# Stored data for newform 859.2.f.a, downloaded from the LMFDB on 14 November 2024. {"Nk2": 3436, "analytic_conductor": 6.859149533627985, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 859, "char_degree": 12, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 13, "char_parity": 1, "char_values": [859, 13, [2], [11]], "cm_discs": [], "conrey_index": 100, "dim": 840, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 343630938971, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 859, 6, 1, 13, 0]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "859.2.f.a", "level": 859, "level_is_powerful": false, "level_is_prime": true, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [859], "level_radical": 859, "minimal_twist": "859.2.f.a", "prim_orbit_index": 6, "related_objects": [], "relative_dim": 70, "rm_discs": [], "sato_tate_group": "1.2.3.c13", "self_twist_discs": [], "self_twist_type": 0, "space_label": "859.2.f", "trace_display": [-10, -5, -20, -3], "traces": [840, -10, -5, -74, -20, 5, -3, 2, -69, 7, -25, -58, -10, 9, -148, -40, -1, 5, -38, -92, 17, 15, -18, 27, -66, 7, -17, 29, 7, -5, 27, 20, 49, 5, 43, 32, -86, -13, 2, 59, 9, 72, 40, 44, -49, 52, -22, 159, -11, -73, 65, 73, 25, 11, 81, -302, -192, 27, -23, -62, 26, 79, 93, -78, 10, 74, 65, 69, -57, 19, 21, -234, -95, 25, -120, -18, -95, -3, -13, -244, -95, -19, -16, -48, 99, 45, -123, 110, 49, 217, -82, 3, -57, -77, -12, 56, 5, 5, -121, -37, 83, 141, -235, 107, -66, 101, -44, 158, 11, -379, 100, -9, -307, 167, -56, 53, -153, 130, 4, -244, -41, 19, 62, -128, -29, -184, 11, -44, 52, -17, -52, 103, 14, 92, -58, 26, -9, -236, 0, 232, 0, -239, -74, -87, 121, 215, -195, 33, 73, -250, 89, -108, -71, -70, 119, -636, 169, 63, -138, 9, -95, 160, 76, 134, -226, -101, 86, -115, 706, 184, 74, 329, 29, 65, -49, 4, -92, 209, -163, -28, 143, -297, -67, 219, -71, -34, -27, 2, 191, -15, 119, 399, -36, -342, -304, 52, 56, -92, 106, -267, 257, 13, -162, 45, -298, 121, 290, -282, -254, 314, 149, 9, -235, 278, 31, 24, 186, 293, -264, -278, -19, 177, 45, 401, 292, 352, 59, 168, 18, -30, 94, -167, 82, 51, 96, 61, -96, -235, -116, -220, 211, 336, 97, -743, -146, -14, -200, 225, 207, 369, -141, 390, 153, 355, -8, 256, 238, 317, -193, -538, -434, -179, -208, 238, 106, -594, 180, 345, 24, -426, -21, -224, 254, -6, 170, -39, -185, 307, -461, 370, -480, -264, 256, -418, -54, 240, 316, 412, 95, -172, 318, -275, 11, -219, 31, -10, -216, 265, -206, -352, -153, -237, 301, 289, -168, 555, -274, 381, 172, 74, 79, 327, 50, 116, 186, 491, 149, -166, -64, -213, 31, 166, -291, -75, -258, 429, 276, 50, 136, -174, 235, -173, -65, -459, -527, -179, 61, -506, -473, -468, 152, -639, -110, -13, -354, 193, 306, 154, -98, 643, -261, 0, 349, 275, 378, -720, 325, -23, -229, -563, 666, 386, -199, -701, -15, 815, -14, 157, 37, -185, -38, 125, -128, 313, -354, -306, 109, -361, -191, 32, -71, -154, 147, -1202, -779, 224, 450, -659, 109, 401, -164, 363, -71, -855, 494, -399, -229, 240, 76, 78, 82, 478, -477, -200, 223, 63, 251, -336, 112, 307, 391, -69, 192, 570, 117, -710, 161, 105, -362, -612, -37, 487, -251, -33, 1, -349, -91, -138, 94, -789, 