# Stored data for newform 784.6.a.bg, downloaded from the LMFDB on 08 November 2025.
{"Nk2": 28224, "analytic_conductor": 125.74091473337681, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [7, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [784, 1, [687, 197, 689], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 4, "field_disc": 40246336, "field_disc_factorization": [[2, 6], [13, 2], [61, 2]], "field_poly": [38414, 400, -399, -2, 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": 1, "hecke_cutters": [[3, [138384, 0, -842, 0, 1]]], "hecke_orbit": 33, "hecke_orbit_code": 144115188176519952, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 98, "hecke_ring_index_factorization": [[2, 1], [7, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0]], "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": "784.6.a.bg", "level": 784, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 7], "level_radical": 14, "minimal_twist": "98.6.a.i", "nf_label": "4.4.40246336.5", "prim_orbit_index": 1, "qexp_display": "q+(\\beta _{1}+\\beta _{3})q^{3}+(-4\\beta _{1}-3\\beta _{3})q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "784.6.a", "trace_display": [0, 0, 0, 0], "trace_hash": 2023716994217303429, "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "3.824", 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