# Stored data for newform 128.4.b.c, downloaded from the LMFDB on 24 April 2024. {"label": "128.4.b.c", "space_label": "128.4.b", "level": 128, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007268041326720, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 640432071701762628, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [0, 1]], [7, [0, 1]]], "qexp_display": "q+iq^{5}+3^{3}q^{9}+23iq^{13}+94q^{17}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 2048, "analytic_conductor": 7.552244480734799, "hecke_ring_index": 4, "level_radical": 2, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [128, 2, [127, 5], [2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2], "conrey_indexes": [65], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.852", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.968", "prec": 20}, {"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "290.888", "prec": 24}], "related_objects": [], "self_twist_discs": [-4], "cm_discs": [-4], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.1.d2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 188, 0, 0, 0, 0, 0, 0, 0, 218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -460, 0, 0, 0, 0, 0, 0, 0, -686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -736, 0, 0, 0, 0, 0, 0, 0, -2196, 0, 0, 0, 0, 0, 0, 0, 1458, 0, 0, 0, 0, 0, 0, 0, 3340, 0, 0, 0, 0, 0, 0, 0, -1188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4004, 0, 0, 0, 0, 0, 0, 0, 2662, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3212, 0, 0, 0, 0, 0, 0, 0, -2272, 0, 0, 0, 0, 0, 0, 0, 5076, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12534, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3168, 0, 0, 0, 0, 0, 0, 0, -10724, 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, 5886, 0, 0, 0, 0, 0, 0, 0, 1196, 0, 0, 0, 0, 0, 0, 0, 10620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3068, 0, 0, 0, 0, 0, 0, 0, 4576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14860, 0, 0, 0, 0, 0, 0, 0, 7846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, -13676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24732, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6596, 0, 0, 0, 0, 0, 0, 0, 13718, 0, 0, 0, 0, 0, 0, 0, -12420, 0, 0, 0, 0, 0, 0, 0, -52256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4796, 0, 0, 0, 0, 0, 0, 0, 14292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20492, 0, 0, 0, 0, 0, 0, 0, 9724, 0, 0, 0, 0, 0, 0, 0, -18522, 0, 0, 0, 0, 0, 0, 0, -32228, 0, 0, 0, 0, 0, 0, 0, 33012, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47476, 0, 0, 0, 0, 0, 0, 0, -24334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -53612, 0, 0, 0, 0, 0, 0, 0, -6908, 0, 0, 0, 0, 0, 0, 0, -19872, 0, 0, 0, 0, 0, 0, 0, -31004, 0, 0, 0, 0, 0, 0, 0, 34060, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30932, 0, 0, 0, 0, 0, 0, 0, 19762, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -57700, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -59292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105248, 0, 0, 0, 0, 0, 0, 0, -43240, 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, 39366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63764, 0, 0, 0, 0, 0, 0, 0, -19300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31392, 0, 0, 0, 0, 0, 0, 0, 86112, 0, 0, 0, 0, 0, 0, 0, 90180, 0, 0, 0, 0, 0, 0, 0, -46540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64484, 0, 0, 0, 0, 0, 0, 0, -112534, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 91988, 0, 0, 0, 0, 0, 0, 0, -16096, 0, 0, 0, 0, 0, 0, 0, -32076, 0, 0, 0, 0, 0, 0, 0, -14300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -61732, 0, 0, 0, 0, 0, 0, 0, -103892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -113516, 0, 0, 0, 0, 0, 0, 0, -59582, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113212, 0, 0, 0, 0, 0, 0, 0, 43232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 8, 2, 1, 2, 0], [1, 1, 8, 4, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "128.4.b.c", "char_is_minimal": true, "conrey_index": 65, "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], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [27, 0], [0, 0], [0, 0], [0, 0], [0, 23], [0, 0], [0, 0], [0, 0], [94, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [109, 0], [0, 0], [0, 0], [0, 0], [0, 71], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -99], [0, 0], [0, 0], [0, 0], [-230, 0], [0, 0], [0, 0], [0, 0], [0, 27], [0, 0], [0, 0], [0, 0], [-343, 0], [0, 0], [0, 0], [0, 0], [0, -143], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -117], [0, 0], [0, 0], [0, 0], [-368, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-1098, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [729, 0], [0, 0], [0, 0], [0, 0], [0, 94], [0, 0], [0, 0], [0, 0], [1670, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-594, 0], [0, 0], [0, 0], [0, 0]]}