# Stored data for newform 4000.2.a.r, downloaded from the LMFDB on 22 January 2026.
{"Nk2": 16000, "analytic_conductor": 31.940160808512154, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [5, 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": [4000, 1, [2751, 2501, 1377], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 8, "field_disc": 578340050000, "field_disc_factorization": [[2, 4], [5, 5], [19, 2], [179, 2]], "field_poly": [80, 0, -220, 0, 129, 0, -21, 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": 1, "hecke_cutters": [[3, [80, 0, -220, 0, 129, 0, -21, 0, 1]], [7, [4205, 0, -2605, 0, 524, 0, -41, 0, 1]], [11, [5, 0, -2445, 0, 684, 0, -49, 0, 1]], [13, [149, 78, -17, -6, 1]]], "hecke_orbit": 18, "hecke_orbit_code": 76561193698856864, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0]], "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": true, "label": "4000.2.a.r", "level": 4000, "level_is_powerful": true, "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, 5], "level_radical": 10, "minimal_twist": "4000.2.a.q", "nf_label": "8.8.578340050000.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{3}+\\beta _{7}q^{7}+(2+\\beta _{2})q^{9}+(\\beta _{1}+\\cdots)q^{11}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": 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