# Stored data for newform 8029.2.a.g, downloaded from the LMFDB on 23 April 2024.
{"label": "8029.2.a.g", "space_label": "8029.2.a", "level": 8029, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021597797785437, "dim": 70, "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": 70, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [31, -1], [37, -1]], "trace_display": [5, 22, 24, 70], "traces": [70, 5, 22, 71, 24, 9, 70, 9, 78, 4, 61, 49, 28, 5, 22, 73, 37, 8, 23, 45, 22, -10, 26, 3, 66, 57, 76, 71, 38, -14, 70, -2, 44, 34, 24, 46, 70, 21, 10, 13, 71, 9, 30, 108, 13, -14, 78, 85, 70, -12, 21, 23, 47, 17, 5, 9, 9, 8, 109, -1, 41, 5, 78, 29, 36, 5, 23, 47, 8, 4, 99, 8, 33, 5, 94, -19, 61, 37, 52, 78, 102, 0, 118, 49, -21, 74, 11, -21, 86, -7, 28, 14, 22, 35, 24, -40, 9, 5, 92, 65, 82, -56, 43, 88, 22, -25, 15, 150, -30, 77, 22, 73, 10, 35, 73, 63, 72, -5, 37, -21, 55, 119, 3, 71, 90, 8, -14, -20, 17, -44, 91, 94, 23, -4, 65, 55, 64, -72, 48, 45, 50, -66, 70, -12, 23, 45, 22, 71, 49, -40, -3, 95, 118, -10, 24, 9, 90, -2, 9, -15, 26, 31, -4, 136, -21, -43, 86, 3, 10, -42, 58, 77, 118, -70, 66, 103, -1, -55, 126, -126, 66, 57, -57, -35, 24, 9, 32, 64, 76, -25, 99, 103, -43, 102, 65, 71, 44, -50, 2, -116, 73, 8, 38, -9, 1, 50, 18, -79, 154, -14, -12, 67, 75, -24, 105, -62, 70, 26, 40, -74, 16, 9, 52, -2, 90, -97, 168, -155, 78, -10, 44, -31, -29, 143, -57, 196, 29, 34, 71, -94, 29, -72, 150, -51, 24, 173, 6, 9, -27, -185, 162, 46, -116, -48, -4, 77, 62, 63, 70, 267, -89, -107, 93, 130, 95, 21, -45, -51, 272, -73, 80, 2, 10, -33, 162, 22, -8, -11, 78, 13, 11, -300, 100, -25, 44, 76, 71, -14, 9, 16, 62, 93, 93, 9, -2, 9, 149, -79, 191, 139, 30, -10, 85, -73, 51, -112, 60, 108, -53, 4, 86, 30, -2, -39, 13, 133, 9, -9, -13, 291, -40, -14, 131, -73, 161, 40, 37, -122, 78, 97, 84, 242, 78, 184, 14, 85, 4, 12, 159, -142, 61, 132, 70, 87, -129, -128, 86, 33, -21, -12, 24, -201, 97, -4, 31, 68, 21, 62, -43, 6, 5, 103, 138, 23, 0, -8, 110, -41, 144, 4, 47, 49, -82, 51, 48, 17, 113, 17, 168, -150, 51, -33, 143, -65, 5, 62, -53, -41, 75, 147, -7, 9, -79, -24, 152, 182, -71, -11, 9, -18, 54, -168, 28, 202, 48, 8, 61, -193, 123, -192, 242, 31, 109, -79, -133, 357, -144, 30, 197, -1, -57, -53, 217, -55, 87, 68, 41, -32, -93, -33, 46, 217, -25, 5, 96, -83, 125, -135, -99, 78, 78, 59, 69, 49, -23, -49, 12, 29, 130, -203, 314, 179, 49, -127, 36, 375, -116, 123, -50, 241, 41, 5, 34, -60, 22, 8, 77, 106, 23, -206, 159, -23, 2, -169, -10, 47, -33, -113, 107, -48, 28, 156, 8, -17, -54, 261, 24, 286, -42, 4, 160, -231, 160, -73, -129, 73, 99, -89, 15, 175, 115, 92, 74, 8, -47, -61, -21, 17, 313, -178, 33, -5, -31, 118, 127, 18, 142, 5, 169, -245, 114, 220, 90, -13, 94, 110, 37, 123, 104, -16, 126, -19, -11, -211, -63, -136, 18, -248, 61, 4, -188, 120, -139, 117, 130, 37, -50, -4, 88, -35, 252, -7, 52, -32, 22, 165, -11, 8, 181, 78, 122, -189, 141, 154, -17, 145, 102, -174, -71, 59, 64, -106, -67, 0, 231, -204, 118, -135, 50, -106, 118, 42, -175, -78, -166, 57, 182, 49, 23, -50, 81, 73, 155, -366, -21, 208, -1, -159, 98, -135, 22, 74, 