# Stored data for newform 441.3.n.b, downloaded from the LMFDB on 25 April 2024. {"label": "441.3.n.b", "space_label": "441.3.n", "level": 441, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504493030900153, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 51048820683164113, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, -3, 1]], [13, [16, -4, 1]]], "qexp_display": "q+(2-\\zeta_{6})q^{2}+3q^{3}+(-1+\\zeta_{6})q^{4}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "n", "char_is_real": false, "Nk2": 3969, "analytic_conductor": 12.016379658289093, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.171", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 6, [344, 199], [1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [128, 410], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.008", "prec": 17}, {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "12.258", "prec": 20}, {"__RealLiteral__": 0, "data": "0.563", "prec": 17}, {"__RealLiteral__": 0, "data": "102.435", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c6", "trace_display": [3, 6, 0, 0], "traces": [0, 2, 3, 6, -1, 0, 9, 0, 0, 18, 6, 0, -3, 4, 0, 0, 11, -27, 27, -11, -6, 0, 3, 0, 0, 26, 12, 54, 0, 78, 18, -32, -27, 0, -27, 0, -9, 34, 0, 12, -60, -21, 0, 61, -3, 0, -48, 84, 33, 0, 39, -81, -8, 0, 81, -12, 0, -33, 156, -87, -18, -56, 0, 0, -142, -24, 9, 31, 0, 0, 0, 0, 0, -65, 0, 78, -11, 0, 36, -38, -66, 162, -21, -84, 0, -54, 0, 234, -30, 216, 54, 0, 48, -96, 84, -66, -81, 115, 0, 0, -13, 0, -81, -80, -60, 0, 0, -243, -27, 52, -18, 102, 0, -156, 0, 192, -78, 36, -174, 0, -180, 236, -168, -63, -32, 0, 0, -32, -105, 183, -24, 0, -9, 0, 0, 0, -135, 0, -144, -5, 0, 252, 54, -12, 99, -156, -195, 0, 34, 0, 117, 40, -165, -243, 0, -192, -24, 40, -114, 0, 54, 0, 243, 106, 0, -36, -168, 330, 0, 153, -162, -99, 61, -402, 468, 0, -33, -261, 432, -108, -54, -464, 0, -168, 480, 204, 0, -27, 0, 0, -132, -402, -426, 265, 0, -72, 0, 0, 27, -290, 0, 93, -78, 0, 0, -42, -120, 0, -44, -33, 0, 94, 0, 0, -486, 366, 0, 0, 156, -195, 6, -108, 0, 52, 0, 234, -156, 0, -33, 532, 288, 0, -390, 351, 108, 168, 87, -114, 0, -696, -198, 238, 354, 486, 112, 0, -63, -88, -480, -252, 228, 0, 0, 96, -48, -162, 179, 0, 0, 0, 0, 702, 276, 0, -90, 0, 0, 648, 31, 324, 162, 268, -297, 0, 327, 0, 144, 112, -15, -288, 0, -84, 252, -374, -54, -198, -12, 0, -243, -46, 0, 345, 130, 438, 0, 174, 510, 0, -264, 192, -39, 0, 60, 0, -242, 336, -243, 1066, 0, -240, -384, 426, -180, -155, 0, 0, 76, 84, 0, -78, 0, -729, 0, 0, -81, 52, 0, 156, -105, 0, -54, -2, 84, 306, 330, 186, 0, -77, 0, -468, 108, -96, 0, 0, 915, 576, -402, -195, -234, -416, 0, 108, 27, 0, -522, -216, -216, 0, -108, 1026, -540, 240, -696, 708, 0, 390, -504, -716, 528, -189, 408, 0, -96, -1160, -81, 0, 420, 0, 0, 166, 66, -96, -402, 0, -315, 0, 0, 549, 115, 0, -72, 432, 0, 0, -216, 228, -27, -362, -870, 0, 143, 0, 0, -256, 78, 0, 0, 102, -405, -221, -126, 0, 40, 0, -432, 168, 0, -15, -66, 1356, 0, 682, 282, 756, 0, -351, 162, 0, 243, -36, 732, 486, 297, -590, 0, -468, -104, 528, -585, -812, 0, 0, -216, -159, 102, -432, 0, 0, 0, 0, 351, -21, 0, 120, 327, 0, -495, -65, 798, -729, -96, -1380, 0, -734, 0, -576, 702, -351, -72, 0, 504, 120, 435, 183, -342, -143, 0, 0, -696, 0, 162, 272, 357, 0, -118, 690, 729, 106, 840, 318, 0, -399, 0, -1404, -132, -108, -704, 0, -504, -1574, -228, 990, 675, 0, 0, 312, 144, 459, 16, 0, -486, 0, 0, -297, 303, 0, 183, 84, 0, -1206, -120, 351, 1404, 250, -276, 0, -78, 0, -99, -478, 