# Stored data for newform 9747.2.a.u, downloaded from the LMFDB on 22 September 2025.
{"Nk2": 38988, "analytic_conductor": 77.83018685014198, "analytic_rank": 2, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [19, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [9747, 1, [6860, 2890], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 81, "field_disc_factorization": [[3, 4]], "field_poly": [-1, -3, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 18, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-3, 0, 3, 1]], [5, [-3, 0, 3, 1]], [7, [19, 24, 9, 1]], [13, [19, 24, 9, 1]]], "hecke_orbit": 21, "hecke_orbit_code": 90071992580974099, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "9747.2.a.u", "level": 9747, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 19], "level_radical": 57, "minimal_twist": "513.2.y.a", "nf_label": "3.3.81.1", "prim_orbit_index": 1, "qexp_display": "q+(-1+\\beta _{1})q^{2}+(1-2\\beta _{1}+\\beta _{2})q^{4}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "9747.2.a", "trace_display": [-3, 0, -3, -9], "trace_hash": 793003274213015501, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.849", "prec": 17}, {"__RealLiteral__": 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