# Stored data for newform 378.2.v.b, downloaded from the LMFDB on 26 March 2023.
{"level_primes": [2, 3, 7], "sato_tate_group": "1.2.3.c9", "rm_discs": [], "conrey_indexes": [67, 79, 193, 205, 319, 331], "cm_discs": [], "level_radical": 42, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 21, "is_cm": false, "hecke_orbit": 2, "analytic_conductor": 3.0183451964043986, "inner_twist_count": 2, "is_rm": false, "char_order": 9, "level_is_square": false, "weight_parity": 1, "label": "378.2.v.b", "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "378.2.v.b", "dim": 72, "traces": [72, 0, 0, 0, 0, 3, 6, -36, 24, -6, 12, 0, -12, -3, -6, 0, -12, 0, -18, 0, -30, -6, 30, 0, 6, -18, -6, 0, 3, 3, 9, 0, -18, 9, -18, 9, 0, 0, -24, 0, -6, 12, 24, 0, 51, 0, 45, -6, -12, 6, -51, 6, -15, 27, 72, -3, -63, 3, -30, -3, 9, -24, -39, -36, 9, 0, -6, 9, -21, -33, 12, -12, 132, -18, -30, 0, -33, 30, -9, -6, 36, -33, -18, 15, 21, -12, -39, -6, -36, 69, 39, 30, -66, -9, -33, 0, -48, -12, -54, -36, 96, 60, 12, 6, 42, -6, -9, -18, 0, 21, 15, -3, -33, -15, 33, -12, 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-162, -111, 222, -21, 117, 45, -72, -93, 228, 87, -138, -33, 255, -60, -246, 201, 420, -30, 183, 24, 234, 0, -432, -171, -180, 87, -189, -24, -225, 24, -249, -117, -72, -108, 102, -111, -177, 6, 174, -138, 120, 30, -147, -42, -45, 81, -252, -111, 51, 156, -150, -195, 243, 72, 210, 126, -198, -135, -441, 57, -195, -12, 60, 39, 276, -99, -6, -180, -336, -30, 198, -75, -168, 36, 348, -195, 315, 12, -39, 102, 120, 39, 90, -213, -252, 6, -396, 369, 288, -96, -42, -102, -225, 33, -177, -39, -363, -90, 18, 120, 387, 30, -108, 45, -36, -102, -474, -72, -12, -9, -186, 294, -24, 24, -21, -144, -159, 9, -96, 282, -399, -6, 54, -57, -90, 0, -180, -78, -48, -21, -210, -54, 318, -42, -150, 96, -42, -105, -132, 54, 396, -12, -27, 186, -204, -111, -177, 66, 279, 6, -138, -21, 354, -33, 348, 138, 189, -15, -522, -6, -75, 0, -63, -111, -54, 21, 138, -90, -72, -45, 402, 279, 219, 24, -414, -219, 246, 297, -174, -9, 312, 6, 342, 327, 21, 42, 276, -12, 75, -39, -252, 282, 291, 21, -3, 81, -192, 36, 414, 90, 48, 138, -357, 318, 426, 48, 42, 3, -81, -24, -114, -252, -30, 12, 99, -135, 273, -60, 633, -78, -168, 48, 285, 123, 30, 39, -159, 222, -327, 9, 276, 231, 6, 192, 261, -228, -216, 63, 171, 72, -402, 15, 252, 570, 120, 9, -213, -231, 219, 15, -18, 105, 930, 126], "has_non_self_twist": 1, "char_values": [378, 9, [29, 325], [4, 6]], "Nk2": 1512, "analytic_rank": 0, "char_orbit_label": "v", "weight": 2, "trace_display": [0, 0, 0, 6], "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": false, "relative_dim": 12, "hecke_cutters": [[5, [1868500722364663689, 6609195619994576349, 50169797917044942591, 62471912431530521313, -171730289677778725248, -395727475629131956494, -65484280268956311066, 592342883383696992810, 3294152992846268845461, -218339119162461893184, -3013271376445732826871, -5024069518134931813341, 10990196962677287148591, -5486180487521730743061, 4971968520534394780068, -5586134727077598084705, 7220134855909346259132, -12468833609291124027471, 12361380473614112197821, -3679109001387446019975, 2663403843262000390164, -292392160038065713311, -1704968316355059282690, 194590847871205097787, 462788024714640905058, 14906745777775980933, 348307523984541460887, -92748848927600278665, 3173884168110064812, 18995268316706593533, 9228536356235390199, 9329617112627489139, 4864471434612914184, -1478806906452196239, 234809796156450426, 232878233408586516, 158934871912785432, 148878581567989266, 53783671329467874, -12018861886728870, 3239235387231465, 4131237297460089, 2008336889738956, 1109507766999348, 249294252863079, -71658350816986, 30306589055244, 27577180014084, 5533800870708, 2296807167924, 1182475597032, -53789537577, 15744317805, 71469798156, 23282298336, 4068399051, 1823500746, 322650720, 48338505, 46857969, 15612168, 1479843, 684360, 77040, -18243, 9936, 5130, -57, 105, 41, -3, 0, 1]]], "space_label": "378.2.v", "level": 378, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 189, 21, 1, 9, 0]], "char_degree": 6, "char_conductor": 189, "char_orbit_index": 22, "hecke_orbit_code": 4505042769936762, "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}