# Stored data for newform 448.8.a.r, downloaded from the LMFDB on 27 November 2025.
{"Nk2": 28672, "analytic_conductor": 139.94849141688655, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [7, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [448, 1, [127, 197, 129], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 249, "field_disc_factorization": [[3, 1], [83, 1]], "field_poly": [-62, -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": [[3, [-1800, -42, 1]]], "hecke_orbit": 18, "hecke_orbit_code": 76561193799516608, "hecke_ring_generator_nbound": 5, "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": false, "label": "448.8.a.r", "level": 448, "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": [2, 7], "level_radical": 14, "minimal_twist": "56.8.a.c", "nf_label": "2.2.249.1", "prim_orbit_index": 1, "qexp_display": "q+(21-3\\beta )q^{3}+(-7+11\\beta )q^{5}+7^{3}q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "448.8.a", "trace_display": [0, 42, -14, 686], "trace_hash": 1954262063670581031, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.920", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, 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