# Stored data for newform 8029.2.a.h, downloaded from the LMFDB on 18 April 2024. {"label": "8029.2.a.h", "space_label": "8029.2.a", "level": 8029, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525197425155933, "dim": 71, "analytic_rank": 0, "is_twist_minimal": true, "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32116, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 64.11188778288601, "level_radical": 8029, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8029, 1, [5736, 778, 4775], [1, 1, 1]], "inner_twist_count": 1, "level_primes": [7, 31, 37], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 71, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, 1], [31, 1], [37, -1]], "trace_display": [6, 8, 0, -71], "traces": [71, 6, 8, 78, 0, 5, -71, 18, 87, 4, 57, 21, -20, -6, 22, 88, -19, 1, 23, 25, -8, 18, 34, 15, 81, -13, 20, -78, 16, 6, -71, 47, -16, 32, 0, 125, 71, 13, 30, 31, 17, -5, 38, 80, -1, 26, 32, 61, 71, 47, 73, -23, 31, 47, 11, -18, 17, -2, 97, 103, -1, -6, -87, 100, 46, 43, 75, -43, 10, -4, 131, -11, -15, 6, 76, 41, -57, 89, 8, 10, 171, 14, 18, -21, 47, 90, -59, 13, 18, 69, 20, 110, -8, 39, 72, 100, 23, 6, 168, 46, -46, 76, -1, 2, -22, 53, 95, 96, 44, 35, 8, -88, 52, 47, 51, 105, -136, 15, 19, 79, 100, 39, 135, -78, 0, -1, 64, 135, 99, 28, 67, -98, -23, 44, 43, 23, 68, -8, 20, -25, -6, -50, -6, 203, -15, 1, 8, 78, 111, -128, 77, 123, -42, -18, 0, 9, -12, 104, 123, 159, -34, -116, 28, 120, 25, 43, -10, -15, 101, 94, 62, 11, -98, -38, -81, 155, 81, -7, 138, 28, -2, 13, 87, 61, 0, -5, 10, -24, -20, 77, 99, 87, -13, 36, 67, 78, 60, -80, 20, 151, 73, -28, -16, 103, 85, -2, 42, -75, 68, -6, 64, 7, 53, 132, 67, 156, 71, 112, 160, -6, 180, 5, 30, -47, 61, 165, 142, -41, 24, -60, 16, 83, 133, -7, 75, 124, -81, -32, 107, 182, 23, 65, 8, 47, 0, 97, 182, -18, 133, -53, 154, -125, 56, 56, 50, 220, -20, 169, -71, 41, 75, -19, 139, 44, 3, -13, 91, 277, -16, 143, 152, -144, -30, -91, 368, 148, 70, 151, -87, -31, 97, 88, 32, 331, -190, -50, -17, 161, 100, 44, 240, -45, -97, 5, 122, 18, -45, -63, 199, 245, -38, -68, 71, 5, -17, 54, 114, -80, -3, -4, 28, 18, -38, 145, 1, -65, 79, -151, 139, 143, -16, -26, 267, 170, 13, -56, -91, 18, -32, 49, 152, 18, 87, -154, 124, -61, 72, 127, -43, 174, -57, -26, -71, 299, 279, -70, 98, 55, -11, -47, 88, 199, -25, -54, 85, 88, -73, -176, 201, -98, 182, -43, -164, 23, -120, 108, -92, 171, 148, 4, -31, -21, 12, 67, 30, -5, 65, -47, 68, 86, 53, -145, -39, 37, -11, 84, 289, 5, -29, -167, -61, 18, -25, 14, 20, -240, -67, -69, -17, -109, 160, -50, 20, 76, 198, 2, 57, 143, 31, -8, 246, 171, -97, 109, 5, 21, -48, 158, 309, -103, -39, 147, 113, 43, -35, 176, 1, 8, -3, -73, 188, 11, 7, 6, -60, 179, -209, -33, 89, 148, 