# Stored data for newform 3234.2.a.bi, downloaded from the LMFDB on 15 March 2026.
{"Nk2": 12936, "analytic_conductor": 25.823620013682078, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [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": [3234, 1, [1079, 199, 2059], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 621, "field_disc_factorization": [[3, 3], [23, 1]], "field_poly": [-3, -6, 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": [[5, [4, -9, 0, 1]], [13, [32, -36, 0, 1]], [17, [-1, 1]]], "hecke_orbit": 35, "hecke_orbit_code": 153122387364154530, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "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": "3234.2.a.bi", "level": 3234, "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, 7, 11], "level_radical": 462, "minimal_twist": "462.2.i.f", "nf_label": "3.3.621.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}+q^{3}+q^{4}+\\beta _{2}q^{5}+q^{6}+q^{8}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "3234.2.a", "trace_display": [3, 3, 0, 0], "trace_hash": 2183443044223410442, "trace_moments": [{"__RealLiteral__": 0, "data": "0.048", "prec": 17}, {"__RealLiteral__": 0, "data": "2.735", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "19.927", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "219.627", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.030", "prec": 17}, "traces": [0, 3, 3, 3, 3, 0, 3, 0, 3, 3, 0, 3, 3, 0, 0, 0, 3, 3, 3, -3, 0, 0, 3, 9, 3, 3, 0, 3, 0, 9, 0, 6, 3, 3, 3, 0, 3, 9, -3, 0, 0, 12, 0, 9, 3, 0, 9, -15, 3, 0, 3, 3, 0, 0, 3, 0, 0, -3, 9, 9, 0, -6, 6, 0, 3, 36, 3, 6, 3, 9, 0, 3, 3, 0, 9, 3, -3, 0, 0, 12, 0, 3, 12, -6, 0, 0, 9, 9, 3, -36, 0, 0, 9, 6, -15, -24, 3, 9, 0, 3, 3, -15, 3, -12, 0, 0, 0, 24, 3, 6, 0, 9, 0, -12, -3, -6, 9, 0, 9, 0, 0, 3, -6, 12, 6, -12, 0, 9, 3, 9, 36, -18, 3, 0, 6, 0, 3, 0, 9, 27, 0, -15, 3, 0, 3, -12, 0, 0, 9, 27, 3, 3, -3, 3, 0, -24, 0, -9, 12, 0, 0, 0, 3, -12, 12, 0, -6, 12, 0, 33, 0, -3, 9, -42, 9, 0, 3, 9, -36, -27, 0, 30, 0, -6, 9, -24, 6, 3, -15, 0, -24, 24, 3, -6, 9, 36, 0, 21, 3, -36, 3, 6, -15, 0, 3, -12, -12, 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