# Stored data for newform 3.15.b.a, downloaded from the LMFDB on 25 April 2024.
{"label": "3.15.b.a", "space_label": "3.15.b", "level": 3, "weight": 15, "hecke_orbit": 1, "hecke_orbit_code": 68971134979, "dim": 4, "is_polredabs": true, "nf_label": "4.0.1929141760.2", "trace_hash": 416533873846150175, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta _{1}q^{2}+(549+3\\beta _{1}-\\beta _{2})q^{3}+(-9824+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 675, "analytic_conductor": 3.7298690445571796, "hecke_ring_index": 2239488, "level_radical": 3, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [3, 2, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [2], "field_disc": 1929141760, "field_disc_factorization": [[2, 9], [5, 1], [7, 3], [13, 3]], "field_poly": [3640, 0, 364, 0, 1], "hecke_ring_index_factorization": [[2, 10], [3, 7]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "3.602", "prec": 17}, {"__RealLiteral__": 0, "data": "0.927", "prec": 17}, {"__RealLiteral__": 0, "data": "62.457", "prec": 20}, {"__RealLiteral__": 0, "data": "42.119", "prec": 20}, {"__RealLiteral__": 0, "data": "1497.404", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "14.2.3.c2", "trace_display": [0, 2196, 0, 825608], "traces": [0, 4, 0, 2196, -39296, 0, -314496, 825608, 0, -1624860, 19918080, 0, -157435776, 201696872, 0, -449729280, 1113997312, 0, -2066238720, 1314947240, 0, 1947743784, -6769002240, 0, 13425205248, 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