87, -65, 201, 21, -115, -157, 0, -100, 204, -184, 130, -97, -91, 205, -46, -95, 26, -283, 126, -389, -75, -43, 26, 256, -22, -178, 15, 22, -75, 30, 53, -267, 42, 25, 22, 43, 121, 131, 45, 358, -20, 0, -10, -14, 226, 97, -36, 134, -158, 4, 216, 503, -208, -91, 127, -88, -131, -191, 123, 287, 113, -254, -106, 11, -29, 199, -19, 1, 51, -44, 15, -12, 101, -140, 315, 452, 60, -6, -49, -109, 50, -52, 52, 95, -76, -20, 19, -397, 261, -34, 214, -41, -127, -67, 21, 158, -18, -46, 57, 94, 190, 172, 17, -189, -84, -89, 142, 234, -132, -125, 154, -97, -8, 404, 22, -89, 109, -1, 135, -10, -92, 237, -59, -28, -185, 215, -171, -270, 119, -241, 108, -34, -63, -14, 69, -9, -32, 120, -122, -278, -18, -550, 101, -136, 30, 1, 16, 21, -23, 298, 183, 88, 21, 212, -47, 222, 111, -281, 218, -339, 88, -90, 301, 338, -142, -365, -55, 49, 59, -129, 122, -99, -132, 55, -166, -13, 247, -188, 126, -25, -19, -141, -18, 8, 335, -76, -7, 180, -19, -69, -115, 124, 23, -24, 275, 355, -20, 22, 428, 301, 99, -293, 19, -110, 10, -62, 61, -102, 97, -190, 8, -146, 2, -147, -148, 110, -51, -39, 192, 243, 20, 104, 41, 195, -72, 1, 18, -305, 153, -72, 209, -100, 189, 38, -170, -371, -213, 130, -23, -66, 127, -18, 21, -315, -102, -6, 14, -96, -77, -367, 163, -291, -168, -140, 179, -554, 81, -141, 178, -46, 190, 684, 23, 136, 70, -436, 46, -142, 164, 13, -23, -111, -34, -76, 15, -31, -223, 26, 46, -217, 1, 243, -77, -68, -3, 64, -104, -2, 291, -325, 233, -219, -22, 177, 22, 180, 235, -179, 193, 25, 216, -53, 210, -15, -75, -278, 81, 30, -95, -791, 96, -389, -143, -164, 61, -96, -71, -65, 165, -287, -170, -101, -44, 589, 352, -483, 117, -340, 62, -35, 271, 130, -52, 170, -81, 204, -8, -112, 595, -405, -128, -65, -237, 88, -68, 357, -149, 144, -100, 207, -52, -601, 154, -56, 157, -121, -251, -47, -130, 590, -200, 116, 57, -50, -51, 13, -207, -213, 43, 23, 189, -105, 77, 18, 148, -513, -114, 43, 136, -354, 297, -633, -81, -105, 422, -15, 353, -163, -211, -396, 34, -258, -19, -95, -77, -345, -20, -197, 402, -79, 69, 302, -59, -238, -146, 309, -100, 100, 361, 256, 34, 142, 77, -39, 39, 385, -205, 18, -90, 109, -135, -3, 202, 284, -267, 79, 373, 78, 133, 248, -160, 119, 40, 84, 0, -130, 117, -224, 207, -216, -71, 1, 146, 212, -352, -142, 257, 15, -64, -84, 427, -261, 152, -303, 181, -135, -47, -20, -16, -489, -233, 119, -99, 103, 50, -656, 40, 30, -250, -28, 176, 279, -155, -14, 141, -17, -67, -489, 323, -132, 10, 45, -69, 98, 81, 475, 12, -413, -3, -6, 23, 427, -149, -16, 187, 61, -81, -44, 183, -300, -151, -320, 79, 422, -43, -387, 243, -500, 97, 336, 172, -23, 155, -126, -148, 87, -63, 314, -68, 385, 71, -13, 122, 81, 68, 8, -18, -95, 213, -126, 251, -106, -20, 11, 87, -144, 19, -594, 258, 25, 94, 365, 