# Stored data for newform 800.6.a.w, downloaded from the LMFDB on 23 April 2026.
{"Nk2": 28800, "analytic_conductor": 128.3070558503845, "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": [800, 1, [351, 101, 577], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 6, "field_disc": 1716827002880400, "field_disc_factorization": [[2, 4], [3, 2], [5, 2], [71, 2], [89, 1], [1031, 2]], "field_poly": [-289161, 0, 27543, 0, -383, 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, [-1872, -348, 10, 1]], [11, [-4638399528960000, 0, 121093324800, 0, -654656, 0, 1]], [13, [-225213825024000000, 0, 1228724736000, 0, -2044496, 0, 1]]], "hecke_orbit": 23, "hecke_orbit_code": 99079191902815008, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 819200, "hecke_ring_index_factorization": [[2, 15], [5, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 20, 4, -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": "800.6.a.w", "level": 800, "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": "160.6.c.d", "prim_orbit_index": 1, "qexp_display": "q+(-3-\\beta _{1})q^{3}+(77-5\\beta _{1}+\\beta _{4})q^{7}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "800.6.a", "trace_display": [0, -20, 0, 452], 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