57, -346, -52, 243, -165, -29, 11, -147, 220, 175, -12, -107, -150, -21, 29, -302, -26, 45, 107, -141, 86, -252, -230, 302, -69, 178, 37, -7, 27, -100, 121, -64, 269, 205, 28, 74, 88, 3, 225, -239, -33, 14, -234, -40, -51, 107, 173, -136, 22, -86, -64, -147, -28, -16, 235, 35, 44, -465, 58, -130, -203, -153, 24, 8, -138, 245, -87, 32, 9, -40, 49, -82, 446, 176, 281, -352, 9, 210, -135, -10, 191, -275, -70, 5, -78, -88, 3, 443, 193, 157, 92, 90, -33, -160, -91, 43, 60, 65, 102, -132, 23, 370, 28, -252, 82, 74, -44, 327, 63, -91, 26, -56, -145, -169, 15, -282, 322, -379, 43, 120, 35, -88, 81, -66, -16, 88, -78, 31, 215, 45, -110, -91, 22, 38, -57, 59, 141, 45, -56, -25, 52, 3, 63, -44, 227, -130, 15, -187, -48, 259, -95, 64, 35, 150, -95, -395, -153, 109, 242, -103, -30, 333, -216, 135, 79, 62, -26, 77, -1, -440, 358, 164, 66, 252, 22, 70, 155, -343, 220, 317, -109, 73, -144, -267, 57, 98, 10, -373, 10, 115, -114, 64, -179, 97, 279, 35, 56, -389, 90, -240, 245, -4, 73, 57, 1, -43, 117, -93, -39, 63, -3, -10, 200, 47, -236, 113, 72, -130, 11, 173, 203, 143, 186, -5, 31, -199, 129, 62, -284, -302, 37, 13, -89, 225, 76, 17, 98, -21, -122, -424, 225, -150, 148, -395, 55, 178, -155, 86, 26, 206, -73, 119, -53, -11, 109, 50, 168, 197, 3, -11, -16, -626, 187, 115, 53, 71, -193, -324, -2, -115, -128, -186, 90, 262, -353, 136, 11, 24, 225, 8, -168, -228, 398, 98, 269, 3, -14, 200, 59, 343, -176, -249, -141, -20, 31, -346, 38, 290, -271, -45, 17, -583, -118, 76, -124, 370, -36, -44, 20, -319, -29, 192, 143, 67, 91, -129, -157, 10, 218, -185, 145, 94, 66, -181, -10, -95, 269, -14, 23, -263, -325, 226, -29, -107, -179, -4, 193, -116, 297, 206, -249, 134, 65, 257, 155, 48, 49, 118, -216, 55, -29, -102, -146, 219, -229, 22, 64, 335, 70, 57, 62, -123, -46, -72, 44, -556, 189, 166, 367, -362, 48, 179, -413, -4, -43, 94, -6, 45, -258, -169, 275, 45, 18, -118, 50, -440, -91, 104, 66, -2, -105, -66, 303, -177, -73, -2, 76, -362, 70, -109, -129, 659, -2, 187, 34, -12, -65, -250, -24, -505, 103, -460, 23, 242, -325, 116, 290, -138, 196, 45, 44, -100, 12, -155, -31, -194, 22, 206, 10, 55, -147, 19, 100, 71, 1, -669, 16, 576, -7, -422, 49, -334, -315, 69, 39, -316, -49, -40, 13, -238, -2, 34, 127, -331, -3, -475, -361, 450, 93, -114, 101, 95, -124, -404, 211, -405, 48, 189, 118, 29, 38, 117, -43, 363, 94, -10, -67, -350, -177, 376, 255, -144, 24, 206, -334, 156, 297, -513, 290, 9, -3, -65, 168, -467, 96, -374, 90, -31, -190, 289, -37, 17, -416, -2, 255, -385, 499, -14, 19, -413, 9, 108, 305, 46, 6, -318, -142, -15, -112, -435, -78, 102, -133, -264, 26, -199, -226, -376, 78, -119, 6, 31, -60, -300, 13, 104, 380, -766, -4, 97, -285, 230, 54, 131, 70, 136, -55, -801, 279, -374, 235, 49, -21, 125, -257, -154, 42, -230, -385, -43, 52, -58, -257, -155, 24, -288, 86, -16, 79, 60, -78, -401, 378, 3, -284, 21, 21, 309, 326, -280, 10, -2, -396, 45, 32, 439, -22, -42, 193, -632, 368, -39, 199, 24, 58, -211, -169, 356, -86, -32, -204, 77, -124, -590, -122, 211, 10, -189, 118, -2, -224, -215, 251, -174, 117, -70, 82, -172, 44, 242, 83, -832, 66, 428, -103, 