# Stored data for newform 486.2.e.c, downloaded from the LMFDB on 07 May 2024.
{"label": "486.2.e.c", "space_label": "486.2.e", "level": 486, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007474166202854, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 450309454073679191, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [9, 0, 9, 3, 0, -3, 1]]], "qexp_display": "q+(\\zeta_{18}-\\zeta_{18}^{4})q^{2}-\\zeta_{18}^{5}q^{4}+(1+\\zeta_{18}+\\cdots)q^{5}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 27, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1944, "analytic_conductor": 3.8807295382342266, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [486, 9, [245], [8]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [55, 109, 217, 271, 379, 433], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.076", "prec": 17}, {"__RealLiteral__": 0, "data": "5.830", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "95.963", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2906.939", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c9", "trace_display": [0, 0, 3, -6], "traces": [0, 6, 0, 0, 0, 3, 0, -6, -3, 0, 3, -15, 0, 6, 3, 0, 0, 6, 0, 9, 3, 0, -15, -12, 0, 9, -18, 0, -12, 3, 0, 9, 0, 0, -21, -3, 0, 15, 6, 0, -6, -24, 0, 0, 3, 0, -3, 9, 0, -6, 0, 0, 6, 12, 0, -18, 3, 0, 12, 15, 0, 9, 12, 0, -3, 15, 0, -9, 6, 0, -12, -12, 0, 3, -15, 0, 6, 15, 0, 6, -6, 0, -6, -18, 0, 9, 0, 0, 3, 15, 0, -12, 6, 0, -9, 24, 0, -3, 3, 0, 6, 6, 0, -9, 6, 0, 3, 30, 0, -6, -9, 0, -6, -45, 0, 9, 3, 0, -3, -15, 0, 9, 18, 0, 9, -12, 0, 3, 0, 0, 15, 48, 0, 54, -6, 0, -12, 30, 0, 39, -12, 0, 33, -39, 0, 0, 36, 0, 3, -21, 0, 9, 9, 0, -3, -3, 0, 9, -39, 0, -6, 12, 0, -48, -24, 0, 0, 45, 0, -48, 0, 0, 12, -9, 0, -33, 12, 0, 15, -15, 0, -12, 18, 0, 6, -3, 0, -81, 18, 0, 60, 51, 0, -45, -3, 0, 21, 6, 0, 0, -9, 0, 33, -12, 0, -9, 3, 0, 9, -75, 0, -12, -15, 0, 3, -12, 0, 30, -27, 0, -18, -33, 0, -18, 6, 0, 0, 9, 0, 36, 0, 0, -15, 3, 0, 0, 6, 0, -15, -54, 0, -42, 24, 0, 12, 0, 0, -93, 9, 0, -30, -24, 0, 9, -36, 0, 0, 27, 0, -24, -3, 0, 3, 51, 0, -18, -18, 0, -9, -78, 0, 66, 6, 0, 3, 12, 0, 27, 6, 0, -3, -42, 0, -9, -21, 0, 33, 15, 0, -39, -18, 0, 36, 69, 0, 9, -30, 0, 6, -24, 0, 60, 9, 0, 15, 24, 0, -6, 24, 0, 33, -51, 0, 30, 21, 0, 0, 24, 0, 9, 3, 0, -15, -42, 0, 72, 3, 0, 21, 0, 0, 33, 0, 0, -36, 15, 0, -24, -12, 0, -36, 24, 0, -27, -18, 0, -9, -54, 0, 21, 24, 0, -6, 12, 0, 0, 15, 0, -15, -27, 0, -48, -15, 0, -27, 42, 0, 