63, -223, -28, 408, 6, 122, 49, -688, 176, -47, 23, 50, 449, 499, 81, 114, 20, 238, 6, -789, 55, 117, -432, 227, 64, -203, -139, 26, 198, 63, -163, -248, 15, -290, 235, -730, 502, -270, -58, -1, 16, 251, 16, -287, 107, -46, -8, -358, 214, 191, -269, 581, 614, -78, 173, 299, 48, -310, 177, -216, -111, -248, 63, -99, 73, -148, 45, 128, 13, 112, -510, -32, -87, 277, -77, 80, 619, -158, 223, -422, -95, -123, 118, -376, -7, -175, 158, 279, 42, 389, 16, -5, -13, 57, 68, 18, 299, 404, 59, 62, 91, 236, 0, -850, 34, -708, 126, -149, 162, -9, 27, 367, -22, -253, -370, 414, 12, 139, 270, -307, 271, 39, -34, -104, -11, 209, -147, 6, -41, 525, -123, 0, 615, -125, 260, -458, 16, -159, 308, -43, -178, 236, -81, -108, 34, -625, -8, -144, 314, -167, -154, 116, 188, 788, 79, -386, -26, -930, -28, 59, 573, -172, 200, 369, -71, -120, -17, -277, 251, 227, -177, 87, -25, 102, 87, -322, 60, 10, 189, -43, 456, 208, -3, 191, 308, -216, 10, -332, 39, 196, -396, -221, 290, 15, 20, -13, 77, 201, -50, 310, -101, 47, 20, -243, 216, -323, 70, -94, 425, -12, -240, -763, -125, 370, -62, -261, 45, -648, -150, -226, -6, -11, 324, -142, -30, -195, -30, -431, 98, -334, 26, 19, -285, -388, -87, 38, 14, 692, -16, -46, 97, 410, 81, -274, 181, -19, -10, 46, -183, -155, -180, 61, -112, -234, -343, -420, -81, -31, 388, -159, -211, 311, 171, 7, 319, -453, 11, -465, -329, -158, -138, 78, 290, -1, 140, 32, 684, -28, -179, 158, -111, -970, 189, 70, 2, -184, 201, -355, -17, -663, -125, -13, 109, 451, -196, -803, 63, 191, -87, 60, 422, -390, -140, 244, -59, -61, 378, 217, 519, 671, 91, 56, 0, -282, -71, -183, -25, -84, -132, 5, -177, 429, -743, -87, 121, -304, -10, -615, 73, -435, -157, -459, 78, 24, -201, -133, 204, -627, -157, -176, 20, 42, -72, -829, -282, -90, 275, -77, 765, 125, -38, -5, -359, 79, -99, -692, 204, -628, -259, -517, -168, -87, -237, 410, -314, -396, -1, -274, 13, -12, 254, -128, 81, 56, -238, -36, -67, 226, -23, -665, -57, -80, -67, -511, 121, 144, 71, -39, 49, -78, 89, 210, -128, 772, -481, 16, -60, -301, 191, -255, -364, -152, 6, 80, 198, 202, 91, -557, 364, 77, -20, 198, 1, -624, 507, -561, -213, -151, -428, -79, 93, 62, -151, 13, -73, 57, 293, 35, 241, -375, 290, 28, 307, -137, 117, -389, -246, 2, 16, 174, -188, -258, -429, -26, -19, -103, -72, 569, 502, -1069, -38, -195, -85, -150, -97, -603, 295, 6, 276, 2, 30, 157, 28, -326, -195, 20, -42, -325, 491, -793, -115, 134, 277, 75, -32, -591, 337, -1083, -150, -77, -68, -396, -181, 260, -451, -441, -136, 6, 149, 382, -442, -274, 249, 563, -64, -308, 238, 31, -154, -568, -119, -7, -44, -430, 352, -61, -235, 368, -53, -96, -46, -578, -686, -677, -188, -132, 481, -93, -11, -47, -96, -47, -67, -461, -220, 35, 10, -700, -59, -156, -89, 432, 