103, -34, -452, 159, 103, -110, -385, -130, -302, 133, 194, -1, 13, 12, -337, 99, -89, -401, -55, -29, -357, 93, -4, -243, -38, 126, -458, -98, 141, 246, 34, 370, -126, -301, -182, 111, 254, -25, -316, 66, 86, 41, 61, 71, 55, -239, 57, -319, -447, 364, 69, 59, -85, -57, -232, 28, -60, -224, 406, -35, -35, -56, -867, 89, -15, 285, -292, 24, 147, -233, -563, 427, 460, 234, 9, -15, -107, -19, -145, 183, -762, 32, 183, -155, -11, -277, -49, -198, 64, -179, -605, 314, 249, 173, -298, 76, 232, -156, 477, -142, -86, -217, -25, 543, 46, 30, 3, -277, 151, 99, -594, 402, 110, 59, 159, 240, 103, -355, -144, -62, -100, 47, -400, -43, -313, -362, -196, 331, 236, -86, 102, 99, -764, 101, -393, -41, 108, 65, -51, 37, 574, 70, -29, -165, 71, 119, -38, -96, 606, -21, -398, 44, 299, -179, -675, -20, -316, 16, -50, -188, -40, -105, 81, -92, -333, 2, 294, 13, -200, -169, 137, 19, -116, 146, -277, 141, -78, 47, 21, 73, -671, -417, -421, 317, 163, 118, 8, -61, -417, 47, -161, 336, -356, 38, -608, -94, 80, 137, -14, 267, -9, 10, -285, -48, 235, 222, -85, 1, -238, -375, -167, 215, -676, -316, 50, 10, -418, 152, -322, 51, 100, 18, -31, 85, 233, -203, 288, -95, -79, 78, -364, 239, 1, -140, -487, 154, 288, -149, 222, 201, -113, 152, -14, -63, -462, -308, 140, 287, -113, -12, -116, 316, 13, 176, -436, 83, 67, 8, -216, 288, 85, 7, -572, 75, -582, -348, 186, -14, 83, -194, -24, 49, -263, -331, -591, 4, -131, 105, -53, 200, 137, 92, -524, 197, -62, -85, -28, -521, 393, 71, -552, 70, -580, -298, -43, 84, -441, -58, 26, -51, -355, 66, -823, 97, -40, 40, -358, -277, 519, -258, -159, -272, -74, 139, -541, 167, -225, 165, -462, 16, 152, -324, -12, 150, -605, 403, 9, -257, -384, -117, 359, 366, -579, 52, 158, -317, -599, 142, 117, -236, -2, -487, -404, 241, -161, 43, -195, 90, -191, -421, 100, 504, 302, 21, -97, -488, -1113, 178, -455, 528, -272, 168, 286, 30, 284, 43, -371, 294, -155, -93, 156, -257, -136, 60, -380, 78, -281, -218, 280, 456, -856, 1, -10, 121, 23, 101, -112, 333, -34, 44, -605, 237, 149, -224, 461, -361, -31, -1, -750, -121, 108, 272, -890, -29, -358, -118, 128, 449, 351, 101, 143, -354, -524, -425, -43, 47, -79, -57, 192, -74, -276, 6, -9, -388, 196, -141, -474, 153, -17, -111, -583, 29, -321, -413, 19, -329, 561, 13, 34, 166, -1102, -95, -160, -217, 133, 71, 17, 86, 42, 93, -611, -113, -94, 121, -241, 153, -63, 29, -89, 29, -697, -399, -85, 476, 85, 143, -72, -883, -313, -96, 393, 152, -316, 150, -14, 19, -214, 5, 328, 280, -51, -20, -815, 359, -401, 52, -254, 24, -232, -217, 112, 89, -241, 101, 173, -258, -438, -426, 125, 454, -386, 6, -716, 164, -700, -111, -220, -10, 9, -303, -406, 78, 38, -372, -338, -27, 6, -199, 809, 204, -114, -369, -185, 54, -1153, 154, -309, 501, -672, 162, 457, 393, 31, 155, -200, 68, 46, -300, -327, 9, 210, -252, -400, -116, -621, -91, -455, 301, 85, -235, -48, -337, -313, -103, -280, 313, -171, -4, -202, 3, 575, -211, 271, -179, 77, -42, -802, -153, 168, -214, 8, 62, -848, -198, 286, -239, 330, 78, 63, -169, -207, -118, 627, 143, -622, 70, 459, -102, -766, 59, -16, -4, 267, -460, -184, 232, 