0, -3, 0, -12, 6, 0, 78, 63, 0, -9, 78, 0, 6, 24, 0, -57, 48, 0, 27, -15, 0, 18, 51, 0, -18, -15, 0, 24, 6, 0, 21, 15, 0, -9, -6, 0, 12, -12, 0, -12, -102, 0, -33, -9, 0, 0, 12, 0, -18, -12, 0, -12, 27, 0, -24, -27, 0, -6, 69, 0, 51, -15, 0, 24, 42, 0, -114, 42, 0, 36, -42, 0, 63, 9, 0, 12, -54, 0, 45, 27, 0, 3, -18, 0, 27, 0, 0, 9, 21, 0, -63, -42, 0, -18, 12, 0, 6, -15, 0, 30, 93, 0, 12, 9, 0, -21, -84, 0, 42, -33, 0, -18, -36, 0, 18, 57, 0, 9, 6, 0, 36, 18, 0, -9, 42, 0, 54, -15, 0, 12, 3, 0, 36, 33, 0, -33, -27, 0, 27, 45, 0, -36, 3, 0, 24, 6, 0, -108, -3, 0, -27, -24, 0, -21, 51, 0, 3, -33, 0, -84, 75, 0, 36, 9, 0, -3, -111, 0, -9, 18, 0, -60, 0, 0, 24, 45, 0, -21, 15, 0, -45, -15, 0, -33, 96, 0, -18, -90, 0, -51, 33, 0, -36, -3, 0, -42, -99, 0, -45, -24, 0, 24, -3, 0, 39, 33, 0, -39, 6, 0, 39, 9, 0, -9, 54, 0, -36, 3, 0, -30, 96, 0, -69, 18, 0, 3, -12, 0, -18, -21, 0, 66, -165, 0, -54, -42, 0, -15, 30, 0, 138, -21, 0, 60, 27, 0, 48, -18, 0, 24, -6, 0, 117, 60, 0, 30, -33, 0, 9, 30, 0, 0, -87, 0, -3, 33, 0, 69, -30, 0, 60, -36, 0, 3, -42, 0, -36, 12, 0, 93, 72, 0, -108, -21, 0, -15, 78, 0, -36, 3, 0, 27, 33, 0, -117, 6, 0, 18, 57, 0, 27, -27, 0, 15, -3, 0, 6, 60, 0, 24, 51, 0, 63, -36, 0, -57, -36, 0, 45, -33, 0, 18, -21, 0, -63, -9, 0, 45, -57, 0, -108, 3, 0, -33, -258, 0, 42, 12, 0, -6, 66, 0, -21, -9, 0, 15, -33, 0, -45, -24, 0, -81, -36, 0, -6, -21, 0, -15, -33, 0, 18, 24, 0, 24, -114, 0, 81, 0, 0, -12, -12, 0, 57, -39, 0, -3, 99, 0, -45, 0, 0, 18, -12, 0, 39, 9, 0, 15, 24, 0, 138, 30, 0, -3, -72, 0, -57, -21, 0, 21, -15, 0, 15, 18, 0, 72, 9, 0, 3, -12, 0, 51, -3, 0, 126, 72, 0, -6, 51, 0, -36, 24, 0, 33, 0, 0, -36, -126, 0, 51, 90, 0, 9, 6, 0, 66, 69, 0, 0, -69, 0, 33, -84, 0, 12, -12, 0, 33, -48, 0, -60, 33, 0, -27, -102, 0, 15, 9, 0, -33, -21, 0, 0, 18, 0, -12, 18, 0, -27, -48, 0, 0, 72, 0, -63, -24, 0, -30, 0, 0, 24, 12, 0, -66, -33, 0, -72, 21, 0, -15, 0, 0, -96, -12, 0, -75, 222, 0, -108, 9, 0, -3, -12, 0, -96, 3, 0, 39, 48, 0, -123, -9, 0, 27, 39, 0, -9, 93, 0, -54, 39, 0, -111, 18, 0, -60, -72, 0, 54, 3, 0, 99, -3, 0, -45, 63, 0, 45, -39, 0, 87, 27, 0, -15, -135, 0, 36, -27, 0, 36, -84, 0, -168, 0, 0, 3, 30, 0, 48, 36, 0, 3, 54, 0, -12, -15, 0, -6, -99, 0, 6, -21, 0, 9, 51, 0, 18, 6, 0, 60, 117, 0, 129, 42, 0, 39, 18, 0, 72, 27, 0, 63, -75, 0, -99, -21, 0, -12, 87, 0, 27, 0, 0, 33, 18, 0, -54, -84, 0, 9, 114, 0, 54, -18, 0, 33, 60, 0, 36, -36, 0, 60, -24, 0, -24, 9, 0, 3, -66, 0, -18, -60, 0, 24], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 27, 5, 1, 9, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "54.2.e.a", "char_is_minimal": false, "conrey_index": 55, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [1, 1, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, -2, -1], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 1, -1, -1, -1], [-2, 1, -3, -1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 2, -3, 2, 0, 0], [1, -1, -2, -1, 1, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [2, 4, -3, -2, -1, -1], [0, 0, 0, 0, 0, 0], [0, 4, -1, 3, -1, 4], [1, 0, -1, -1, -1, 0], [0, 0, 0, 0, 0, 0], [-3, -3, 1, 1, 2, -1], [-2, 2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [2, -2, 1, -1, 2, -2], [-3, 2, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, -1, 1], [2, -1, 3, -3, 1, -2], [0, 0, 0, 0, 0, 0], [0, -3, 0, 3, 3, 4], [0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [-3, 0, 3, -1, -2, -4], [0, -2, -1, -1, -1, -2], [0, 0, 0, 0, 0, 0], [5, 3, -2, -5, -1, -1], [-1, 3, 3, 4, 0, -4], [0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, -1, 0], [-5, 2, -1, 2, -5, 0], [0, 0, 0, 0, 0, 0], [2, 4, -2, -4, 0, 4], [1, -2, -1, -1, 3, 3], [0, 0, 0, 0, 0, 0], [0, -2, 2, -1, 2, -2], [2, 0, -2, -1, 3, 1], [0, 0, 0, 0, 0, 0], [1, 1, 1, -4, 3, -1], [1, 1, 0, -2, -2, 2], [0, 0, 0, 0, 0, 0], [2, -3, 2, -2, 3, -2], [2, -1, -1, 0, -2, 3], [0, 0, 0, 0, 0, 0], [-3, -4, -4, 0, -1, 5], [0, -2, -1, 1, 2, 0], [0, 0, 0, 0, 0, 0], [3, -1, 0, -2, -2, 1], [4, 4, -1, -3, -1, 1], [0, 0, 0, 0, 0, 0], [-1, 0, 1, 5, 2, 4], [0, 3, 0, 4, 0, 3], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, 0], [4, -1, 1, -3, 0, 3], [0, 0, 0, 0, 0, 0], [-3, 3, -1, 3, -3, 0], [3, -4, -2, -4, 3, 0], [0, 0, 0, 0, 0, 0], [-1, -1, -3, -2, 0, 2], [-4, -5, 6, 4, -1, -1], [0, 0, 0, 0, 0, 0], [0, -2, 7, 1, 7, -2], [-2, 0, 2, -1, -5, -3], [0, 0, 0, 0, 0, 0], [3, 3, 3, -4, 1, -3], [-1, -6, 0, 7, 7, -1], [0, 0, 0, 0, 0, 0], [-3, 0, -8, 8, 0, 3], [-1, -1, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0], [-1, -3, -3, 0, 5, -2], [-4, 0, -2, 2, 0, 4], [0, 0, 0, 0, 0, 0], [5, 2, 0, -7, -7, 0], [-2, -2, 4, 4, -2, -4], [0, 0, 0, 0, 0, 0], [-1, 0, 1, 3, -1, 2], [0, -3, 4, 5, 4, -3], [0, 0, 0, 0, 0, 0], [-4, -1, 5, 4, -4, -4], [2, -1, 0, -2, 0, 2], [0, 0, 0, 0, 0, 0], [-2, 1, 3, 1, -2, 0], [3, 2, 10, 2, 3, 0], [0, 0, 0, 0, 0, 0], [1, 6, -2, -3, 0, 3], [1, -3, 4, -1, -1, -1], [0, 0, 0, 0, 0, 0], [0, -1, -1, 2, -1, -1]]}