161, -63, 17, 192, -71, 48, 217, -149, 252, 105, -370, -112, -67, -95, -48, -761, -277, -102, -160, -224, 39, -439, 134, -163, 618, 6, 215, 427, -21, 285, -419, 18, -180, -504, 110, -47, -374, -185, -83, -5, 11, 304, -951, -13, 122, -739, -30, -300, 233, -459, 60, -409, -294, 47, -175, 152, 681, -479, -357, -179, -61, -581, 317, 54, -48, -562, -73, -165, 156, -533, 204, -121, 122, -528, -142, 250, 38, -294, -227, -637, 306, 41, -59, 64, 319, -515, 14, 288, -24, -35, -530, -456, 168, -510, -269, 60, 639, 23, -629, 26, -611, 528, -16, -403, 329, -609, -22, -223, -619, -83, 217, 226, 263, 80, -416, 214, -133, 206, 256, -204, -21, -465, -239, 7, 548, -116, -345, -497, -31, -117, -75, -22, -222, 50, -10, -969, 206, -124, -93, 214, 165, -127, -27, -217, 81, -567, 467, -649, 187, 457, -1, 32, 150, -278, -187, 308, -85, 147, -107, -47, 118, 468, -713, -487, 533, -182, 104, -340, -313, -773, -517, -129, -23, 267, -245, -713, 130, -923, 51, -65, -283, -103, -172, -857, 160, 8, -8, 26, 433, -204, -11, -140, 286, -47, 386, -113, -285, -245, -160, -96, 0, -848, -383, -524, -331, -199, 161, -97, 426, 722, -246, -285, 224, 78, -182, 224, 200, -708, -17, -654, 596, 18, 85, 506, 32, -286, 2, -98, -133, 410, -167, -427, -228, -740, -93, 53, 450, -569, -166, 7, -93, 122, -154, -525, -201, -205, -477, -744, 436, 125, -48, -469, -17, -1270, -218, 256, -56, 31, -129, -309, 285, 61, -293, -56, 15, 335, 77, -324, 355, -255, -50, -550, 223, -557, -511, -253, -331, -220, -282, 314, -313, -12, -346, 2, 20, 1, -74, 246, 41, -532, 66, -169, -93, -129, 152, -967, 95, 562, 71, -49, -106, -136, 175, 420, 362, -41, 34, -240, 8, -289, -427, 331, -75, -321, -97, -1123, 61, -505, -72, 19, 217, -227, -503, -101, -666, -869, -139, -109, -387, -116, -445, -369, 236, -44, 521, 47, 257, -304, -453, 424, -3, -81, 166, -744, 413, -103, 32, 13, -164, -179, -272, -1033, -283, -490, -91, -190, 14, -1004, -304, 133, 612, -277, -123, -106, 246, -168, 16, -233, 16, -628, 63, 250, 73, -551, 289, -143, 1, 362, -308, -84, -208, 315, -152, -288, 47, -474, -140, -1002, -48, 144, 185, 157, 212, -900, 176, 395, 30, -152, 272, -779, -224, 46, -613, 91, -46, 23, -389, 6, -334, -23, -368, -728, -204, 33, -68, -1161, 711, -148, -493, -199, 313, -444, -241, -166, -70, 259, -25, -200, 154, -369, 50, -151, 157, -155, -194, -717, 96, 369, 87, -437, 6, -888, 98, 313, -321, 31, 31, 401, -359, 225, -644, 552, -97, 312, -35, -702, 224, -569, -250, -88, -75, -435, -253, -418, 105, 353, -32, -371, -72, -100, -382, -394, -122, -331, 655, -194, -202, -687, -503, -52, 190, -392, -8, 47, -422, -305, -586, 50, 629, 312, 396, -87, -410, -815, 17, -815, 392, -111, -226, -297, -46, -161, 6, -183, 392, -143, -381, 114, -100, 856, -308, -618, 