# Stored data for newform 847.4.a.k, downloaded from the LMFDB on 25 January 2026.
{"Nk2": 13552, "analytic_conductor": 49.9746177748623, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[7, -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": [847, 1, [122, 365], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 8, "field_disc": 365522533862077247196, "field_disc_factorization": [[2, 2], [3, 1], [467, 1], [65225291552833199, 1]], "field_poly": [1488, 1820, -2076, -787, 584, 73, -45, -2, 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, [1488, 1820, -2076, -787, 584, 73, -45, -2, 1]]], "hecke_orbit": 11, "hecke_orbit_code": 45035996340814671, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "847.4.a.k", "level": 847, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [7, 11], "level_radical": 77, "minimal_twist": "847.4.a.j", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+(\\beta _{1}+\\beta _{3})q^{3}+(4+\\beta _{2})q^{4}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "847.4.a", "trace_display": [2, 2, 2, 56], "trace_hash": 1067876712256183944, "trace_moments": [{"__RealLiteral__": 0, "data": "0.120", "prec": 17}, {"__RealLiteral__": 0, 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