# Stored data for newform 7742.2.a.i, downloaded from the LMFDB on 27 September 2025.
{"Nk2": 30968, "analytic_conductor": 61.82018124487527, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [7, -1], [79, 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": [7742, 1, [2845, 4901], [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": [[3, [2, 1]], [5, [-2, 1]], [11, [4, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028797052526142, "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": "7742.2.a.i", "level": 7742, "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, 7, 79], "level_radical": 1106, "minimal_twist": "158.2.a.e", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{8}+\\cdots", "related_objects": ["EllipticCurve/Q/7742/i"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "7742.2.a", "trace_display": [1, -2, 2, 0], "trace_hash": 268065703040483254, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.990", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.963", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.865", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, "traces": [0, 1, 1, -2, 1, 2, -2, 0, 1, 1, 2, -4, -2, -2, 0, -4, 1, 2, 1, 0, 2, 0, -4, 0, -2, -1, -2, 4, 0, 8, -4, -8, 1, 8, 2, 0, 1, 4, 0, 4, 2, 10, 0, -2, -4, 2, 0, 0, -2, 0, -1, -4, -2, -8, 4, -8, 0, 0, 8, -14, -4, 0, -8, 0, 1, -4, 8, 8, 2, 0, 0, 8, 1, -6, 4, 2, 0, 0, 4, -1, 2, -11, 10, -12, 0, 4, -2, -16, -4, -6, 2, 0, 0, 16, 0, 0, -2, -10, 0, -4, -1, 14, -4, 8, -2, 0, -8, -14, 4, 4, -8, -8, 0, -14, 0, 0, 8, -2, -14, 0, -4, 5, 0, -20, -8, -12, 0, 8, 1, 4, -4, 0, 8, 0, 8, 8, 2, -18, 0, -22, 0, 0, 8, 8, 1, 16, -6, 0, 4, -16, 2, -16, 0, 2, 0, -16, 4, -12, -1, 16, 2, 0, -11, -20, 10, 16, -12, -16, 0, -9, 4, 0, -2, 20, -16, 0, -4, 28, -6, -4, 2, 18, 0, 0, 0, 8, 16, -8, 0, 0, 0, -12, -2, 14, -10, 8, 0, 12, -4, 12, -1, -16, 14, 0, -4, 20, 8, 0, -2, 0, 0, 14, -8, 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