220, -749, 308, -44, 322, 83, 23, 344, 11, 700, -240, -56, 178, -148, -221, 155, 341, 45, -146, -43, -47, -315, -617, -202, 97, -799, -77, -220, -333, -1041, -418, -5, 335, 931, -279, -1236, 65, 577, -122, 234, -116, -324, 120, -924, -33, -18, 297, 134, 52, -436, -75, -204, 45, -322, 296, -332, -317, -362, -504, 63, -184, 566, -228, 146, 232, 286, -199, -572, -104, 630, -2, -368, 40, -245, 74, 566, -523, -40, -207, -128, 38, 43, 17, 154, 197, -542, 282, 68, 441, 512, -313, -1092, -640, -126, -71, 91, 479, -952, 181, -241, 18, -5, 539, -58, -90, -212, -472, -261, 17, -642, 150, -388, -10, -36, -118, -54, -401, 418, -248, -2, 120, 251, -114, 42, -49, -242, 649, 235, -222, 80, 493, 651, 471, -963, -117, -217, 3, 255, 113, 557, -252, -204, 356, 4, 849, 1124, -416, 848, -553, -504, -28, -582, 550, -492, -46, -99, 97, -18, 145, -280, 319, 292, 160, 697, 38, 237, -80, 190, 367, -1192, -169, -145, 550, 19, -131, -189, 88, 505, -1, -531, 48, -632, -193, 53, -102, 65, -70, 633, -200, 292, -102, -125, -79, 103, 385, 218, -420, -235, 31, 151, 376, 845, -651, -730, 60, 11, -139, 586, -981, 409, -85, -410, -346, -143, 396, 185, 176, -261, -109, 381, 16, 322, 325, -948, -422, -7, 296, 26, 70, 892, -1, 168, 643, -430, -267, 1126, 15, 506, -271, 257, 474, -170, -320, -188, 164, -367, -163, -205, -13, 615, 225, -512, 355, -1102, 368, 56, 975, -235, 95, -360, -647, 679, 91, 435, 539, -774, 280, -6, -21, -18, -29, 1106, 677, -135, 247, 315, 32, -651, -209, -442, 169, 68, -203, -49, 198, 488, -74, -276, 235, -642, -152, 317, 354, -644, 297, -63, 436, -18, -76, 207, 402, -690, -36, 1282, -87, -226, 202, -286, -610, 437, 18, 154, 862, 816, -507, 101, -225, 52, -124, -1443, 203, -532, -484, 21, 408, 61, -415, -39, 748, -41, -121, 413, -72, 504, -88, 54, -286, -419, 9, -127, 487, 100, -85, -202, 179, 344, 43, 199, 681, 51, 198, -833, -23, -174, 41, 314, -3, 76, -4, 168, 57, 274, 86, -321, -850, 85, -90, 26, 279, 881, -194, -411, -343, 774, 71, 518, 334, 618, 46, 361, 420, -299, 461, 860, 583, 743, -492, 520, -279, 184, 155, -89, -268, -385, 105, 70, 601, -28, -194, -65, -250, -100, -98, -454, 319, 265, 486, -118, -247, -55, -18, 460, 236, -497, -58, 43, 11, 401, 10, -70, 68, -228, -8, 47, -132, 72, 49, -233, -244, 318, -88, 107, 82, -267, -283, 317, -211, -199, 155, 1032, 260, 501, -191, 4, 25, -375, 57, 569, 606, 725, -375, 54, 75, -10, -98, 190, -294, 1008, -85, 29, -267, -561, 33, -253, 39, -88, -28, -219, 409, -1183, -298, 641, 73, 657, 297, -238, -464, 633, -394, 176, 1213, 113, -20, -337, -171, 556, -201, 120, -175, -43, -123, -132, 118, 98, 488, 805, 419, 14, -275, 745, -182, -289, 497, 37, 318, -665, -413, 43, -538, 780, -231, 336, -585, 663, 164, -14, -363, 815, -298, 338, 