# Stored data for newform 92.2.b.b, downloaded from the LMFDB on 19 April 2024. {"label": "92.2.b.b", "space_label": "92.2.b", "level": 92, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503668380401756, "dim": 6, "is_polredabs": true, "nf_label": "6.0.8869743.1", "trace_hash": 654170474770386342, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [92, 0, 81, 0, 18, 0, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(-\\beta _{2}-\\beta _{4})q^{3}+\\beta _{2}q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 92, "char_orbit_label": "b", "char_is_real": true, "Nk2": 368, "analytic_conductor": 0.7346236985957796, "hecke_ring_index": 2, "level_radical": 46, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.925", "prec": 17}, "analytic_rank_proved": true, "char_values": [92, 2, [47, 5], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 23], "conrey_indexes": [91], "field_disc": -8869743, "field_disc_factorization": [[-1, 1], [3, 6], [23, 3]], "field_poly": [8, 0, 0, -3, 0, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "4.705", "prec": 17}, {"__RealLiteral__": 0, "data": "2.876", "prec": 17}, {"__RealLiteral__": 0, "data": "473.455", "prec": 24}, {"__RealLiteral__": 0, "data": "367.510", "prec": 24}, {"__RealLiteral__": 0, "data": "53355.741", "prec": 30}], "related_objects": [], "self_twist_discs": [-23], "cm_discs": [-23], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.1.d2", "trace_display": [0, 0, 0, 0], "traces": [0, 6, 0, 0, 0, 0, -3, 0, -9, -18, 0, 0, 15, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 30, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, -42, 0, 0, 3, 0, 9, 0, 0, 0, -15, 0, 0, 0, 45, 0, -21, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, -51, 0, 0, 54, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -39, 0, -57, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, -45, 0, 0, 0, 0, 0, 0, 0, 63, -60, 0, 0, 0, -66, 0, 0, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 69, 0, 0, 84, 57, 0, 3, 0, 9, 0, 0, 0, -15, 0, 0, 0, 0, 0, -21, 0, 0, 0, 0, 0, -138, 0, 27, 0, 0, 0, 0, 78, 0, 0, 0, -108, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, -69, 0, -39, 0, -81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -45, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0, 0, 132, 0, 0, 138, 0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 0, 138, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 93, 0, 0, 0, 0, 0, 0, 0, -63, 0, 0, 0, 0, 0, 0, -156, -87, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -69, 0, -99, 0, 0, 0, -3, 0, -9, 0, 0, 0, 15, 102, 0, 0, -93, 0, 21, 0, 0, 0, 0, 0, 75, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 138, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 111, 0, 0, 0, 0, 0, -138, 0, 0, 0, 105, 0, 0, -114, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -57, 0, 0, 0, 0, -36, 0, 0, 0, -204, 0, 0, -93, 0, 117, 0, 0, 0, 0, 0, 63, 60, -111, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 69, 0, 99, -84, 0, 0, 0, 0, 0, 0, 0, 0, -123, 0, 0, 0, 0, 0, -117, 0, 0, 0, 0, 0, -75, 0, 0, 126, 0, 0, 0, 0, 0, 0, 0, 108, 105, 0, 0, 228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -81, 0, -3, 0, -138, 0, 0, 0, 138, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, -138, 0, 0, -132, 0, 0, 87, 0, 0, 0, -33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 135, 0, 129, 0, 0, 0, 0, 0, 0, 0, 138, 0, -117, 0, 0, 0, 0, -138, 0, 0, 0, -252, 0, 0, 0, 156, -51, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -99, 0, -57, 0, 6, 0, 0, 0, 0, 0, 123, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -105, 0, 0, 0, 0, -180, 0, 0, 0, 0, 69, 0, 0, 0, 0, 0, -141, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 276, -75, 0, 111, 150, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -81, 0, -135, 0, 147, 0, 0, 0, -153, 204, 0, 0, 0, 0, 117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 87, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -138, 0, 9, 0, 0, 0, 15, 0, 0, 0, 93, 0, 138, 0, 0, 0, 0, 0, 0, 0, 27, -300, 0, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, -390, 0, 0, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, -45, 0, -159, 0, 0, 0, 0, 0, 0, 0, 165, 0, 0, 0, 0, 0, 51, 0, 0, 0, -105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 57, 0, 135, 0, 0, 0, 0, 0, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -63, 0, -54, 252, 0, 0, 0, 0, 0, 0, 0, 0, -171, 0, 0, 324, 0, 0, 0, 0, 0, 0, -69, -12, 0, 0, 0, 0, 141, 0, 0, 36, 0, 0, 0, 174, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 75, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 171, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -177, 84, 81, 0, 0, 0, -147, 0, 0, 0, -123, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276, 0, 0, -165, 0, 0, 0, 0, 0, -87, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 177, 0, 0, 0, 0, 0, -129, 0, 0, 0, -153, -348, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 171, 0, 0, 0, 0, -186, 0, 0, 0, 0, 0, 0, 99, 0, 0, 0, 138, 0, 9, 0, 0, 0, -15, 0, 0, 0, -183, 0, 138, 0, 0, 0, 0, 0, 0, 0, 27, 300, 0, 0, 0, -156, 189, 0, 0], "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, 23, 2, -1, 2, -23], [1, 1, 4, 2, -1, 2, 0], [1, 1, 92, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "92.2.b.b", "char_is_minimal": true, "conrey_index": 91, "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], [1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, -1, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [-3, -2, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [3, 1, 0, -1, -1, -1], [0, 2, -1, 0, -1, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0], [3, 3, 1, 1, -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], [1, 0, 0, -2, 0, 0], [0, -3, 1, 0, 3, -1], [5, 0, 0, 0, 0, 0], [-5, 0, -3, 1, -1, 1], [-2, 0, 3, 4, 3, 0], [0, 0, 0, 0, 0, 0], [0, 2, 3, 0, -1, -2], [0, 0, 0, 0, 0, 0], [0, 4, -1, 0, 1, -2], [0, 0, -3, 0, -2, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-5, -3, -3, -1, -1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, -4, -1, -4, -3, 2], [0, 0, 0, 0, 0, 0], [0, -2, 3, 0, 1, -4], [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, 2, 2], [0, -4, 3, 0, 1, 2], [7, 0, 1, -1, -2, 2], [-7, 0, 0, 0, 0, 0], [0, -5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 5, 0, 3, -1, -1], [0, 0, 0, 0, 0, 0], [3, 2, -3, -3, -7, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 1, -3, 3, -3], [-2, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [7, 0, -3, 1, 1, -1], [0, 0, 0, 0, 0, 0], [-5, 0, 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, 0, 0], [0, -6, -1, 0, 3, -2], [0, 0, 0, 0, 0, 0], [0, 4, 3, 0, 5, -2], [3, 5, 5, 3, 3, -1], [0, -2, -5, 0, 1, 4], [0, 0, 0, 0, 0, 0], [0, 0, -5, 0, -5, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-9, -2, 5, 1, 5, 3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [9, 12, 2, 0, -6, 4], [7, 0, 5, -3, 3, -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, 4, -5, -4, -3, -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, -3, 0, -4, 4], [-2, 2, -5, 0, -1, 6], [-5, 0, 1, -3, -3, 3], [0, 0, 0, 0, 0, 0], [-9, -7, 0, -1, 1, 1], [0, 0, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0]]}