# Stored data for newform 845.4.a.i, downloaded from the LMFDB on 21 September 2025.
{"Nk2": 13520, "analytic_conductor": 49.85661395485082, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, 1], [13, -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": [845, 1, [677, 171], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 7, "field_disc": 365630171546639376, "field_disc_factorization": [[2, 4], [3, 4], [13, 1], [195761, 1], [110858117, 1]], "field_poly": [96, -480, -568, 409, 64, -40, -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": 0, "hecke_cutters": [[2, [-96, -480, 568, 409, -64, -40, 2, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028797086073677, "hecke_ring_generator_nbound": 3, "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": "845.4.a.i", "level": 845, "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": [5, 13], "level_radical": 65, "minimal_twist": "65.4.c.a", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{2}+\\beta _{4}q^{3}+(4+\\beta _{2})q^{4}-5q^{5}+\\cdots", "related_objects": [], "relative_dim": 7, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "845.4.a", "trace_display": [-2, 0, -35, -54], "trace_hash": 720057546776953008, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": 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