# Stored data for newform 616.4.a.k, downloaded from the LMFDB on 26 December 2024.
{"Nk2": 9856, "analytic_conductor": 36.34517656353622, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [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": [616, 1, [463, 309, 353, 57], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 7, "field_disc": 25391987029624199256, "field_disc_factorization": [[2, 3], [3, 4], [499253, 1], [78487590799, 1]], "field_poly": [18816, -34432, -6504, 5172, 354, -144, -3, 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, [18816, -34432, -6504, 5172, 354, -144, -3, 1]], [5, [-7697280, -3193632, -41856, 72712, 2820, -468, -11, 1]]], "hecke_orbit": 11, "hecke_orbit_code": 45035996340814440, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 64, "hecke_ring_index_factorization": [[2, 6]], "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": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "616.4.a.k", "level": 616, "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, 11], "level_radical": 154, "minimal_twist": "616.4.a.k", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{3}+(2-\\beta _{2})q^{5}+7q^{7}+(15+\\beta _{3}+\\cdots)q^{9}+\\cdots", "related_objects": [], "relative_dim": 7, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "616.4.a", "trace_display": [0, 3, 11, 49], "trace_hash": 881074827878340825, "trace_moments": [{"__RealLiteral__": 0, "data": "0.153", "prec": 17}, {"__RealLiteral__": 0, "data": "6.442", "prec": 17}, {"__RealLiteral__": 0, "data": "3.997", "prec": 17}, {"__RealLiteral__": 0, "data": "121.831", "prec": 24}, {"__RealLiteral__": 0, "data": "157.316", "prec": 24}, {"__RealLiteral__": 0, "data": "3701.510", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 7, 0, 3, 0, 11, 0, 49, 0, 108, 0, 77, 0, 26, 0, 67, 0, 44, 0, 34, 0, 21, 0, -29, 0, 182, 0, 99, 0, 94, 0, -173, 0, 33, 0, 77, 0, 255, 0, -60, 0, 508, 0, 656, 0, 466, 0, -18, 0, 343, 0, 850, 0, 1806, 0, 121, 0, 1154, 0, 665, 0, 608, 0, 756, 0, 588, 0, 669, 0, 2067, 0, 1169, 0, 380, 0, 1254, 0, 539, 0, -110, 0, 2847, 0, -496, 0, 3446, 0, -582, 0, 1321, 0, 182, 0, 1493, 0, -50, 0, 3927, 0, 1188, 0, 630, 0, -286, 0, 469, 0, 2850, 0, 1504, 0, -3573, 0, 2705, 0, -827, 0, 3666, 0, 308, 0, 847, 0, -3662, 0, 5565, 0, -1046, 0, 5748, 0, 1882, 0, 238, 0, 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