# Stored data for newform 147.4.c.b, downloaded from the LMFDB on 25 May 2022.
{"level_primes": [3, 7], "sato_tate_group": "3.2.3.c2", "rm_discs": [], "conrey_indexes": [146], "cm_discs": [], "level_radical": 21, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 3, "is_cm": false, "hecke_orbit": 2, "analytic_conductor": 8.67328077084387, "inner_twist_count": 4, "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": 1, "label": "147.4.c.b", "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "147.4.c.b", "dim": 24, "traces": [24, 0, 0, -96, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 256, 864, 0, -32, 0, 0, 0, -384, 0, 0, 744, 0, 0, 0, 0, -1704, 0, 0, 0, 0, 0, 584, 432, 0, -2368, 0, 0, 0, -624, 0, 0, 3744, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 2032, 6384, 0, -5832, 0, 0, 0, -3504, 0, 0, 3792, 0, 0, 0, 0, -7472, 0, 0, 0, 0, 0, 2248, 2784, 0, -1968, 0, 0, 0, -3744, 0, 0, -624, 0, 0, 0, 0, -3232, 0, 0, 0, 0, 0, 1320, 5520, 0, 5792, 0, 0, 0, 7680, 0, 0, 3120, 0, 0, 0, 0, -7144, 0, 0, 0, 0, 0, -1432, -4968, 0, -5656, 0, 0, 0, -18432, 0, 0, 1776, 0, 0, 0, 0, 17584, 0, 0, 0, 0, 0, 7088, 2688, 0, 3240, 0, 0, 0, 32976, 0, 0, -12000, 0, 0, 0, 0, 14888, 0, 0, 0, 0, 0, -27016, -15024, 0, 3664, 0, 0, 0, -936, 0, 0, -21024, 0, 0, 0, 0, 24944, 0, 0, 0, 0, 0, 7296, -34320, 0, 28864, 0, 0, 0, -5088, 0, 0, 11520, 0, 0, 0, 0, -5464, 0, 0, 0, 0, 0, -21608, -23520, 0, 2320, 0, 0, 0, 15504, 0, 0, -37248, 0, 0, 0, 0, 12280, 0, 0, 0, 0, 0, 27968, 3024, 0, 25744, 0, 0, 0, -2688, 0, 0, -11040, 0, 0, 0, 0, 2664, 0, 0, 0, 0, 0, -50344, -37440, 0, 30128, 0, 0, 0, -37344, 0, 0, 11664, 0, 0, 0, 0, 13552, 0, 0, 0, 0, 0, 11512, 52800, 0, -7736, 0, 0, 0, 72864, 0, 0, -13680, 0, 0, 0, 0, 14256, 0, 0, 0, 0, 0, 22400, 9816, 0, -41680, 0, 0, 0, -12480, 0, 0, -46656, 0, 0, 0, 0, -1824, 0, 0, 0, 0, 0, 34960, 30864, 0, -46376, 0, 0, 0, -8688, 0, 0, 118944, 0, 0, 0, 0, -67064, 0, 0, 0, 0, 0, -26336, -46608, 0, -32800, 0, 0, 0, -37920, 0, 0, 42432, 0, 0, 0, 0, -12512, 0, 0, 0, 0, 0, 11136, 73248, 0, 10104, 0, 0, 0, -35664, 0, 0, -10632, 0, 0, 0, 0, -58552, 0, 0, 0, 0, 0, 28544, 45456, 0, -40016, 0, 0, 0, -6672, 0, 0, 122016, 0, 0, 0, 0, 28936, 0, 0, 0, 0, 0, 23272, 58128, 0, 15112, 0, 0, 0, 12000, 0, 0, -3840, 0, 0, 0, 0, -140304, 0, 0, 0, 0, 0, -8928, 57792, 0, -14408, 0, 0, 0, -77904, 0, 0, -133344, 0, 0, 0, 0, -27168, 0, 0, 0, 0, 0, 26544, -72864, 0, -35144, 0, 0, 0, 1920, 0, 0, 21888, 0, 0, 0, 0, -56272, 0, 0, 0, 0, 0, 25736, 66624, 0, -84952, 0, 0, 0, 107232, 0, 0, 7104, 0, 0, 0, 0, 18832, 0, 0, 0, 0, 0, 25232, 42336, 0, -7448, 0, 0, 0, -102336, 0, 0, -36192, 0, 0, 0, 0, 129136, 0, 0, 0, 0, 0, 38136, -54000, 0, 105840, 0, 0, 0, -113280, 0, 0, 287760, 0, 0, 0, 0, -15864, 0, 0, 0, 0, 0, -142768, 12000, 0, 40768, 