# Stored data for newform 678.4.a.f, downloaded from the LMFDB on 29 November 2025.
{"Nk2": 10848, "analytic_conductor": 40.00329498389214, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [113, 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": [678, 1, [227, 229], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 6, "field_disc": 21034713533352, "field_disc_factorization": [[2, 3], [3, 1], [876446397223, 1]], "field_poly": [9504, 10908, 3410, -87, -137, -3, 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": [[5, [-855862, 168276, 27761, -3104, -316, 12, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998203962022, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "678.4.a.f", "level": 678, "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": true, "level_primes": [2, 3, 113], "level_radical": 678, "minimal_twist": "678.4.a.f", "prim_orbit_index": 1, "qexp_display": "q+2q^{2}-3q^{3}+4q^{4}+(-2-\\beta _{5})q^{5}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "678.4.a", "trace_display": [12, -18, -12, -16], "trace_hash": 949484712550201424, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.828", "prec": 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