355, -303, -311, -89, -353, 109, -221, 93, 365, -218, -107, -101, -991, 105, 35, 696, -401, 93, -193, -307, 62, -349, 145, 58, 130, -136, -12, 551, -248, 227, -298, 95, -431, -134, 22, 641, -1, 86, 21, -382, -487, -276, 103, -79, 178, -45, -110, 226, 104, -54, -161, -502, -51, -201, -866, -198, -712, -14, -969, 272, 264, -525, 180, 21, 227, 197, -73, 41, 26, 182, 94, 228, -1027, 80, 216, -229, -736, -152, -244, 244, 2, -705, -297, 182, 84, -162, -715, 10, -430, -238, -441, 74, -280, -123, -33, -84, -477, 57, 5, 788, 23, 162, -664, -308, 155, 162, 51, 733, 22, -157, 19, -667, -339, -315, -394, -8, -501, -181, -272, -28, 369, -12, -11, -659, -5, 266, 383, 26, 331, 78, -639, -238, -334, -86, -785, -169, 13, 47, -437, 49, -373, 0, -264, 11, -582, -163, 588, 184, 143, -70, -300, -41, -421, 181, -106, 603, -1329, 100, -253, -100, 29, 2, -502, 54, -25, -377, -122, -168, 301, -73, -102, 44, 432, 82, 17, 82, 219, -478, 76, -183, -96, 228, 593, 84, -429, 71, 215, -206, 507, -506, -123, 36, -14, -438, -431, -2, -889, 71, -112, 9, -48, 89, 196, 360, -719, -176, 16, -42, -161, -241, -266, 5, 134, 62, -744, 372, 90, 271, -269, 257, 93, -222, 5, -133, -368, 155, -142, 93, -319, -223, 212, 407, 419, -70, 9, -23, -637, -21, 232, 341, -635, -2, -20, -144, 484, 228, 522, -57, 9, -403, -346, 52, 708, 23, -486, 149, -176, -210, -372, 205, 244, -728, -79, -288, -432, 38, -566, 354, -56, 191, -54, -584, 190, -68, 30, 548, 139, -54, -478, -41, -556, -13, -72, 30, 47, 9, -148, 399, -526, -266, -10, -31, 41, 207, -84, 220, 488, 85, -895, -183, 536, 257, 47, -292, -73, -93, -102, 102, -128, -88, -257, 51, -258, -140, 50, 8, 656, -88, -112, -9, -846, 510, 8, 412, -831, 60, 108, 417, -412, -225, 149, 44, 108, -459, -649, -155, 455, -151, -199, -53, -567, -83, -327, 256, 296, -64, 4, 201, -1068, -272, -220, -95, -208, 86, 137, 262, 652, -284, 399, 109, 30, -333, -386, 339, 224, -96, 141, -2, 461, -514, 330, -17, -198, -355, -39, -232, -219, 99, 247, 234, 307, 13, -525, 224, 230, 38, -199, 316, 133, -338, -225, -154, -28, 248, -317, 9, -1, -637, 512, -204, 403, -63, -9, 42, -527, 255, 658, 286, 8, -13, -394, -99, 597, -81, 414, -152, 291, -80, -99, -140, 1177, 47, -429, -40, -488, 15, -1224, 444, 421, 78, -14, -370, 116, 41, 398, 143, -548, 131, 496, 33, 662, 201, 151, 258, -73, -68, -796, -60, 41, 305, -1205, 161, 343, -927, -350, -129, 176, -110, 40, -249, -47, 351, 452, 169, -665, 37, -223, 43, 334, 102, 5, 97, -122, 59, -426, 99, -283, 53, 145, 78, -214, 133, 528, -295, -8, -27, 97, -6, -757, 170, 348, 579, -616, 84, 109, 94, -14, -159, 869, -18, 242, 94, -429, 96, 384, -150, -28, 78, 510, -104, -558, 242, 113, 458, 184, -76, -998, 3, 97, -173, -752, 14, 321, 511, -28, -168, -37, 530, 85, -21, -223, 0, -19, 441, -569, 4, -324, -524, 666, 58, 241, 1, 12, -185, 29, 493, -718, -17, 534, 159, -145, 161, 323, -242, 359, 197, -142, -403, -76, -667, 398, -348, -78, 61, 388, -32, -287, 82, -301, 78, 132, -297, -127, 104, -825, 183, -1232, 70, 222, -410, 402, 36, 3, -286, 87, -145, 158, 451, 575, 282, -270, -129, -366, -387, 37, 334, -1047, 373, -128, -309, -152, -130, 