# Stored data for newform 784.6.a.y, downloaded from the LMFDB on 08 November 2025.
{"Nk2": 28224, "analytic_conductor": 125.74091473337681, "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": [784, 1, [687, 197, 689], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 184, "field_disc_factorization": [[2, 3], [23, 1]], "field_poly": [-46, 0, 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": 1, "hecke_cutters": [[3, [-184, 0, 1]]], "hecke_orbit": 25, "hecke_orbit_code": 108086391157555984, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0]], "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": "784.6.a.y", "level": 784, "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": [2, 7], "level_radical": 14, "minimal_twist": "98.6.a.e", "nf_label": "2.2.184.1", "prim_orbit_index": 1, "qexp_display": "q+\\beta q^{3}+7\\beta q^{5}-59q^{9}-476q^{11}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "784.6.a", "trace_display": [0, 0, 0, 0], "trace_hash": 1559545028706318313, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.925", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.353", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "135.700", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, -118, 0, -952, 0, 0, 0, 2576, 0, 0, 0, 0, 0, 0, 0, -7392, 0, 11782, 0, 0, 0, 2788, 0, 0, 0, 0, 0, 0, 0, 24180, 0, -26128, 0, 0, 0, -19448, 0, 0, 0, 0, 0, 0, 0, 24288, 0, 8620, 0, 0, 0, 17296, 0, 0, 0, 0, 0, 0, 0, -182896, 0, -40472, 0, 0, 0, -59584, 0, 0, 0, 0, 0, 0, 0, 66352, 0, -82462, 0, 0, 0, 170016, 0, 0, 0, 0, 0, 0, 0, 52256, 0, 121072, 0, 0, 0, 56168, 0, 0, 0, 0, 0, 0, 0, -251816, 0, 178340, 0, 0, 0, -59404, 0, 0, 0, 0, 0, 0, 0, 131050, 0, -412896, 0, 0, 0, 486224, 0, 0, 0, 0, 0, 0, 0, -777952, 0, -665684, 0, 0, 0, -794144, 0, 0, 0, 0, 0, 0, 0, -404660, 0, -691520, 0, 0, 0, 365792, 0, 0, 0, 0, 0, 0, 0, -254952, 0, -1226176, 0, 0, 0, 1112502, 0, 0, 0, 0, 0, 0, 0, -565616, 0, 1250472, 0, 0, 0, -252080, 0, 0, 0, 0, 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