# Stored data for newform 152.1.u.a, downloaded from the LMFDB on 19 April 2024.
{"label": "152.1.u.a", "space_label": "152.1.u", "level": 152, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 1374406312088, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 373065239775203077, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-\\zeta_{18}^{5}q^{2}+(\\zeta_{18}^{6}-\\zeta_{18}^{7})q^{3}-\\zeta_{18}q^{4}+\\cdots", "char_order": 18, "char_parity": -1, "char_degree": 6, "char_conductor": 152, "char_orbit_label": "u", "char_is_real": false, "Nk2": 152, "analytic_conductor": 0.07585788192021636, "hecke_ring_index": 1, "level_radical": 38, "projective_image": "D9", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "field_poly_is_real_cyclotomic": false, "projective_field_label": "9.1.69564674215936.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.729", "prec": 17}, "analytic_rank_proved": true, "char_values": [152, 18, [39, 77, 97], [9, 9, 4]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 19], "conrey_indexes": [35, 43, 99, 123, 131, 139], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.035", "prec": 20}, {"__RealLiteral__": 0, "data": "5.936", "prec": 17}, {"__RealLiteral__": 0, "data": "17.650", "prec": 20}, {"__RealLiteral__": 0, "data": "278.457", "prec": 24}, {"__RealLiteral__": 0, "data": "1996.949", "prec": 27}, {"__RealLiteral__": 0, "data": "24903.718", "prec": 30}], "related_objects": [], "self_twist_discs": [-8], "cm_discs": [-8], "rm_discs": [], "relative_dim": 1, "trace_display": [0, -3, 0, 0], "traces": [0, 6, 0, -3, 0, 0, -3, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, -3, 0, 0, -3, 0, 0, 6, 0, 0, 0, 6, -3, -3, 3, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, -3, -3, 3, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, -3, 0, 6, 0, 0, 0, 0, 0, 3, 0, 6, -6, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, -3, 0, 6, -3, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, -3, -6, 0, 0, 0, -3, 6, 3, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, -3, -3, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, -3, -6, 0, 0, -6, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 6, 0, 0, 3, 0, 0, -3, 0, 0, 0, -3, 0, 3, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 6, 0, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 6, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 12, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, -3, -3, 0, 0, 3, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 0, -6, -3, 0, -6, 0, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, -3, 6, -3, 0, -3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 6, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, -6, 0, 6, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 6, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 3, -3, 0, 0, 0, 0, -6, -3, 0, 0, -3, 0, 0, 0, -3, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 6, -3, 0, 6, 0, 0, -3, 0, -6, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 12, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 0, -6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, -6, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -6, 6, 0, -3, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, 0, 0, 0, 12, 0, 0, -3, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, -3, 0, 0, 0, 0, -3, 6, 0, 0, 0, 6, -6, -3, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, -3, 0, -6, 0, 0, 0, 0, 6, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 0, 0, 0, 6, 3, 0, 6, 3, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, -3, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 12, 0, -3, -3, 0, 6, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 6, 3, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -9, 0, 3, 0, 0, 3, 0, -3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, -3, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, -3, 0, 3, 6, 0, -3, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 3, 6, 0, 0, 0, -3, 12, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -3, 6, 0, -3, 0, 0, 0, 0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 6, 0, -6, -3, 0, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, -6, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3, 0, -3, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, 0, 3, -3, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -6, 3, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, -3, 0, -3, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, -6, 6, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, 6, 0, 0, -3, 0, 6, 0, 0, 0, 0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, 3, 6, 0, 3, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 6, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 3, 6, -6, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 6, 0, 0, 0, 6, -3, 0, -3, -6, 0, 0, 0, 6, -9, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, -3, 6, 0, 0, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 6, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 3, 0, 6, -3, 0, 3, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, -3, 0, 3, 0, 0, 9, 0, 0, 0, 0, 0, 0, -3, 0, 12, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0], "projective_field": [-284, -84, 96, 164, -149, 67, -20, 4, -3, 1], "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, 8, 4, -1, 2, -8], [1, 1, 19, 5, 1, 9, 0], [1, 1, 152, 21, -1, 18, 0]], "char_orbit_index": 21, "prim_orbit_index": 21, "minimal_twist": "152.1.u.a", "char_is_minimal": true, "conrey_index": 35, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[-1, 5]], [[1, 6], [-1, 7]], [[-1, 1]], [], [[1, 2], [-1, 3]], [], [[1, 6]], [[-1, 3], [1, 4], [-1, 5]], [], [[1, 4], [1, 8]], [[-1, 7], [1, 8]], [], [], [], [[1, 2]], [[1, 5]], [[1, 0], [-1, 1], [1, 8]], [[-1, 1]], [], [], [[1, 0], [1, 4]], [], [[-1, 3], [1, 4]], [[-1, 7]], [], [[1, 0], [-2, 1], [1, 1], [2, 2], [-1, 2], [-1, 3]], [], [], [], [], [[-1, 7]], [[-1, 1], [1, 2], [-1, 5], [1, 6]], [[1, 1]], [], [[1, 4], [-1, 5], [1, 6]], [], [[1, 6]], [], [], [[-1, 1], [-1, 3]], [], [[-1, 8]], [[1, 0], [-1, 5]], [], [], [], [[1, 0], [1, 8]], [[1, 6]], [[-1, 3]], [[-1, 2], [1, 3]], [], [], [[-1, 5], [1, 6], [-1, 7], [1, 8]], [], [], [[-1, 7], [1, 8]], [], [[-1, 3], [-1, 7]], [], [], [], [], [[-1, 3]], [], [[-1, 1], [1, 2], [1, 6], [-1, 7]], [[-1, 3], [-1, 5]], [[-1, 6]], [], [], [], [[1, 0], [-1, 1], [1, 2]], [[1, 0], [1, 4]], [], [[1, 4], [-1, 5]], [[1, 2]], [], [], [], [], [[2, 0], [-1, 0], [-1, 1], [1, 6], [-1, 7], [1, 8]], [[1, 6], [1, 8]], [[1, 2], [1, 4]], [], [], [[-1, 4]], [], [[-1, 1], [-1, 5]], [[1, 7]], [], [], [], [], [], [], [[1, 4], [-1, 5]], [[1, 4], [1, 6]], [[1, 2]], [[1, 0], [1, 2], [-1, 3], [1, 4], [-1, 7], [1, 8]], [[1, 8]]]}