# Stored data for newform 400.2.u.a, downloaded from the LMFDB on 23 April 2024. {"label": "400.2.u.a", "space_label": "400.2.u", "level": 400, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1374423089552, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 349957983844750366, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [25, 25, 15, 5, 1]]], "qexp_display": "q+(-2+2\\zeta_{10}+\\zeta_{10}^{3})q^{3}+(-2+\\zeta_{10}+\\cdots)q^{5}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 25, "char_orbit_label": "u", "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": 10, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [400, 5, [351, 101, 177], [5, 5, 2]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [81, 161, 241, 321], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.952", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "53.043", "prec": 20}, {"__RealLiteral__": 0, "data": "23.456", "prec": 20}, {"__RealLiteral__": 0, "data": "1340.979", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [0, -5, -5, -6], "traces": [0, 4, 0, -5, 0, -5, 0, -6, 0, -2, 0, -6, 0, -7, 0, 5, 0, -8, 0, 9, 0, 10, 0, -9, 0, -5, 0, -5, 0, -3, 0, -13, 0, 0, 0, 5, 0, 1, 0, 25, 0, 16, 0, -22, 0, 10, 0, -4, 0, -14, 0, 20, 0, -19, 0, 20, 0, -10, 0, 6, 0, -23, 0, -2, 0, 20, 0, 22, 0, 15, 0, -10, 0, -11, 0, 0, 0, 4, 0, -15, 0, 11, 0, 1, 0, 20, 0, 30, 0, -4, 0, -2, 0, 60, 0, -35, 0, 36, 0, 8, 0, -36, 0, 1, 0, 5, 0, -40, 0, 26, 0, -25, 0, -22, 0, 40, 0, -4, 0, 22, 0, 15, 0, -20, 0, 25, 0, 22, 0, 25, 0, -8, 0, -31, 0, 20, 0, -5, 0, 17, 0, -25, 0, 28, 0, -30, 0, 10, 0, -20, 0, -6, 0, -16, 0, 5, 0, 8, 0, -25, 0, 11, 0, -21, 0, -20, 0, -37, 0, 14, 0, 18, 0, -21, 0, 20, 0, -20, 0, -5, 0, 0, 0, 35, 0, -35, 0, -8, 0, 5, 0, -22, 0, -4, 0, -90, 0, 12, 0, -42, 0, -60, 0, 17, 0, 10, 0, -8, 0, 34, 0, -9, 0, 35, 0, 30, 0, 22, 0, -55, 0, -26, 0, -16, 0, -10, 0, 54, 0, -34, 0, -10, 0, -6, 0, 25, 0, -30, 0, -15, 0, 3, 0, 0, 0, 25, 0, 23, 0, -40, 0, 68, 0, -4, 0, -10, 0, -10, 0, 11, 0, -16, 0, -3, 0, 25, 0, -20, 0, 6, 0, 24, 0, -20, 0, -30, 0, 15, 0, -26, 0, -5, 0, -28, 0, -20, 0, -14, 0, 33, 0, 45, 0, -16, 0, -15, 0, 0, 0, 2, 0, 28, 0, 65, 0, 100, 0, -52, 0, 40, 0, -23, 0, 16, 0, -20, 0, 17, 0, 22, 0, 65, 0, -18, 0, -10, 0, -50, 0, 1, 0, 68, 0, 22, 0, -50, 0, -9, 0, 20, 0, 42, 0, 48, 0, -55, 0, 11, 0, 20, 0, 10, 0, 42, 0, -35, 0, -60, 0, -29, 0, 8, 0, -15, 0, 0, 0, 40, 0, -28, 0, 36, 0, 2, 0, 25, 0, -51, 0, -5, 0, 50, 0, 11, 0, -20, 0, 16, 0, -31, 0, -22, 0, 50, 0, 30, 0, -27, 0, 80, 0, -48, 0, -56, 0, -55, 0, -4, 0, 35, 0, 25, 0, 1, 0, 35, 0, 55, 0, 51, 0, -16, 0, 22, 0, 10, 0, 27, 0, -10, 0, -5, 0, -23, 0, 15, 0, 56, 0, -23, 0, 22, 0, 96, 0, 0, 0, 55, 0, -118, 0, -64, 0, 5, 0, -35, 0, 0, 0, -10, 0, 43, 0, 13, 0, -85, 0, -28, 0, -58, 0, -15, 0, 38, 0, 20, 0, 42, 0, 21, 0, 32, 0, -50, 0, -45, 0, -5, 0, 5, 0, 11, 0, 56, 0, -20, 0, 35, 0, -78, 0, 130, 0, -38, 0, 25, 0, -90, 0, -13, 0, -11, 0, 30, 0, -40, 0, -14, 0, -45, 0, -25, 0, -22, 0, -50, 0, 26, 0, -18, 0, 2, 0, -58, 0, 35, 0, -65, 0, 36, 0, 42, 0, 60, 0, -10, 0, 37, 0, -16, 0, -138, 0, 25, 0, 120, 0, -76, 0, 51, 0, 0, 0, 49, 0, -25, 0, -44, 0, -23, 0, -71, 0, 50, 0, -45, 0, 42, 0, 20, 0, 16, 0, -4, 0, 40, 0, -17, 0, -98, 0, -90, 0, 38, 0, -50, 