# Stored data for newform 693.4.a.d, downloaded from the LMFDB on 15 March 2026.
{"Nk2": 11088, "analytic_conductor": 40.888323633978246, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [7, 1], [11, 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": [693, 1, [155, 199, 442], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [2, 1]], [5, [11, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798949221045, "hecke_ring_generator_nbound": 1, "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": "693.4.a.d", "level": 693, "level_is_powerful": false, "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, 7, 11], "level_radical": 231, "minimal_twist": "231.4.a.c", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-2q^{2}-4q^{4}-11q^{5}-7q^{7}+24q^{8}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "693.4.a", "trace_display": [-2, 0, -11, -7], "trace_hash": 626288500918325174, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.029", "prec": 17}, {"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "2.112", 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