# Stored data for newform 448.6.a.bd, downloaded from the LMFDB on 10 March 2026.
{"Nk2": 16128, "analytic_conductor": 71.85195127621532, "analytic_rank": 0, "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": 4, "field_disc": 786816828, "field_disc_factorization": [[2, 2], [3, 4], [7, 1], [19, 2], [31, 2]], "field_poly": [5999, 43, -198, -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, [82320, 6328, -672, -18, 1]], [5, [3096576, 7680, -7452, -30, 1]]], "hecke_orbit": 30, "hecke_orbit_code": 130604389294408128, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 128, "hecke_ring_index_factorization": [[2, 7]], "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": "448.6.a.bd", "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": "224.6.a.g", "prim_orbit_index": 1, "qexp_display": "q+(4+\\beta _{1})q^{3}+(7+\\beta _{1}+\\beta _{2})q^{5}-7^{2}q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "448.6.a", "trace_display": [0, 18, 30, -196], "trace_hash": 355677012629478580, "trace_moments": [{"__RealLiteral__": 0, "data": "0.071", "prec": 17}, {"__RealLiteral__": 0, "data": "3.809", "prec": 17}, {"__RealLiteral__": 0, "data": "0.919", "prec": 17}, {"__RealLiteral__": 0, "data": "39.357", "prec": 20}, {"__RealLiteral__": 0, "data": "18.638", "prec": 20}, {"__RealLiteral__": 0, "data": "592.237", "prec": 24}], "trace_zratio": 0, "traces": [0, 4, 0, 18, 0, 30, 0, -196, 0, 696, 0, 484, 0, -686, 0, 2184, 0, -1700, 0, 654, 0, -882, 0, -136, 0, 3304, 0, 14388, 0, -3812, 0, -12748, 0, -1536, 0, -1470, 0, -820, 0, -34704, 0, 22340, 0, 32924, 0, 59070, 0, 2620, 0, 9604, 0, 55788, 0, -22984, 0, -24360, 0, 15132, 0, 108158, 0, -4258, 0, -34104, 0, -95028, 0, 109496, 0, 82392, 0, -54600, 0, -12384, 0, 315198, 0, -23716, 0, -78184, 0, 114384, 0, 115582, 0, -101652, 0, 17772, 0, -31560, 0, 33614, 0, -218040, 0, 67032, 0, 41068, 0, 301284, 0, -68826, 0, 122540, 0, -107016, 0, 65248, 0, 212900, 0, 233388, 0, -169044, 0, 434616, 0, -244446, 0, 83300, 0, 92708, 0, 341868, 0, 487140, 0, 522800, 0, 251424, 0, 60966, 0, -32046, 0, 1611456, 0, -245456, 0, 214546, 0, 111336, 0, 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