# Stored data for newform 289.4.a.d, downloaded from the LMFDB on 16 April 2024.
{"label": "289.4.a.d", "space_label": "289.4.a", "level": 289, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220641, "dim": 4, "is_polredabs": true, "nf_label": "4.4.2555057.1", "trace_hash": 577329817648951513, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [36, -4, -21, -1, 1]], [3, [63, -88, -55, -2, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(1-\\beta _{1}-\\beta _{2})q^{3}+(3+\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4624, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 17.05155199165904, "hecke_ring_index": 1, "level_radical": 17, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [289, 1, [3], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [17], "conrey_indexes": [1], "field_disc": 2555057, "field_disc_factorization": [[2555057, 1]], "field_poly": [36, -4, -21, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.668", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "34.625", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "485.658", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[17, -1]], "trace_display": [1, 2, -14, -36], "traces": [0, 4, 1, 2, 11, -14, -38, -36, 60, 6, 7, -10, 29, -22, -73, 54, 63, 0, -334, 22, -330, -352, 79, -380, 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