0, 50, 0, 16, 0, -130, 0, 44, 0, 15, 0, 62, 0, -25, 0, 62, 0, -37, 0, 20, 0, -61, 0, -49, 0, -15, 0, -4, 0, -25, 0, -50, 0, 68, 0, 41, 0, 75, 0, -40, 0, 62, 0, -10, 0, -73, 0, -112, 0, -40, 0, -42, 0, -24, 0, -70, 0, -54, 0, -10, 0, 88, 0, 58, 0, 2, 0, 40, 0, 75, 0, 53, 0, 10, 0, -8, 0, -32, 0, -25, 0, -3, 0, -69, 0, -60, 0, -29, 0, 25, 0, 20, 0, 107, 0, -36, 0, 8, 0, -20, 0, -52, 0, 0, 0, -36, 0, -89, 0, 20, 0, 94, 0, -43, 0, 40, 0, 33, 0, -60, 0, -105, 0, -77, 0, 11, 0, 25, 0, 110, 0, -14, 0, 7, 0, 34, 0, -15, 0, -55, 0, 12, 0, -14, 0, -145, 0, 24, 0, -5, 0, 2, 0, 90, 0, 136, 0, -65, 0, 10, 0, 60, 0, 50, 0, 36, 0, -14, 0, -20, 0, -3, 0, -34, 0, 15, 0, -52, 0, 85, 0, 35, 0, 96, 0, 30, 0, 25, 0, -5, 0, 52, 0, 45, 0, 23, 0, 14, 0, 95, 0, -3, 0, -12, 0, 32, 0, 44, 0, -70, 0, 60, 0, -47, 0, 27, 0, 0, 0, -45, 0, -32, 0, 26, 0, 18, 0, 66, 0, 50, 0, 22, 0, -8, 0, -75, 0, -2, 0, 55, 0, 25, 0, 30, 0, -30, 0, -30, 0, 20, 0, -40, 0, 150, 0, 64, 0, -22, 0, 60, 0, -26, 0, -49, 0, -10, 0, 48, 0, 40, 0, -15, 0, -10, 0, 74, 0, -78, 0, -50, 0, 16, 0, 10, 0, 60, 0, 36, 0, 70, 0, -60, 0, 2, 0, 66, 0, 76, 0, 65, 0, 40, 0, -74, 0, 68, 0, -45, 0, -60, 0, -88, 0, -22, 0, -45, 0, -74, 0, -135, 0, 7, 0, -17, 0, 60, 0, -40, 0, 55, 0, -28, 0, -26, 0, 21, 0, -40, 0, -20, 0, 12, 0, -20, 0, 19, 0, -116, 0, -30, 0, -102, 0, 198, 0, -20, 0, 74, 0, 20, 0, -120, 0, -5, 0, -78, 0, -10, 0, -10, 0, 6, 0, 150, 0, 15, 0, 7, 0, 125, 0, -3, 0, 16, 0, -28, 0, 19, 0, 90, 0, 10, 0, 52, 0, -15, 0, -260, 0, 55, 0, 33, 0, 20, 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, 25, 4, 1, 5, 0]], "char_orbit_index": 21, "prim_orbit_index": 4, "minimal_twist": "200.2.m.a", "char_is_minimal": false, "conrey_index": 81, "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, 0, 0, 0], [-2, 2, 0, 1], [0, 0, 0, 0], [-2, 1, -2, 0], [0, 0, 0, 0], [-1, 0, 1, -1], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 2], [0, 0, 0, 0], [-1, -4, -1, 0], [0, 0, 0, 0], [5, -5, 5, -5], [0, 0, 0, 0], [0, -2, 4, -2], [0, 0, 0, 0], [0, 1, -7, 1], [0, 0, 0, 0], [3, -3, 0, 1], [0, 0, 0, 0], [-1, -3, 3, 1], [0, 0, 0, 0], [0, 0, 5, 0], [0, 0, 0, 0], [-1, -1, 1, 1], [0, 0, 0, 0], [1, -1, 0, -6], [0, 0, 0, 0], [0, -6, 1, -6], [0, 0, 0, 0], [0, -2, -4, -2], [0, 0, 0, 0], [3, -4, 3, 0], [0, 0, 0, 0], [-2, 7, -2, 0], [0, 0, 0, 0], [7, 2, -2, -7], [0, 0, 0, 0], [6, -2, 6, 0], [0, 0, 0, 0], [-6, 0, -1, 1], [0, 0, 0, 0], [0, 4, -2, 4], [0, 0, 0, 0], [-3, 3, 0, 5], [0, 0, 0, 0], [-5, 0, -3, 3], [0, 0, 0, 0], [2, 0, -6, 6], [0, 0, 0, 0], [-8, 8, 0, 5], [0, 0, 0, 0], [6, 0, 2, -2], [0, 0, 0, 0], [4, 0, 13, -13], [0, 0, 0, 0], [1, 3, 1, 0], [0, 0, 0, 0], [-3, -7, 7, 3], [0, 0, 0, 0], [-2, 4, -2, 0], [0, 0, 0, 0], [0, 9, -2, 9], [0, 0, 0, 0], [0, 6, -10, 6], [0, 0, 0, 0], [0, 2, -11, 2], [0, 0, 0, 0], [-1, 1, 0, -7], [0, 0, 0, 0], [-11, 11, -11, 11], [0, 0, 0, 0], [-5, 0, -10, 10], [0, 0, 0, 0], [0, 2, -2, 0], [0, 0, 0, 0], [-7, 7, 0, 6], [0, 0, 0, 0], [0, 0, -11, 0], [0, 0, 0, 0], [0, 4, 7, 4], [0, 0, 0, 0], [6, -6, 0, 2], [0, 0, 0, 0], [11, -3, 11, 0], [0, 0, 0, 0], [-4, 4, -4, 4], [0, 0, 0, 0], [-3, 7, -3, 0], [0, 0, 0, 0], [17, 0, 4, -4], [0, 0, 0, 0], [-13, 13, 0, 4], [0, 0, 0, 0], [15, -15, 0, -9], [0, 0, 0, 0], [4, 0, 4, -4], [0, 0, 0, 0]]}