# Stored data for newform 441.2.bb.c, downloaded from the LMFDB on 23 April 2024. {"label": "441.2.bb.c", "space_label": "441.2.bb", "level": 441, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9009054714167737, "dim": 48, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1681, -67650, 794998, -2037571, 664507, 290591, 6519914, -10918434, 29086251, -43480464, 26379556, 5695537, 34664346, 21893625, -121731052, 8168195, -6287702, 184521159, -37641322, 61785561, 52537497, -211737064, 315974536, -225086287, 140937360, -39914208, -6798801, 13604129, -2929504, -2883777, 2105581, -270255, -194520, 60683, -93517, 75361, 4119, -24778, 10794, 1464, -2615, 258, 317, -63, -12, 10, -5, -1, 1]]], "char_order": 21, "char_parity": 1, "char_degree": 12, "char_conductor": 49, "char_orbit_label": "bb", "char_is_real": false, "Nk2": 1764, "analytic_conductor": 3.521402729138465, "level_radical": 21, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [441, 21, [344, 199], [21, 16]], "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [37, 46, 100, 109, 163, 172, 235, 289, 298, 352, 415, 424], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c21", "trace_display": [1, 0, 0, 0], "traces": [48, 1, 0, 3, 0, 0, 0, -6, 0, 30, 9, 0, 0, 42, 0, 29, 5, 0, -26, 5, 0, 1, 4, 0, -56, 62, 0, 7, -12, 0, -36, 14, 0, -76, -7, 0, -20, 60, 0, 28, -41, 0, 12, -44, 0, 16, -13, 0, -84, 12, 0, 92, -14, 0, -38, -105, 0, 3, -57, 0, 11, 16, 0, -110, -21, 0, 34, -22, 0, 0, -6, 0, -69, 90, 0, -49, 0, 0, 34, -55, 0, 91, -28, 0, -44, 26, 0, 45, -11, 0, 0, -84, 0, 90, -150, 0, 124, -119, 0, -31, 148, 0, 168, -23, 0, 54, 16, 0, -37, 86, 0, -63, 16, 0, 80, -39, 0, 58, 0, 0, -65, 74, 0, -64, 50, 0, 7, -20, 0, 72, -95, 0, 49, 164, 0, -133, 25, 0, 19, 133, 0, 24, 79, 0, -112, -68, 0, -82, 211, 0, -75, -136, 0, -42, -87, 0, 61, 266, 0, -98, 21, 0, -27, 63, 0, 6, 100, 0, 22, -18, 0, -46, 82, 0, -105, -37, 0, 2, -61, 0, 14, -98, 0, 52, -118, 0, -66, -162, 0, 176, -183, 0, 106, -105, 0, -182, 210, 0, 91, 14, 0, 33, -147, 0, -48, -60, 0, -204, -21, 0, -56, -84, 0, 36, -105, 0, 196, -72, 0, -122, 16, 0, -121, 28, 0, 60, -77, 0, 119, 60, 0, -76, -72, 0, 32, 24, 0, 112, -43, 0, 64, -177, 0, 196, 210, 0, -125, -10, 0, 70, 44, 0, 96, -51, 0, -27, 56, 0, 70, 130, 0, 7, -113, 0, -53, -14, 0, 60, 29, 0, -152, 160, 0, -37, -22, 0, 4, 18, 0, -7, 140, 0, -116, 80, 0, 154, 161, 0, 159, -28, 0, -92, -60, 0, 44, 413, 0, -122, 154, 0, 301, -121, 0, 29, 175, 0, -116, 42, 0, -70, -39, 0, 33, 77, 0, -17, 93, 0, -126, 178, 0, 182, -49, 0, 28, -56, 0, -107, 161, 0, -86, 176, 0, -274, 91, 0, 119, -62, 0, 114, 124, 0, -147, -258, 0, -179, 8, 0, -60, -126, 0, -44, 26, 0, 76, -142, 0, -124, -152, 0, 90, -195, 0, -35, -23, 0, -133, -72, 0, 329, -56, 0, 186, -224, 0, 337, -115, 0, -19, 28, 0, -188, -165, 0, 161, -89, 0, 217, 239, 0, -32, 301, 0, -50, -345, 0, -215, -165, 0, 97, -195, 0, 