# Stored data for newform 729.2.g.a, downloaded from the LMFDB on 21 March 2023.
{"level_primes": [3], "sato_tate_group": "1.2.3.c27", "rm_discs": [], "conrey_indexes": [28, 55, 109, 136, 190, 217, 271, 298, 352, 379, 433, 460, 514, 541, 595, 622, 676, 703], "cm_discs": [], "level_radical": 3, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 7, "is_cm": false, "hecke_orbit": 1, "analytic_conductor": 5.82109430735134, "inner_twist_count": 2, "is_rm": false, "char_order": 27, "level_is_square": true, "weight_parity": 1, "label": "729.2.g.a", "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "81.2.g.a", "dim": 144, "traces": [144, -9, 0, 9, -9, 0, 9, 18, 0, -18, -9, 0, 9, -9, 0, 9, 18, 0, -18, -45, 0, 9, 45, 0, 9, -45, 0, -9, -36, 0, 9, 99, 0, 9, -9, 0, -18, -18, 0, 9, -27, 0, 9, -54, 0, -18, 99, 0, 9, -126, 0, -27, -45, 0, -9, 225, 0, 9, -72, 0, 9, -81, 0, -18, 81, 0, -45, -117, 0, -99, 90, 0, -18, -81, 0, -153, -81, 0, -99, 288, 0, -36, -45, 0, -99, -81, 0, -153, 81, 0, -18, -207, 0, -99, 171, 0, -45, -81, 0, -18, -117, 0, 9, 243, 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[729, 27, [2], [22]], "Nk2": 2916, "analytic_rank": 0, "char_orbit_label": "g", "weight": 2, "trace_display": [-9, 0, -9, 9], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "level_is_prime": false, "char_is_minimal": false, "self_twist_discs": [], "char_is_real": false, "level_is_prime_power": true, "relative_dim": 8, "hecke_cutters": [[2, [13966276041, 372264913611, 3993668752419, 19992334465377, 55059807693222, 672941733749199, 11965594258003194, 121380428032544844, 820686471902695287, 4128646613916436119, 16526540090355413571, 52597141575027461604, 117222537417578934057, 103975499556972972675, -383220150463226685573, -1957516581873910205655, -4946261039109406386387, -11055260999383687740699, -16014647105031337594902, 102236834672782329238722, 1160520735789266788833930, 6274627413117896302776747, 23532924193041672011520513, 67868933484593224827328050, 158283691011545979907991646, 307683041314259006991020430, 509235999522185225869767846, 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86223811689736830, 41453165442193218, 32753015871459138, 21523191090750099, 11007310989190572, 4891209493816557, 1977012772721325, 919349274586599, 627477815956698, 408479199437313, 195085966515210, 61892917835184, 10966697549613, 323668808820, 909810782226, 1599127218702, 1035345474576, 310916617497, -20104832907, -65072688174, -34465238064, -9826913223, 189786780, 1993058199, 1093451751, 225040788, -59765709, -60793686, -21360807, -2421738, 1950750, 1650564, 766611, 227907, 27108, -13287, -10926, -4932, -1599, -306, 45, 75, 36, 9, 1]]], "space_label": "729.2.g", "level": 729, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 81, 7, 1, 27, 0]], "char_degree": 18, "char_conductor": 81, "char_orbit_index": 7, "hecke_orbit_code": 412350415577, "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}