# Stored data for newform 312.6.a.e, downloaded from the LMFDB on 23 December 2025.
{"Nk2": 11232, "analytic_conductor": 50.039751781649954, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, -1], [13, -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": [312, 1, [79, 157, 209, 145], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 54905, "field_disc_factorization": [[5, 1], [79, 1], [139, 1]], "field_poly": [20, -60, -1, 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, [-67264, -4532, 8, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014398610145592, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 8, "hecke_ring_index_factorization": [[2, 3]], "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": "312.6.a.e", "level": 312, "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": [2, 3, 13], "level_radical": 78, "minimal_twist": "312.6.a.e", "nf_label": "3.3.54905.1", "prim_orbit_index": 1, "qexp_display": "q+9q^{3}+(-3+\\beta _{1}-2\\beta _{2})q^{5}+(-14+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "312.6.a", "trace_display": [0, 27, -8, -46], "trace_hash": 1968244390719403747, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.964", "prec": 17}, 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