0, 0, 0, 227424, 0, 0, -104088, 0, 0, 0, 0, 93160, 0, 0, 0, 0, 0, -109480, -25104, 0, 22720, 0, 0, 0, -13392, 0, 0, -209904, 0, 0, 0, 0, -57264, 0, 0, 0, 0, 0, -27016, -307104, 0, -27840, 0, 0, 0, -23856, 0, 0, 124080, 0, 0, 0, 0, 219064, 0, 0, 0, 0, 0, 212528, -99744, 0, 148672, 0, 0, 0, 208800, 0, 0, -160512, 0, 0, 0, 0, 5840, 0, 0, 0, 0, 0, -73008, 110592, 0, -82520, 0, 0, 0, -99504, 0, 0, -164208, 0, 0, 0, 0, 26848, 0, 0, 0, 0, 0, -143544, -51048, 0, -54792, 0, 0, 0, 5760, 0, 0, 34320, 0, 0, 0, 0, 81872, 0, 0, 0, 0, 0, 98288, 81696, 0, 244968, 0, 0, 0, 53136, 0, 0, -33216, 0, 0, 0, 0, 156752, 0, 0, 0, 0, 0, -25840, 14784, 0, 210880, 0, 0, 0, 73632, 0, 0, -177696, 0, 0, 0, 0, -34584, 0, 0, 0, 0, 0, -192960, -213984, 0, 125792, 0, 0, 0, -253392, 0, 0, -29568, 0, 0, 0, 0, 22232, 0, 0, 0, 0, 0, -82704, 46128, 0, -75696, 0, 0, 0, 272064, 0, 0, -58752, 0, 0, 0, 0, 35464, 0, 0, 0, 0, 0, 59552, -261792, 0, -106472, 0, 0, 0, 85344, 0, 0, -70128, 0, 0, 0, 0, -104912, 0, 0, 0, 0, 0, 221504, 145920, 0, 4200, 0, 0, 0, -197520, 0, 0, 341088, 0, 0, 0, 0, -180016, 0, 0, 0, 0, 0, -163488, -354096, 0, -142696, 0, 0, 0, -175440, 0, 0, -178080, 0, 0, 0, 0, 37664, 0, 0, 0, 0, 0, 279528, 244128, 0, -126368, 0, 0, 0, 181056, 0, 0, 407616, 0, 0, 0, 0, 130000, 0, 0, 0, 0, 0, -93616, 197616, 0, -44328, 0, 0, 0, -144816, 0, 0, 219840, 0, 0, 0, 0, -25920, 0, 0, 0, 0, 0, -215760, 81312, 0, 152976, 0, 0, 0, 50424, 0, 0, -96960, 0, 0, 0, 0, -393328, 0, 0, 0, 0, 0, -130000, 182736, 0, -236608, 0, 0, 0, -182160, 0, 0, -90336, 0, 0, 0, 0, 323008, 0, 0, 0, 0, 0, 403184, 109296, 0, -37632, 0, 0, 0, 246336, 0, 0, -54048, 0, 0, 0, 0, -156496, 0, 0, 0, 0, 0, 268192, 518112, 0, -455432, 0, 0, 0, 228816, 0, 0, 301824, 0, 0, 0, 0, -236976, 0, 0, 0, 0, 0, 82440, 96, 0, 175320, 0, 0, 0, -311760, 0, 0, -223440, 0, 0, 0, 0, -177776, 0, 0, 0, 0, 0, -240056, -83088, 0, -44888, 0, 0, 0, -374064, 0, 0, -13920, 0, 0, 0, 0, -237920, 0, 0, 0, 0, 0, 116232, 208104, 0, -223920, 0, 0, 0, -78240, 0, 0, 297792, 0, 0, 0, 0, 28496, 0, 0, 0, 0, 0, -93616, -209328, 0, 446152, 0, 0, 0, 53184, 0, 0, 307200, 0, 0, 0, 0, -455280, 0, 0, 0, 0], "has_non_self_twist": 1, "char_values": [147, 2, [50, 52], [1, 1]], "Nk2": 2352, "analytic_rank": 0, "char_orbit_label": "c", "weight": 4, "trace_display": [0, 0, 0, 0], "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": true, "level_is_prime_power": false, "relative_dim": 24, "hecke_cutters": [[2, [3136, 0, 66864, 0, 76839, 0, 18948, 0, 1812, 0, 72, 0, 1]]], "space_label": "147.4.c", "level": 147, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 21, 3, 1, 2, 0]], "char_degree": 1, "char_conductor": 21, "char_orbit_index": 3, "hecke_orbit_code": 4503737133432979, "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}