# Stored data for newform 1089.4.a.bk, downloaded from the LMFDB on 24 June 2026.
{"Nk2": 17424, "analytic_conductor": 64.25307999625153, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [11, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [1089, 1, [848, 244], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 6, "field_disc": 7765781125, "field_disc_factorization": [[5, 3], [62126249, 1]], "field_poly": [44, 208, 211, 3, -30, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [436, -520, 45, 107, -20, -5, 1]], [5, [-1144711, 386217, 40162, -5679, -510, 9, 1]], [7, [28881, 74451, 39913, 980, -547, 1, 1]]], "hecke_orbit": 37, "hecke_orbit_code": 162129586652447809, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 11, "hecke_ring_index_factorization": [[11, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "1089.4.a.bk", "level": 1089, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [3, 11], "level_radical": 33, "minimal_twist": "33.4.e.c", "prim_orbit_index": 1, "qexp_display": "q+(1-\\beta _{1})q^{2}+(3-\\beta _{1}+\\beta _{2}-\\beta _{3})q^{4}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1089.4.a", "trace_display": [5, 0, -9, -1], "trace_hash": 1025165047746549787, "trace_moments": [{"__RealLiteral__": 0, "data": "0.028", 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