# Stored data for newform 900.2.k.n, downloaded from the LMFDB on 18 April 2024. {"label": "900.2.k.n", "space_label": "900.2.k", "level": 900, "weight": 2, "hecke_orbit": 14, "hecke_orbit_code": 58547482384139140, "dim": 12, "is_polredabs": true, "nf_label": "12.0.426337261060096.1", "trace_hash": 1939497762989923848, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [4096, 0, 0, 0, 7440, 0, 0, 0, 200, 0, 0, 0, 1]], [11, [128, 0, 260, 0, 36, 0, 1]], [13, [32, 96, 144, 32, 2, -2, 1]], [17, [800, -160, 16, 80, 50, 10, 1]], [19, [-512, 0, 400, 0, -40, 0, 1]], [23, [65536, 0, 0, 0, 37120, 0, 0, 0, 4640, 0, 0, 0, 1]]], "qexp_display": "q+\\beta _{4}q^{2}-\\beta _{2}q^{4}+(\\beta _{4}+\\beta _{7})q^{7}+(-1+\\cdots)q^{8}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 20, "char_orbit_label": "k", "char_is_real": false, "Nk2": 3600, "analytic_conductor": 7.186536181915234, "hecke_ring_index": 64, "level_radical": 30, "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": "0.627", "prec": 17}, "analytic_rank_proved": true, "char_values": [900, 4, [451, 101, 577], [2, 4, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [307, 343], "field_disc": 426337261060096, "field_disc_factorization": [[2, 24], [71, 4]], "field_poly": [64, 0, 0, -32, -12, 8, 8, 4, -3, -4, 0, 0, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "10.615", "prec": 20}, {"__RealLiteral__": 0, "data": "3.636", "prec": 17}, {"__RealLiteral__": 0, "data": "960.416", "prec": 24}, {"__RealLiteral__": 0, "data": "1428.481", "prec": 27}, {"__RealLiteral__": 0, "data": "149661.578", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 0], "traces": [0, 12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 4, 0, 0, 12, -20, 0, 0, 0, 0, -12, 0, 0, 0, -16, 0, 4, 0, 0, 0, 20, 0, 0, 0, 0, -4, 16, 0, 0, -16, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 8, 4, 0, 0, 64, 0, 20, 0, 0, -32, -56, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, -44, 0, 0, 8, 48, 0, 0, 0, 0, -16, 0, 0, 0, -64, 0, -60, 0, 0, 0, 56, 0, 0, 0, 0, 20, 24, 0, 0, 40, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 36, -52, 0, 0, 24, 0, 4, 0, 0, -12, -64, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 80, 0, 0, 24, -12, 0, 0, 0, 0, -16, 0, 0, 0, -48, 0, 8, 0, 0, 0, 64, 0, 0, 0, 0, -12, 40, 0, 0, -64, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 88, 100, 0, 0, 16, 0, 24, 0, 0, 72, -40, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, -4, 0, 0, 68, -12, 0, 0, 0, 0, -44, 0, 0, 0, -80, 0, 64, 0, 0, 0, 32, 0, 0, 0, 0, -64, 72, 0, 0, 88, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -20, -84, 0, 0, 96, 0, 8, 0, 0, -32, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 4, -84, 0, 0, 0, 0, -76, 0, 0, 0, 48, 0, -88, 0, 0, 0, 40, 0, 0, 0, 0, 68, 8, 0, 0, 48, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -52, 140, 0, 0, 24, 0, -44, 0, 0, 32, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -100, 0, 0, 0, 124, 0, 0, 0, 0, 72, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, -56, 0, 0, -96, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 20, -124, 0, 0, 72, 0, 140, 0, 0, -68, -40, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 60, 0, 0, -104, 32, 0, 0, 0, 0, 24, 0, 0, 0, -96, 0, 36, 0, 0, 0, -28, 0, 0, 0, 0, 188, -8, 0, 0, -184, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -76, 48, 0, 0, -104, 0, -40, 0, 0, 64, 40, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 68, 0, 0, 8, -64, 0, 0, 0, 0, -24, 0, 0, 0, -32, 0, -84, 0, 0, 0, -40, 0, 0, 0, 0, -52, -72, 0, 0, 104, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 44, -160, 0, 0, -128, 0, -144, 0, 0, -104, 64, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, -32, 0, 0, 176, -160, 0, 0, 0, 0, 148, 0, 0, 0, -32, 0, 52, 0, 0, 0, -84, 0, 0, 0, 0, -112, -40, 0, 0, 88, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 40, 96, 0, 0, -96, 0, 68, 0, 0, 56, 56, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, -96, 0, 0, -184, 132, 0, 0, 0, 0, -48, 0, 0, 0, 240, 0, 144, 0, 0, 0, -56, 0, 0, 0, 0, -132, -8, 0, 0, 96, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -64, -12, 0, 0, -104, 0, -96, 0, 0, 112, 112, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 84, 0, 0, -56, 12, 0, 0, 0, 0, 16, 0, 0, 0, 208, 0, -80, 0, 0, 0, -136, 0, 0, 0, 0, -36, 32, 0, 0, -208, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -32, 84, 0, 0, 