# Stored data for newform 315.4.a.k, downloaded from the LMFDB on 19 April 2024.
{"label": "315.4.a.k", "space_label": "315.4.a", "level": 315, "weight": 4, "hecke_orbit": 11, "hecke_orbit_code": 45035996340814139, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 1174041046909414366, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-7, -2, 1]]], "qexp_display": "q+(1+\\beta )q^{2}+(1+2\\beta )q^{4}-5q^{5}-7q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5040, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 18.585601651808293, "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": [315, 1, [281, 127, 136], [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": "1.895", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.306", "prec": 17}, {"__RealLiteral__": 0, "data": "0.636", "prec": 17}, {"__RealLiteral__": 0, "data": "64.902", "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, 0, -10, -14], "traces": [0, 2, 2, 0, 2, -10, 0, -14, 18, 0, -10, 16, 0, -76, -14, 0, -78, 124, 0, -96, -10, 0, -304, 16, 0, 50, -108, 0, -14, -188, 0, -120, -414, 0, 156, 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