# Stored data for newform 57.1.h.a, downloaded from the LMFDB on 19 April 2024.
{"label": "57.1.h.a", "space_label": "57.1.h", "level": 57, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 481053114425, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1728791927144614380, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\zeta_{6}^{2}q^{3}-\\zeta_{6}q^{4}-q^{7}-\\zeta_{6}q^{9}+q^{12}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 57, "char_orbit_label": "h", "char_is_real": false, "Nk2": 57, "analytic_conductor": 0.028446705720081136, "hecke_ring_index": 1, "level_radical": 57, "projective_image": "D3", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "artin_degree": 18, "artin_image": "18.3", "field_poly_is_real_cyclotomic": false, "artin_field_label": "6.0.9747.1", "projective_field_label": "3.1.1083.1", "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [57, 6, [20, 40], [3, 4]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [3, 19], "conrey_indexes": [11, 26], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "1.975", "prec": 17}, {"__RealLiteral__": 0, "data": "2.047", "prec": 17}, {"__RealLiteral__": 0, "data": "17.885", "prec": 20}, {"__RealLiteral__": 0, "data": "50.117", "prec": 20}, {"__RealLiteral__": 0, "data": "241.216", "prec": 24}], "related_objects": ["ArtinRepresentation/2.3_19.6t5.1"], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "trace_display": [0, -1, 0, -2], "traces": [0, 2, 0, -1, -1, 0, 0, -2, 0, -1, 0, 0, 2, 1, 0, 0, -1, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 2, 1, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, 1, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 2, 0, 0, 0, 4, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -1, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 1, 0, 2, 0, 0, 1, 4, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, 4, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 1, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, -2, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 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, 0, 0, -1, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, -2, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -2, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, 0, -2, -2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 4, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -1, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 2, 0, -2, -1, 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, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 4, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0], "projective_field": [-12, -6, -1, 1], "artin_field": [1, -3, 4, -2, 1, -1, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 19, 3, 1, 3, 0], [1, 1, 57, 8, -1, 6, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "embedded_related_objects": [["ArtinRepresentation/2.3_19.6t5.1c2"], ["ArtinRepresentation/2.3_19.6t5.1c1"]], "minimal_twist": "57.1.h.a", "char_is_minimal": true, "conrey_index": 11, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "qexp": [[], [[1, 0]], [], [[1, 2]], [[-1, 1]], [], [], [[-1, 0]], [], [[-1, 1]], [], [], [[1, 0]], [[1, 1]], [], [], [[1, 2]], [], [], [[1, 0]], [], [[-1, 2]], [], [], [], [[-1, 1]], [], [[1, 0]], [[1, 1]], [], [], [[-1, 0]], [], [], [], [], [[1, 2]], [[-1, 0]], [], [[-1, 0]], [], [], [], [[-1, 2]], [], [], [], [], [[-1, 1]], [], [], [], [[-1, 2]], [], [], [], [], [[1, 2]], [], [], [], [[1, 1]], [], [[1, 1]], [[1, 0]], [], [], [[1, 1]], [], [], [], [], [], [[-1, 2]], [], [[1, 0]], [[-1, 1]], [], [], [[-1, 2]], [], [[1, 2]], [], [], [[-1, 0]], [], [], [], [], [], [], [[-1, 1]], [], [[-1, 2]], [], [], [], [[1, 2], [1, 2]], [], [], [[1, 2]]]}