# Stored data for newform 735.4.a.o, downloaded from the LMFDB on 23 April 2024.
{"label": "735.4.a.o", "space_label": "735.4.a", "level": 735, "weight": 4, "hecke_orbit": 15, "hecke_orbit_code": 63050394850296543, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 649369543237933904, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-7, 2, 1]], [11, [-3136, 16, 1]], [13, [1412, -76, 1]]], "qexp_display": "q+(-1+\\beta )q^{2}+3q^{3}+(1-2\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 11760, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 43.36640385421935, "hecke_ring_index": 2, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [735, 1, [491, 442, 346], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 7], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.896", "prec": 17}, {"__RealLiteral__": 0, "data": "0.136", "prec": 17}, {"__RealLiteral__": 0, "data": "9.307", "prec": 17}, {"__RealLiteral__": 0, "data": "2.022", "prec": 17}, {"__RealLiteral__": 0, "data": "64.904", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [7, -1]], "trace_display": [-2, 6, -10, 0], "traces": [0, 2, -2, 6, 2, -10, -6, 0, -18, 18, 10, -16, 6, 76, 0, -30, -78, 124, -18, 96, -10, 0, -304, -16, -54, 50, -108, 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