158, -104, 0, -140, -72, 0, 176, -14, 0, 124, -7, 0, -35, -160, 0, 109, -47, 0, 60, -95, 0, 352, -129, 0, 84, 243, 0, -513, -190, 0, -58, 70, 0, -44, 207, 0, -73, 44, 0, 164, 294, 0, -259, 55, 0, 70, -79, 0, -146, 149, 0, -123, -210, 0, -51, 267, 0, -42, 73, 0, -94, -221, 0, -80, 180, 0, -168, -17, 0, 37, -107, 0, -18, -77, 0, -218, -40, 0, -29, 92, 0, -109, 5, 0, -200, -189, 0, -70, 72, 0, -286, -397, 0, -57, -119, 0, 116, -153, 0, 54, -48, 0, -165, -101, 0, 185, -224, 0, 28, 131, 0, 142, 176, 0, 45, -378, 0, 82, -136, 0, -69, -272, 0, -268, -30, 0, 36, 90, 0, 175, -97, 0, 70, -87, 0, -262, 42, 0, -83, 108, 0, 159, 94, 0, 23, 133, 0, -111, 75, 0, 49, 90, 0, 178, -153, 0, -69, 70, 0, -72, 236, 0, 140, 346, 0, -67, -10, 0, 5, 280, 0, -161, 221, 0, 24, 335, 0, 110, 168, 0, 288, 105, 0, 150, -8, 0, -168, 249, 0, -224, 79, 0, 105, -31, 0, 63, 56, 0, -34, 77, 0, -149, -129, 0, -8, 86, 0, 36, 145, 0, 159, 236, 0, 35, -67, 0, -38, -12, 0, 73, 56, 0, 227, 23, 0, -226, 251, 0, 107, 262, 0, 137, 51, 0, -392, 96, 0, 9, 236, 0, 41, 49, 0, -58, -102, 0, 136, 166, 0, 207, -56, 0, 0, -111, 0, 266, -73, 0, -49, -368, 0, 26, 56, 0, -1, -97, 0, 170, -90, 0, 225, -289, 0, 45, -331, 0, 70, -216, 0, 180, 87, 0, 40, -343, 0, 243, 327, 0, 20, -238, 0, 120, -9, 0, 275, 471, 0, 49, -174, 0, 267, 187, 0, 164, -63, 0, -22, -182, 0, 323, 298, 0, -6, 44, 0, 71, 41, 0, 14, -176, 0, 216, -7, 0, 134, 259, 0, 70, 67, 0, -280, 48, 0, 224, 261, 0, 130, -40, 0, -518, -122, 0, 114, 260, 0, -78, -189, 0, -66, 290, 0, -75, -156, 0, 104, -146, 0, -387, -30, 0, -371, 54, 0, -208, 125, 0, 39, 49, 0, 252, -288, 0, 244, -129, 0, -257, -226, 0, -134, -279, 0, -91, 154, 0, 100, -476, 0, -38, -28, 0, 3, -112, 0, -158, -196, 0, 85, -420, 0, -168, -97, 0, -21, -26, 0, 157, -492, 0, 104, -392, 0, -220, -55, 0, 22, 144, 0, 126, -129, 0, 64, -12, 0, -329, 154, 0, -107, -313, 0, -158, -98, 0, 93, 102, 0, 134, -18, 0, -198, 11, 0, -373, 219, 0, -56, -300, 0, -338, 96, 0, -55, 308, 0, 78, 73, 0, -152, 278, 0, 24, 129, 0, -179, 362, 0, 7, 29, 0, 151, 252, 0, -354, 350, 0, -272, 259, 0, -10, -56, 0, -288, 117, 0, 252, 30, 0, -203, 247, 0, -160, 165, 0, -150, 210, 0, -281, 178, 0, -173, 199, 0, -18, 231, 0, -241, 182, 0, -98, -140, 0, -96, 325, 0, -447, 112, 0, -265, -115, 0, -321, -25, 0, -78, 316, 0, -236, -101, 0, 231, 256, 0, 575, -21, 0, 60, -7, 0, -29, -176, 0, 105, -661, 0, -264, -398, 0, 160, -163, 0, 126, -174, 0, -232, -336, 0, 427, 42, 0, 68, -417, 0, -313, -398, 0, 127, -50, 0, 91, -211, 0, 63, 462, 0, 277, -149, 0, 142, -567, 0, 574, -145, 0, 103, 172, 0, -206, -118, 0, 254, 66, 0, 105, -153, 0, 61, -20, 0, -36], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 49, 7, 1, 21, 0]], "char_orbit_index": 28, "prim_orbit_index": 7, "minimal_twist": "147.2.m.a", "char_is_minimal": true, "conrey_index": 37, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}