# Stored data for newform 400.6.a.r, downloaded from the LMFDB on 25 April 2024.
{"label": "400.6.a.r", "space_label": "400.6.a", "level": 400, "weight": 6, "hecke_orbit": 18, "hecke_orbit_code": 76561193765962128, "dim": 2, "is_polredabs": true, "nf_label": "2.2.241.1", "trace_hash": 144519834608765006, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-225, 8, 1]]], "qexp_display": "q+(-4-\\beta )q^{3}+(4+2\\beta )q^{7}+(14+8\\beta )q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 14400, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 64.15352792519225, "hecke_ring_index": 2, "level_radical": 10, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [400, 1, [351, 101, 177], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 5], "conrey_indexes": [1], "field_disc": 241, "field_disc_factorization": [[241, 1]], "field_poly": [-60, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.961", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.895", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "70.508", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, 1]], "trace_display": [0, -8, 0, 8], "traces": [0, 2, 0, -8, 0, 0, 0, 8, 0, 28, 0, 200, 0, -592, 0, 0, 0, 278, 0, 840, 0, -996, 0, 1952, 0, 0, 0, -2024, 0, -4680, 0, 5008, 0, -10922, 0, 0, 0, 12500, 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