181, -23, 476, 392, -431, 411, 10, 261, 120, 241, 296, -251, -336, -53, 679, -108, 160, 514, -1001, -946, 24, -462, 92, -941, 211, 117, -18, -352, 113, -171, -338, 892, 652, -733, 142, 107, -148, 204, -140, 132, -82, 396, 176, -4, 498, 787, -303, -93, 168, 208, 31, 263, -434, 302, -59, -226, -216, 21, -491, 523, -329, 107, -26, 118, -12, -334, -15, 0, 321, -1001, -169, -67, 1628, -865, -211, 165, 387, 136, -30, 399, 131, -494, 27, -562, 527, 5, 63, 845, -47, -331, -628, 777, -65, -577, -71, -566, 1, -60, -401, 47, -113, 351, 229, -701, 397, 655, -68, 603, 450, -598, 326, -466, -313, -86, -572, 1289, 519, -11, -513, -90, -53, 394, -322, 112, 290, -651, -394, 145, 265, 937, -532, -293, -285, 869, 39, 65, -120, 159, -203, 237, 34, -37, -43, 1114, 668, 23, -202, -490, 11, -74, 59, -43, 438, 1386, -15, -84, -218, -733, -110, 724, -300, -83, -289, 285, 449, 915, -319, -611, 1149, -5, -51, -23, 66, 317, 349, -265, 29, 797, 68, -283, 92, -13, 138, 167, 137, 1016, -499, 187, 188, -146, 61, 6, 173, -476, 83, 815, 321, -18, 186, 371, 37, -226, -81, -456, 25, 243, -172, -927, -72, -227, 4, -14, -18, -723, -33, 753, -344, 883, -20, 195, -28, -815, -459, -5, 828, 240, 143, 1021, 76, -333, 465, 160, 67, 441, 31, 200, -207, -896, -345, 69, -243, -427, -345, -69, 120, -38, 17, -362, 400, -93, -54, -242, -269, 109, 295, -587, 353, 412, -157, 429, -160, 969, -24, -119, -61, 41, -75, 50, -225, 925, 550, -809, 428, 965, -20, 50, -202, -632, 192, -10, -654, -76, 139, 347, 479, -181, -418, 186, -198, 581, 225, -325, -138, 450, 748, -2, 392, 426, -198, 550, -1040, 879, -57, -351, 99, -110, 154, 66, -126, -143, 146, 482, -585, 1204, -285, -266, -31, -1059, -302, 33, 785, 219, -46, 8, 110, 850, -260, -546, -36, -277, -246, -206, -85, -75, -105, -529, 8, -171, 552, 89, -12, 636, -739, 532, 97, 160, 480, 872, -652, 563, 466, -109, 400, 109, 109, -344, -448, 225, -5, 283, 31, -536, -317, 880, 198, -21, -61, -39, -128, -354, -206, 905, 48, -1268, 404, 715, 8, 709, -483, -158, 475, 1024, 383, 64, 123, 868, -309, 268, 90, 238, -515, 332, 774, 103, 542, 454, -69, -354, -72, 376, 39, 872, 110, 806, 288, -23, -351, -147, -280, 1112, -688, 572, -119, 10, -113, -211, 761, 150, 372, 250, -132, -43, -74, 368, -40, 502, -921, -332, 35, -100, -3, -325, -425, -377, 278, -176, -220, -656, -276, -702, -234, 157, -1, -169, -96, -1117, 276, 954, -230, -8, 171, 742, 102, -1547], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "8029.2.a.h", "char_is_minimal": true, "conrey_index": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "hecke_cutters": null, "qexp_display": 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, "projective_field": null, "artin_field": null, "embedded_related_objects": null}