247, 547, 393, 93, -62, 367, -789, 415, -471, 149, -127, -332, 161, 188, 194, 250, -255, -16, 91, 399, 2, -624, 561, 289, 172, 70, 134, 96, 282, 9, -14, 229, 173, 444, -901, -137, -190, -180, -545, -221, -247, 54, -688, 169, -29, 139, -196, 695, 324, -228, 312, -439, 779, 30, -74, 200, -64, -35, -198, -300, 231, 717, 397, 263, -234, 53, 595, -898, 265, 98, 431, 165, 65, 54, 175, -292, -179, -1191, 270, 364, -108, 543, -538, -224, -511, 504, 302, -120, 212, 544, 4, 81, -383, 515, 178, -265, 490, -296, 174, 661, -79, -480, -205, -216, -73, -495, 497, 52, 134, 43, -383, 353, -185, 208, 504, 120, 62, 325, 236, 1019, -286, 843, 404, -1015, -145, 81, -213, -194, -458, 166, -961, -1, 205, 331, 525, 591, 564, 246, -20, -435, 379, 458, -121, -598, 247, 636, 9, 65, -218, 125, 198, 193, -35, -624, 492, 60, -102, -987, -693, -674, 663, 112, -65, 1012, 236, 597, 274, -1110, -1994, -1624, -467, -428, -384, 475, -283, 1195, 7, -1427, 295, 611, 73, 896, 238, -246, 529, 435, -93, 200, 200, -740, -299, -57, -167, 283, -511, 504, 267, 515, 45, 102, -149, 317, 374, 178, 124, 273, -392, 739, 783, -455, 239, -1507, 400, -793, -2204, -799, 439, 1111, 55, 452, 659, 517, 229, 168, 501, -341, 300, -593, -167, 113, 293, 609, 117, 242, 244, -173, 153, 518, -709, 44, 136, -1409, -184, -94, 625, 211, -529, 918, 225, 991, 337, 597, 478, 439, -334, 518, 297, -518, -598, -80, -694, -881, 794, 647, 98, 1261, 208, 296, -222, -231, -789, -684, -75, -276, 94, -11, 148, -437, 211, 175, -935, -29, 536, 936, -164, 221, 230, 317, -16, -1093, 298, -136, 577, 371, -93, 432, 223, -672, -1305, -1473, -401, -130, -494, -17, 222, -83, -189, 38, -394, 484, -83, 407, 242, 1413, 209, 105, 507, 140, 41, 944, -65, 44, 593, -206, -528, 1108, 470, -1502, 576, -5, 631, 393, 425, -255, 240, 412, -416, -997, -315, 846, -710, 257, -94, 1, 131, 843, -94, 78, -157, -381, -518, 365, -495, -866, 33, -1008, 303, 73, 791, -271, 802, -145, 264, 68, -943, 989, 568, -1108, -88, 112, 411, 196, -154, -489, 541, -586, 358, -544, 513, -559, 625, 708, -564, -942, 245, 114, -870, -480, -215, -506, -33, 264, -377, 471, -744, 177, 65, -1941, 217, 43, 538, 362, -368, 480, -137, -493, -50, 354, -420, -10, 41, -655, -354, 134, 99, -1500, -272, 634, 633, -647, -106, 639, 243, -463, 238, -947, -81, -932, -1039, -788, -451, -166, 257, 537, -369, 499, -582, 432, -128, -834, -187, -208, -882, -1902, 93, -202, 268, 160, 248, 112, 517, -2213, -243, -774, 376, -158, 366, 1951, -542, 571, -13, 526, -579, -909, -45, -1934, -502, -907, -91, 1126, 322, 902, -472, 702, -850, -816, 951, -247, -375, 686, 685, 312, 65, -216, -456, -869, -195, -722, 497, 906, -513, 169, 345, 438, 788, -845, -513, 645, -84, -1014, -327, -490, 131, -696, -707, -1063, 300, -323, -96, 833, -598, 789, 135, 975, 223, -1672, 606, 1215, -203, 335, 25, 765, -132, -1302, -479, -488, 225, -538, -40, 1876, 247, -398, 816, 254, 277, -53, 1099, -1, -1292, 1439, 698, -667, 160, 582, 375, 76, 31, -332, -81, 851, 799, -383, 216, -1100, -1063, -27, -414, -871, -15, -818, 169, -561, 77, -787, -364, -638, -762, -691, 866, -1046], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}