# Stored data for newform 729.2.k.a, downloaded from the LMFDB on 27 March 2023. {"level_primes": [3], "sato_tate_group": "1.2.3.c243", "rm_discs": [], "conrey_indexes": [4, 7, 13, 16, 22, 25, 31, 34, 40, 43, 49, 52, 58, 61, 67, 70, 76, 79, 85, 88, 94, 97, 103, 106, 112, 115, 121, 124, 130, 133, 139, 142, 148, 151, 157, 160, 166, 169, 175, 178, 184, 187, 193, 196, 202, 205, 211, 214, 220, 223, 229, 232, 238, 241, 247, 250, 256, 259, 265, 268, 274, 277, 283, 286, 292, 295, 301, 304, 310, 313, 319, 322, 328, 331, 337, 340, 346, 349, 355, 358, 364, 367, 373, 376, 382, 385, 391, 394, 400, 403, 409, 412, 418, 421, 427, 430, 436, 439, 445, 448, 454, 457, 463, 466, 472, 475, 481, 484, 490, 493, 499, 502, 508, 511, 517, 520, 526, 529, 535, 538, 544, 547, 553, 556, 562, 565, 571, 574, 580, 583, 589, 592, 598, 601, 607, 610, 616, 619, 625, 628, 634, 637, 643, 646, 652, 655, 661, 664, 670, 673, 679, 682, 688, 691, 697, 700, 706, 709, 715, 718, 724, 727], "cm_discs": [], "level_radical": 3, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 11, "is_cm": false, "hecke_orbit": 1, "analytic_conductor": 5.82109430735134, "inner_twist_count": 2, "is_rm": false, "char_order": 243, "level_is_square": true, "weight_parity": 1, "label": "729.2.k.a", "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "729.2.k.a", "dim": 12960, "traces": [12960, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -81, -162, 243, 648, -162, 648, 243, -162, 243, 648, -162, 1458, 648, -162, 243, 1458, -162, 1458, 648, -162, 648, 648, -162, 1458, 648, -162, 243, 2268, -162, 810, 1053, -81, 1053, 729, -162, 2268, 243, -162, 648, 1458, -162, 648, 648, -162, 648, 1458, -162, 1458, 243, -162, 648, 1458, -162, 648, 243, -162, 243, 648, -162, 648, 243, -162, -81, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -81, 486, -162, 891, 648, -162, 810, 1539, -162, 2349, 648, -162, 1458, 2025, -162, 1701, 1458, -162, 648, 3483, -162, 2592, 1458, -162, 1458, 2511, -162, 3402, 648, -162, 1458, 2673, -162, 3483, 2268, -162, 1458, 3726, -162, 3402, 1458, 0, 1539, 2430, -81, 2592, 1458, -162, 1458, 3402, -162, 3726, 1458, -162, 2268, 3483, -162, 2673, 1458, -162, 648, 3402, -162, 2511, 1458, -162, 1458, 2592, -162, 3483, 648, -162, 1458, 1701, -162, 2025, 1458, -162, 648, 2349, -162, 1539, 810, -162, 648, 891, -162, 486, -81, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -648, -1134, 324, -3078, -1134, 810, -1134, -3564, -162, -2430, -2106, 1539, -2106, -4050, 810, -4050, -2106, -162, -3078, -5994, 810, -2106, -2106, 2754, -3564, -2106, -162, -7290, -3078, 1782, -2106, -6966, 1053, -5994, -2106, -162, -2106, -4050, 1782, -5994, -3078, 1782, -2106, -7614, -162, -4050, -2106, 3240, -3564, -4779, 810, -6156, -4050, -324, -4050, -5751, 810, -5022, -3564, 3240, -2106, -4050, -162, -7614, -2106, 1782, -3078, -5994, 1782, -4050, -2106, -162, -2106, -5994, 1053, -6966, -2106, 1782, -3078, -7290, -162, -2106, -3564, 2754, -2106, -2106, 810, -5994, -3078, -162, -2106, -4050, 810, -4050, -2106, 1539, -2106, -2430, -162, -3564, -1134, 810, -1134, -3078, 324, -1134, -648, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, -162, 162, 729, -162, 1134, 1458, -162, 1458, 1539, -162, 2592, 2268, -162, 1458, 2835, -162, 4050, 1458, -162, 2268, 3483, -162, 2997, 3078, -162, 3078, 5022, -162, 3321, 1458, -162, 3888, 2349, -162, 2916, 4698, -162, 3078, 3726, -162, 5427, 3078, -162, 2268, 5103, -162, 5184, 3888, -162, 3078, 5265, -162, 2997, 1458, -162, 4698, 6480, -162, 5103, 2511, 0, 4779, 2997, -81, 3159, 4698, 162, 2511, 4779, -162, 6480, 4698, -162, 1458, 2997, -162, 5265, 3078, -162, 3888, 5184, -162, 5103, 2268, -162, 3078, 5427, -162, 3726, 3078, -162], "has_non_self_twist": 1, "char_values": [729, 243, [2], [1]], "Nk2": 2916, "analytic_rank": 0, "char_orbit_label": "k", "weight": 2, "trace_display": [-162, -162, -162, -162], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "level_is_prime": false, "char_is_minimal": true, "self_twist_discs": [], "char_is_real": false, "level_is_prime_power": true, "relative_dim": 80, "hecke_cutters": [], "space_label": "729.2.k", "level": 729, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 729, 11, 1, 243, 0]], "char_degree": 162, "char_conductor": 729, "char_orbit_index": 11, "hecke_orbit_code": 687228322521, "id": null, "is_polredabs": null, "trace_hash": null, "projective_field": null, "hecke_ring_index_proved": null, "embedded_related_objects": null, "field_disc_factorization": null, "field_poly_is_real_cyclotomic": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "trace_zratio": null, "hecke_ring_index_factorization": null, "artin_image": null, "nf_label": null, "field_poly": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "field_poly_root_of_unity": null, "hecke_ring_index": null, "artin_field": null, "qexp_display": null, "field_disc": null, "hecke_ring_generator_nbound": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "trace_moments": null, "artin_degree": null}