705, 466, -584, 86, 238, -539, -759, -158, 728, 77, 33, -212, -676, 80, 19, 706, 5, -21, 131, -790, 758, 364, -92, 52, -12, 52, -708, 57, -245, 318, -476, 24, 61, 690, -373, 259, -205, -155, -201, -187, 416, -204, 167, -347, -388, 97, -515, -157, 177, 1172, -489, 85, -4, 23, 78, -120, -274, 818, -178, 31, 187, -27, 133, 197, 1101, 95, 68, -376, -775, 5, 17, 62, -313, 21, -262, -15, 240, 340, 795, -354, 62, -13, -635, -346, 91, 102, -272, -43, 120, 113, 47, 243, 332, -320, 6, 230, -623, 305, 512, 33, -747, 5, -73, -601, -129, -422, 419, -369, 103, 380, -106, 131, -1170, 553, 679, 138, 0, 161, 421, 262, -28, 19, 23, -54, -272, -343, 283, 8, 319, 0, 29, -378, 685, 336, 159, 225, -8, -468, 580, 69, -116, 162, -772, 110, 233, 87, 211, 118, 898, 65, -41, -200, -726, 524, -357, -2, -377, 144, 184, -142, -44, -82, 160, 72, 4, 6, -452, -391, 413, 904, -234, 47, -359, 130, -612, 142, 190, 296, 49, -349, -725, -879, -33, -150, -236, -82, -170, -667, 210, 443, 593, -145, 51, -72, -865, 305, 11, 173, 166, 48, 783, 99, 1056, 243, -478, -321, 17, 93, 45, -21, 117, -438, 383, 113, -1647, 469, -252, 185, -20, 7, 17, -113, -907, -73, -293, 599, -277, 168, -541, -122, 808, -530, 356, 151, -150, 250, -697, 559, 8, -259, 74, 51, -206, -194, 892, 486, 639, -298, -33, 25, -131, -386, 633, -819, -659, 143, 291, 160, -519, -211, -263, -54, -65, -53, -116, 80, 549, 38, -412, 5, 268, 11, 491, 196, 814, 33, 62, -232, -274, -16, 1078, 380, 355, -53, -53, 125, 55, -269, -265, -725, -41, -443, -853, -324, 453, 451, 225, 75, -201, -118, 511, 396, -21, 424, 147, -173, -214, -209, 417, -30, -286, -7, 5, 281, 168, 43, -209, -69, 9, -296, -63, 323, 270, -177, -110, -79, -147, -670, 429, -168, 551, -56, -24, 86, -279, 99, 351, 842, -297, 152, 935, -52, 401, 243, -217, 780, 182, -343, 121, 94, 737, 55, -904, -71, 303, 111, 552, 3, -426, -213, -11, -451, -677, 265, -7, 278, -422, 9, 36, 362, 61, -128, -332, 183, -18, 35, 541, -57, -478, -707, -47, 54, -295, -143, 93, 535, -19, 659, -168, -741, 385, -136, 697, 982, -73, 28, 214, -38, -226, -102, -132, -70, 202, -559, -11, 321, 399, -30, -568, 48, 75, -265, 935, 210, 636, -236, 8, -86, -238, 174, 46, 28, -679, 61, 1223, -31, 14, 276, 436, 350, -193, -330, -432, 71, 784, 165, -892, 123, 201, -216, 47, -27, 871, 446, -192, -208, -862, -136, 740, 912, 495, 242, 274, 129, 1221, -107, -99, 22, 31, -456, 37, 424, -81, 135, -16, 109, 560, 188, 750, 98, -459, 84, -79, -392, -159, -579, 216, -56, -11, -133, 431, 725, 270, 435, -168, -418, 357, -369, 35, 166, -433, 368, -311, -144, 590, -510, 659, 52, 917, -633, 30, 105, 84, -549, 204, 783, -84, 197, 676, -254, -660, 153, -50, 370, -1, -306, 692, -143, 636, 24, -142, -57, 240, -418, -674, 478, 449, -371, -53, -94, -220, 764, -292, 659, 78, 217, 79, -311, -376, -490, -196, 0, -55, -18, -472, 318, -190, -217, 414, 87, -40, -195, 143, 903, 105, 108, 68, -498, 642, 240, 552, 230, 589, 41, -1185, -456, 201, 20, -622, -194, -32, 102, -352, 442, -529], "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.g", "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}