# Stored data for newform 4010.2.a.m, downloaded from the LMFDB on 09 May 2024.
{"label": "4010.2.a.m", "space_label": "4010.2.a", "level": 4010, "weight": 2, "hecke_orbit": 13, "hecke_orbit_code": 54043195562004394, "dim": 20, "is_polredabs": true, "trace_hash": 574212420024939124, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [104, 1972, 7920, -8984, -68876, 37365, 211360, -189098, -150697, 190617, 34362, -83577, 2776, 19157, -2591, -2392, 460, 154, -35, -4, 1]], [7, [814592, -1700672, -9615552, 35241520, -27706332, -26591471, 41762271, 2277150, -21177395, 3269369, 5124325, -1295078, -634313, 211579, 37502, -17399, -594, 703, -31, -11, 1]], [11, [-24378448, -182436384, 705716048, 821789228, -2275086887, 152229420, 1250476406, -289821722, -290696103, 92360842, 33806267, -13789522, -1902776, 1114552, 29044, -49510, 1845, 1122, -85, -10, 1]]], "qexp_display": "q-q^{2}+\\beta _{1}q^{3}+q^{4}+q^{5}-\\beta _{1}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16040, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 32.02001121053343, "hecke_ring_index": 4, "level_radical": 4010, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [4010, 1, [2407, 3211], [1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 5, 401], "conrey_indexes": [1], "field_disc": 24426588539479981003021705799789932795072512, "field_disc_factorization": [[2, 12], [3, 1], [10957, 1], [1052663, 1], [172345756364881971027950305489, 1]], "field_poly": [104, 1972, 7920, -8984, -68876, 37365, 211360, -189098, -150697, 190617, 34362, -83577, 2776, 19157, -2591, -2392, 460, 154, -35, -4, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.350", "prec": 17}, {"__RealLiteral__": 0, "data": "16.240", "prec": 20}, {"__RealLiteral__": 0, "data": "20.035", "prec": 20}, {"__RealLiteral__": 0, "data": "849.125", "prec": 24}, {"__RealLiteral__": 0, "data": "2012.878", "prec": 27}, {"__RealLiteral__": 0, "data": "77781.412", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 20, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, -1], [401, 1]], "trace_display": [-20, 4, 20, 11], "traces": [0, 20, -20, 4, 20, 20, -4, 11, -20, 26, -20, 10, 4, -9, -11, 4, 20, -11, -26, 17, 20, -2, -10, -3, -4, 20, 9, -2, 11, 6, -4, 28, -20, 2, 11, 11, 26, 33, -17, 36, -20, 32, 2, 30, 10, 26, 3, 13, 4, 43, -20, 43, -9, 0, 2, 10, -11, 19, -6, 52, 4, 25, -28, 16, 20, -9, -2, 40, -11, 39, -11, 25, -26, -5, -33, 4, 17, -9, -36, 40, 20, 48, -32, 10, -2, -11, -30, 10, -10, 17, -26, 88, 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