# Stored data for newform 343.4.a.a, downloaded from the LMFDB on 10 March 2025.
{"Nk2": 5488, "analytic_conductor": 20.23765513196903, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[7, 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": [343, 1, [3], [1]], "cm_discs": [-7], "conrey_index": 1, "dim": 3, "field_disc": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 14, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-43, -30, 1, 1]], [3, [0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 67109207, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": true, "label": "343.4.a.a", "level": 343, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [7], "level_radical": 7, "minimal_twist": "343.4.a.a", "nf_label": "3.3.49.1", "prim_orbit_index": 1, "qexp_display": "q+(-1+3\\beta _{1}+\\beta _{2})q^{2}+(18-5\\beta _{1}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.1.d1", "self_twist_discs": [-7], "self_twist_type": 1, "space_label": "343.4.a", "trace_display": [-1, 0, 0, 0], "trace_hash": 291589778556178326, "trace_moments": [{"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "2.726", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, 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