0, -783, 0, -84, 1296, 486, 465, -324, 324, 0, -162, -650, 0, -1392, 486, -312, 0, -623, -327, -504, 39, -858, 1440, 0, 168, 612, 10, -918, 0, 488, 0, -81, -168, -195, 0, -312, 0, 0, -540, -1131, -396, -545, 0, -1206, 0, 0, -1278, 871, 0, 795, -156, 0, 0, 0, 975, -216, 438, -3, 0, -352, 0, 0, 748, 324, 81, 0, 264, -870, 192, -978, 0, -461, 0, 279, -20, 0, -234, -224, 297, 0, 336, 336, 0, -902, 1599, -126, 0, -615, -360, -1598, 192, 0, 852, 0, -132, -262, -465, -99, 40, 0, 0, 1660, 570, 282, 84, 0, 0, 0, 0, 0, -210, 0, -1458, 13, 0, 1098, -297, -810, 0, 87, 156, 0, 106, 0, 468, -1104, -231, -585, 0, -1704, 18, 382, -6, -324, 420, 0, 0, 1248, 0, 156, 372, 168, 0, -578, -231, 702, 153, -1212, -468, 0, 810, 0, -192, 1809, -99, -1308, 0, 1596, 1342, 0, 864, -182, 0, 0, -390, 30, -1170, 189, 0, 1053, 0, 0, 324, 374, 0, 504, 3, 0, 261, 700, -324, -342, -1080, 1536, 0, -24, 0, -2088, 2052, -1026, -594, 0, 720, 714, 232, 1014, 1062, 664, 0, 1458, 390, 0, 336, -1340, -1074, 0, -432, 93, -189, -317, -204, -264, 0, -1074, -1440, 1056, -1740, -756, 54, 0, 684, 2620, 924, 0, 312, 0, 0, 436, 249, 288, 330, 0, -144, 0, 0, -486, -966, 0, 537, -1022, 0, 0, 265, -2052, 0, -416, 1725, 0, 894, 0, 0, -108, 1296, 2106, 0, 240, 828, 130, 216, 0, 228, 0, -270, 224, 0, 0, 580, 546, 0, -756, -351, 1944, 681, 195, 93, 0, -384, 972, 780, 243, 486, 598, 0, 804, 204, 636, -891, 671, 0, 0, 84, -1050, 981, 814, 0, 0, 0, 0, 432, 718, 0, 336, -284, 0, -45, 660, 33, -864, 1356, -1380, 0, 1187, 0, -252, -188, 918, 756, 0, 0, -1122, -351, -1632, -162, -1424, 0, -594, 1215, 0, -36, 622, -366, 0, 486, -1782, -729, -804, -885, -138, 0, 114, 0, 248, -780, 1035, 1056, 0, 390, 208, -2436, 1314, -66, 0, 0, 238, 108, 522, -159, 0, 1530, 0, 0, 0, 52, 0, -792, -216, 0, 576, 1107, -2496, -117, 0, -63, 0, -780, 0, 180, 1390, -327, 0, 0, -3000, -726, 84, -195, 1008, -266, 0, -729, -56, 0, 3198, -2760, -216, 0, 442, -2202, -720, -702, 1380, -1152, 0, -351, 1278, -702, 162, -540, 940, 0, -465, -336, 696, 0, 336, 0, 0, 366, 3, 228, 260, 0, 252, 0, 0, 0, -804, 0, -234, -1050, 0, 0, -63, 408, -2187, -119, 1590, 0, -1202, 0, 0, 1380, -324, -243, 0, 318, 156, 616, 723, 0, -216, 0, 468, -399, 0, -315, 864, -2106, 0, 44, -2928, -162, 1420, 864, -6, 0, 1740, 252, 1048, -2361, 918, -2280], "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, 63, 14, -1, 6, 0]], "char_orbit_index": 14, "prim_orbit_index": 14, "minimal_twist": "9.3.d.a", "char_is_minimal": false, "conrey_index": 128, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [2, -1], [3, 0], [-1, 1], [-2, 4], [6, -3], [0, 0], [-5, 10], [9, 0], [0, 6], [-1, 2], [-3, 3], [0, 4], [0, 0], [-6, 12], [0, 11], [-18, 9], [18, -9], [-11, 11], [-2, -2], [0, 0], [0, 3], [16, -32], [-15, 30], [13, 0], [4, 4], [27, 0], [0, 0], [26, 26], [0, 18], [-32, 32], [-9, -9], [-3, 6], [-27, 27], [0, 0], [-9, 9], [34, -34], [-11, 22], [0, 12], [-30, 0], [-14, 7], [0, 0], [61, -61], [-1, -1], [-18, 36], [0, -48], [56, -28], [0, 33], [0, 0], [26, -13], [-54, 27], [-4, 0], [0, 0], [54, -27], [-6, 0], [0, 0], [-33, 33], [78, 0], [-29, -29], [-6, -6], [0, -56], [-32, 64], [0, 0], [-71, 0], [-16, 8], [0, 9], [31, -31], [9, -18], [48, -96], [0, 0], [-18, 36], [-45, 90], [0, -65], [34, -68], [39, 0], [0, -11], [0, 0], [12, 12], [0, -38], [-44, 22], [81, 0], [-21, 21], [-28, -28], [0, 0], [0, -54], [61, -122], [78, 78], [-15, 0], [72, 72], [0, 54], [0, 0], [16, 16], [-96, 96], [84, -84], [-22, -22], [-27, -27], [115, -115], [0, 0], [-9, 18], [-13, 13]]}