# Stored data for newform 2016.4.a.w, downloaded from the LMFDB on 14 June 2026.
{"Nk2": 32256, "analytic_conductor": 118.94785057157308, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, -1], [7, 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": [2016, 1, [127, 1765, 1793, 577], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 621, "field_disc_factorization": [[3, 3], [23, 1]], "field_poly": [-3, -6, 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": 0, "hecke_cutters": [[5, [-768, -204, -6, 1]], [11, [-48832, -3456, 0, 1]]], "hecke_orbit": 23, "hecke_orbit_code": 99079191869261792, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 8, "hecke_ring_index_factorization": [[2, 3]], "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": "2016.4.a.w", "level": 2016, "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, 3, 7], "level_radical": 42, "minimal_twist": "224.4.a.f", "nf_label": "3.3.621.1", "prim_orbit_index": 1, "qexp_display": "q+(2+2\\beta _{1}+\\beta _{2})q^{5}-7q^{7}+(-3\\beta _{1}+\\cdots)q^{11}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "2016.4.a", "trace_display": [0, 0, 6, -21], "trace_hash": 484788518592232177, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.951", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "23.146", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "268.299", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.005", "prec": 17}, "traces": [0, 3, 0, 0, 0, 6, 0, -21, 0, 0, 0, 0, 0, -6, 0, 0, 0, 66, 0, -168, 0, 0, 0, 336, 0, 69, 0, 0, 0, -90, 0, -504, 0, 0, 0, -42, 0, 18, 0, 0, 0, 450, 0, 0, 0, 0, 0, 504, 0, 147, 0, 0, 0, 78, 0, -1176, 0, 0, 0, -504, 0, 498, 0, 0, 0, -1068, 0, 1008, 0, 0, 0, 504, 0, -234, 0, 0, 0, 0, 0, -168, 0, 0, 0, -3024, 0, 1476, 0, 0, 0, -246, 0, 42, 0, 0, 0, -2184, 0, -2514, 0, 0, 0, 654, 0, -1008, 0, 0, 0, -1680, 0, -2646, 0, 0, 0, -1254, 0, 1848, 0, 0, 0, -462, 0, 2919, 0, 0, 0, 4692, 0, 672, 0, 0, 0, -1008, 0, 1176, 0, 0, 0, 594, 0, -5544, 0, 0, 0, -1848, 0, -1044, 0, 0, 0, -1218, 0, -3360, 0, 0, 0, 3024, 0, -3126, 0, 0, 0, -2352, 0, -3024, 0, 0, 0, 2688, 0, 2013, 0, 0, 0, -7242, 0, 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