# Stored data for newform 828.4.a.f, downloaded from the LMFDB on 08 December 2025.
{"Nk2": 13248, "analytic_conductor": 48.85358148475323, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [23, -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": [828, 1, [415, 461, 649], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 1229, "field_disc_factorization": [[1229, 1]], "field_poly": [6, -7, -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, [2096, -228, -10, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998203962172, "hecke_ring_generator_nbound": 13, "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": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "828.4.a.f", "level": 828, "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, 23], "level_radical": 138, "minimal_twist": "92.4.a.a", "nf_label": "3.3.1229.1", "prim_orbit_index": 1, "qexp_display": "q+(4+\\beta _{1}-3\\beta _{2})q^{5}+(-18+5\\beta _{1}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "828.4.a", "trace_display": [0, 0, 10, -46], "trace_hash": 797846607537658512, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.914", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", 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