# Stored data for newform 690.3.f.a, downloaded from the LMFDB on 25 February 2021.
{"level_primes": [2, 3, 5, 23], "sato_tate_group": "2.2.3.c2", "rm_discs": [], "conrey_indexes": [229], "cm_discs": [], "level_radical": 690, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 3, "is_cm": false, "hecke_orbit": 1, "analytic_conductor": 18.801138240860485, "inner_twist_count": 4, "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": -1, "label": "690.3.f.a", "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "690.3.f.a", "dim": 48, "traces": [48, 0, 0, -96, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 96, 64, 0, 0, -152, 0, -8, 0, 0, 0, 56, 288, 0, 0, -48, 0, 40, 0, 0, 0, 0, -160, 0, 0, 424, 96, 0, 0, 0, 0, 32, 0, 0, 0, 360, 0, 0, 0, 0, -384, 0, 0, 0, 0, 192, -496, -152, 0, 0, 0, 144, 0, 0, 0, 0, 0, 432, 0, 0, 0, -136, 0, 0, 0, 0, 0, 0, 0, 0, 256, 496, 0, 0, 0, 0, -192, 40, 0, 0, -128, 240, 0, 0, 0, 0, 352, 0, 0, 0, 0, 264, 304, 0, 0, -1352, 0, -1264, 0, 0, 16, 0, 0, 0, 0, 0, 0, 1328, 0, 0, 0, 0, 0, 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0, 1920, 0, 0, 0, 0, 0, 160, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, -3696, 1296, 8160, 0, 0, 0, -432, 2208, 0, 0, 11152, -1088, 0, 0, 0, 0, 160, 0, 0, 0, 0, -624, 80, 0, 0, -5760, 0, -384, 0, 0, -6240, 0, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, 0, 0, -864, -8128, 288, 0, 0, -760, 0, 1488, 0, 0, 0, -5080, -192, 0, 0, -1296, 0, -8720, 0, 0, 0, 0, -640, 0, 0, -12328, 3376, 0, 0, 0, 0, 8528, 0, 0, 0, -10200, 0, 0, 0, 0, 3008, 0, 0, 0, 0, 5328, 1504, -3064, 0, 0, 0, 408, 0, 0, 0, 0, 0, 2256, 0, 0, 0, -4744, 0, 0, 0, 0, 0, 0, 0, 0, 1696, 8, 144, 0, 0, 0, 2352, 2040, 0, 0, 2880, -960, 0, 0, 0, 0, 384, 0, 0, 0, 0, -1472, 2656, 0, 0, -9624, 0, 3704, 0, 0, -9216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2856, -5056, 3744, 0, 0, -2112, 0, -6592, 0, 0, 0, -1920, -888, 0, 0, 2256, 0, -768, 0, 0, 0, 0, 7080, 0, 0, -8288, -1488, 0, 0, 0, 3256, 768, 0, 0, 0, 0, 0, 0, 0, 0, -9248, 0, 0, 0, 0, 5872, -8328, -2592, 0, 0, 0, 128, 0, 0, 0, 0, 0, 9568, 0, 0, 0, -9568, 0, 0, 0, 0, 0, 0, 0, 0, 18264, 576, 5496, 0, 0, 0, 96, -1056, 0, 0, -120, -3680, 0, 0, 0, 0, 3024, 0, 0, 0, 0, 1536, -2304, 0, 0, 480, 0, 5664, 0, 0, 3176, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, 1440, -720, 7712, 0, 0, -9824, 0, 1200, 0, 0, 0, -2784, -656, 0, 0, 6032, 0, 2088, 0, 0, 0, 0, -2208, 0, 0, -12336, -496, 0, 0, 0, 8672, 6768, 0, 0, 0, -3136, 0, 0, 0, 0, 960, 0, 0, 0, 0, 1696, -1056, -4744, 0, 0, 0, 2608, 0, 0, 0, 0, 0], "has_non_self_twist": 1, "char_values": [690, 2, [461, 277, 511], [2, 1, 1]], "Nk2": 6210, "analytic_rank": 0, "char_orbit_label": "f", "weight": 3, "trace_display": [0, 0, 0, 0], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": true, "level_is_prime": false, "char_is_minimal": true, "self_twist_discs": [], "char_is_real": true, "level_is_prime_power": false, "relative_dim": 48, "hecke_cutters": [], "space_label": "690.3.f", "level": 690, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 1, 23, 2, -1, 2, 0], [1, 1, 115, 3, -1, 2, 0]], "char_degree": 1, "char_conductor": 115, "char_orbit_index": 6, "hecke_orbit_code": 343647716018, "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}