104, 0, -120, 0, 0, -160, 128, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, -76, 0, 0, -12, 68, 0, 0, 0, 0, 64, 0, 0, 0, 32, 0, 40, 0, 0, 0, -72, 0, 0, 0, 0, 128, 0, 0, 0, 352, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, -40, -160, 0, 0, -176, 0, 152, 0, 0, -240, 48, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 172, 0, 0, -168, -160, 0, 0, 0, 0, -48, 0, 0, 0, 48, 0, 120, 0, 0, 0, -48, 0, 0, 0, 0, 36, -136, 0, 0, -24, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -132, 204, 0, 0, -152, 0, 12, 0, 0, 256, -16, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 16, 0, 0, 72, 284, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -84, 0, 0, 0, -96, 0, 0, 0, 0, 32, -40, 0, 0, -224, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, -64, 44, 0, 0, -16, 0, -236, 0, 0, 268, 40, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, -12, 0, 0, 120, -60, 0, 0, 0, 0, 184, 0, 0, 0, 112, 0, 64, 0, 0, 0, -64, 0, 0, 0, 0, 116, -152, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, -96, 0, 0, 96, 0, 248, 0, 0, 24, 104, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, -176, 0, 0, -232, -112, 0, 0, 0, 0, 140, 0, 0, 0, 224, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 12, -112, 0, 0, 56, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -104, -116, 0, 0, -32, 0, 0, 0, 0, -76, 56, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -16, 0, 0, -120, -204, 0, 0, 0, 0, -132, 0, 0, 0, -48, 0, -112, 0, 0, 0, 8, 0, 0, 0, 0, -108, 16, 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, 4, 2, -1, 2, 0], [1, 1, 5, 3, -1, 4, 0], [1, 1, 20, 5, 1, 4, 0]], "char_orbit_index": 11, "prim_orbit_index": 5, "minimal_twist": "60.2.j.a", "char_is_minimal": true, "conrey_index": 307, "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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 1, 0, -1, -1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, -2, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 0, 1, -1, 0, 0, 0, 1, 1, 1, 0], [-1, 0, 0, 0, -1, 1, -1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 1, 2, 1, 0], [0, -2, -1, 1, 0, 0, 0, 0, -1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 0, 0, 1, 0, 0, 1, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 1, 0, 0, 2, 0, 0, -1, 0, 1, 0], [0, -1, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0], [1, 0, 0, 0, 2, -2, 1, 1, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -1, -2, -2, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, -1, -1, 0, -1, -1, 0, 0], [2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, -1, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, 1, 0, -1, 0, 0, -1, 0, -2, -1], [0, 0, -2, 0, 0, -4, 2, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, -1, 0, 0, 0, -1, 0, -1, 2, -1], [0, 0, 1, 0, 0, 0, 0, -1, -1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 2, 1, -1, 0, -1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0], [1, -1, 1, 1, 0, 0, -1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, -1, 2, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, 0, -2, 0, 1, 0, 1, 0], [0, 0, -1, 1, 0, 1, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 3, 0, -1, -3, 0, 0, 0, -2, -1, -4, 0], [-4, 0, -2, 0, 0, 0, -4, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 1, 1, 0, 2, -2, 0, -1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 2, 1, 0, -1, -1, 1, -2, 0], [0, -2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 1, 2, 0, 0, 3, -2, 1, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 2, -2, -2, 0, 0, 5, 0, -2, 0, -2, 0], [0, -1, 0, 0, -1, 2, 2, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 2, 0], [4, 0, -1, 0, 2, -1, 4, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 1, 0, 4, 0, -3, 0, -1, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, -2, -2, 2, -2, 0, 0, 0], [0, 0, -1, -1, 0, -2, 0, 0, 1, 0, -1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 1, 0, 0, 0, -1, 2, 1, 4, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 1, 2, 0, 0, 4, 0, 1, 0, 1, 2], [0, -1, 2, 1, -1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 1, 2, 0, 0, 1, -2, 1, -2, 1], [6, 0, 0, 0, -4, 2, 6, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, -1, 0, -2, 0, -1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 2, 0, -6, 4, 3, 0, 2, 2, -2, 0], [2, -1, 2, 0, 0, 2, -2, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}