 36, 0, -44, -6, 0, 0, 0, 0, -32, 10, 12, 0, -40, 0, -40, -20, 0, -18, 4, 4, 0, 0, 24, 0, 0, -8, 0, 62, 16, 0, -16, 0, 12, 44, 24, -54, 0, 0, -16, -96, 0, 0, -68, 0, 52, 0, 0, 24, 2, -36, -36, 0, 0, 4, 0, 0, 0, -20, 0, 42, 16, 0, -48, 0, 0, -46, 0, -12, 0, 92, 0, 0, 0, 2, -8, 28, 0, 64, 0, 0, -12, 0, -32, -46, 12, 0, 0, 0, 0, -12, 0, 0, 32, 0, 32, 100, 0, 44, -56, -10, -20, 0, -8, -24, 52, 0, 0, 20, -24, 0, 24, 0, 44, 30, -68, 12, 0, 0, -8, -36, -20, 0, -56, -50, -24, 32, 0, -8, -36, -8, -40, 0, -32, -12, 0, 0, 0, -78, 24, -16, -12, 0, -16, 0, 32, 4, 0, 22, -32, -68, -24, 0, 24, -66, -24, -46, 0, -12, -16, 0, 12, 0, 0, -64, 0, 0, 0, 0, -36, 40, 36, 0, 16, 0, 40, -60, 0, -36, -40, -10, 0, 0, -56, -16, 0, 6, 0, 0, 64, 0, 0, 0, -28, 26, 0, 0, 0, 0, 24, -4, 0, 0, -16, -10, -28, 60, 0, 4, 6, 42, -8, 0, 0, 4, 24, 0, 0, 10, -96, -48, -28, 0, 32, 0, -60, 48, 0, 20, 0, 40, 24, 0, 0, 54, 60, 22, 0, -16, 48, 0, 64, 0, -28, 44, -32, 0, 0, 0, 0, 20, 16, 0, 32, 0, 0, -60, 0, 18, 0, -60, -20, 0, -8, -56, -40, 32, 0, -58, 60, 0, -24, 0, 20, -10, 0, -8, 0, 0, -16, -48, 20, 0, 0, -12, 80, -32, 0, 66, -12, -14, 0, 0, 48, 4, -36, 0, 0, -38, -28, 12, 4, 0, 72, 0, 4, 8, 0, 6, -76, -68, 0, 0, 24, -32, 0, 60, 0, 64, 64, 0, -40, 0, 8, 74, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 80, 17, 1, 4, 0]], "char_orbit_index": 17, "prim_orbit_index": 17, "minimal_twist": "16.2.e.a", "char_is_minimal": false, "conrey_index": 149, "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, -2], [0, 0], [2, 0], [2, 0], [-2, -2], [0, -1], [0, 0], [1, 1], [2, -2], [1, 1], [2, -2], [0, 0], [-4, 0], [0, -2], [-1, -1], [-3, 3], [0, 0], [2, 2], [2, 0], [6, 0], [0, -4], [0, 0], [2, 0], [4, -4], [0, -4], [-3, 3], [0, 0], [-8, 0], [-4, 4], [0, 2], [-2, -2], [0, 0], [-2, 0], [-3, 3], [0, 6], [0, 2], [0, 0], [0, 0], [4, 0], [5, -5], [2, -2], [0, 0], [6, -6], [0, 8], [-4, -4], [-3, 0], [0, 0], [2, -2], [2, -2], [-5, 5], [0, -8], [0, 0], [-4, -4], [-6, 0], [0, 6], [3, 3], [0, 0], [-9, 9], [-8, 8], [0, -2], [0, 8], [0, 0], [2, 2], [-5, -5], [-4, 0], [6, 6], [0, 0], [0, -10], [-2, 2], [-4, 0], [0, 6], [0, 0], [6, 6], [2, 2], [2, 2], [0, 0], [0, 0], [5, 0], [0, 0], [1, 1], [4, -4], [0, 0], [0, -10], [-6, 0], [0, -4], [0, -4], [0, 0], [2, 2], [0, -12], [-8, -8], [8, 8], [0, 0], [-8, 0], [0, -2], [-3, 3], [1, -1], [0, 0]]}