# Stored data for newform 8026.2.a.b, downloaded from the LMFDB on 19 April 2024.
{"label": "8026.2.a.b", "space_label": "8026.2.a", "level": 8026, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660932954, "dim": 81, "analytic_rank": 1, "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": 32104, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 64.08793266227964, "level_radical": 8026, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8026, 1, [4015], [1]], "inner_twist_count": 1, "level_primes": [2, 4013], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 81, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [4013, 1]], "trace_display": [-81, -10, -26, 3], "traces": [81, -81, -10, 81, -26, 10, 3, -81, 59, 26, -41, -10, 33, -3, -7, 81, -9, -59, -32, -26, -23, 41, -28, 10, 81, -33, -37, 3, -35, 7, -29, -81, -7, 9, -67, 59, 13, 32, -42, 26, -66, 23, -22, -41, -65, 28, -71, -10, 64, -81, -43, 33, -37, 37, 12, -3, -1, 35, -162, -7, 19, 29, -16, 81, -45, 7, -43, -9, -21, 67, -99, -59, 53, -13, -61, -32, -31, 42, 4, -26, 1, 66, -112, -23, 17, 22, -15, 41, -111, 65, -49, -28, -19, 71, -53, 10, 50, -64, -97, 81, -97, 43, 35, -33, 27, 37, -62, -37, -1, -12, -128, 3, 1, 1, -69, -35, 57, 162, -133, 7, 62, -19, -54, -29, -138, 16, 47, -81, -29, 45, -129, -7, 61, 43, -18, 9, -66, 21, -76, -67, -48, 99, -67, 59, 27, -53, -64, 13, -81, 61, -31, 32, 19, 31, -100, -42, 44, -4, -58, 26, -160, -1, -55, -66, -41, 112, -99, 23, 22, -17, -165, -22, -39, 15, -6, -41, -5, 111, -161, -65, -43, 49, -3, 28, -132, 19, -50, -71, -89, 53, -109, -10, 78, -50, -85, 64, -76, 97, -60, -81, -131, 97, -153, -43, 58, -35, -24, 33, -105, -27, -65, -37, -37, 62, -135, 37, 139, 1, -92, 12, -153, 128, -5, -3, 4, -1, -139, -1, -66, 69, -112, 35, -25, -57, -29, -162, 31, 133, -203, -7, 2, -62, -91, 19, -208, 54, -17, 29, -63, 138, -269, -16, 25, -47, -77, 81, -81, 29, -76, -45, -95, 129, -69, 7, -5, -61, -103, -43, -206, 18, -25, -9, -44, 66, -234, -21, 63, 76, -171, 67, -118, 48, -73, -99, -27, 67, -113, -59, 74, -27, -191, 53, -69, 64, -14, -13, 24, 81, -257, -61, 16, 31, 22, -32, -118, -19, -113, -31, -48, 100, -210, 42, 75, -44, -218, 4, -117, 58, -20, -26, -50, 160, -202, 1, 125, 55, 44, 66, -168, 41, -150, -112, 45, 99, -176, -23, 96, -22, -216, 17, -229, 165, 18, 22, -75, 39, -158, -15, -126, 6, -238, 41, -178, 5, -80, -111, -70, 161, -286, 65, 73, 43, -147, -49, -102, 3, 4, -28, -134, 132, -296, -19, 116, 50, 12, 71, -159, 89, -143, -53, -135, 109, -194, 10, 3, -78, -107, 50, -230, 85, -58, -64, 17, 76, -258, -97, -6, 60, -147, 81, -254, 131, -87, -97, -228, 153, -114, 43, 30, -58, -138, 35, -51, 24, 80, -33, 31, 105, -352, 27, -42, 65, -181, 37, -166, 37, -119, -62, -89, 135, -184, -37, 172, -139, -127, -1, -101, 92, 34, -12, -101, 153, -187, -128, 80, 5, -69, 3, -272, -4, -188, 1, 6, 139, -275, 1, 67, 66, -82, -69, -358, 112, 10, -35, -68, 25, -169, 57, 55, 29, -107, 162, -80, -31, -115, -133, -62, 203, -201, 7, 19, -2, -68, 62, -132, 91, 2, -19, -207, 208, -334, -54, 150, 17, 23, -29, -76, 63, -196, -138, -95, 269, -86, 16, 29, -25, -107, 47, -372, 77, -118, -81, -57, 81, -267, -29, 106, 76, -66, 45, -211, 95, -113, -129, -68, 69, -184, -7, 43, 5, -448, 61, -128, 103, 18, 43, 65, 206, -354, -18, 5, 25, -12, 9, -141, 44, -19, -66, -101, 234, -326, 21, 69, -63, -101, -76, -211, 171, -198, -67, -219, 118, -195, -48, 67, 73, -59, 99, -107, 27, -63, -67, -62, 113, -197, 59, 72, -74, -311, 27, -296, 191, 59, -53, -99, 69, -361, -64, 35, 14, -183, 13, -164, -24, -188, -81, 8, 257, -224, 61, -15, -16, -222, -31, -240, -22, 120, 32, -74, 118, -252, 19, 32, 113, -67, 31, -215, 48, -232, -100, -103, 210, -114, -42, 41, -75, -118, 44, -192, 218, -181, -4, -35, 117, -242, -58, 133, 20, -172, 26, -201, 50, -186, -160, -125, 202, -242, -1, 82, -125, -198, -55, -84, -44, 12, -66, -42, 168, -256, -41, -109, 150, -125, 112, -289, -45, -123, -99, -260, 176, -486, 23, 115, -96, -195, 22, -71, 216, 21, -17, -191, 229, -186, -165, 17, -18, -170, -22, -280, 75, -226, -39, 0, 158, -196, 15, 54, 126, -321, -6, -230, 238, 44, -41, -50, 178, -243, -5, -87, 80, -45, 111, -224, 70, -188, -161, 78, 286, -343, -65, 31, -73, -168, -43, -129, 147, 89, 49, -214, 102, -481, -3, 122, -4, -75, 28, -35, 134, -202, -132, -204, 296, -93, 19, 111, -116, -258, -50, -404, -12, -76, -71, 111, 159, -297, -89, 57, 143, -140, 53, -432, 135, -116, -109, -57, 194, -177, -10, -47, -3, -318, 78, -215, 107, -73, -50, -107, 230, -267, -85, 1, 58, -40, 64, -171, -17, -98, -76, -5, 258, -246, 97, 101, 6, -130, -60, -160, 147, -139, -81, -331, 254, -245, -131, 57, 87, 3, 97, -182, 228, -293, -153, -10, 114, -237, -43, 77, -30, -314, 58, -258, 138, 31, -35, -170, 51, -224, -24, 41, -80, -85, 33, -31, -31, 11, -105, -19, 352, -403, -27, -46, 42, -207, -65, -284, 181, -27, -37, -21, 166, -295, -37, 166, 119, -112, 62, 36, 89, -210, -135, -337, 184, -265, 37, 94, -172, -209, 139, -409, 127, -131, 1, 38, 101, -406, -92, 119, -34, -10, 12, -229, 101, -111, -153, -132, 187, -71, 128, -123, -80, -257, -5, -14, 69, -150, -3, 81, 272, -447, 4, 185, 188, -24, -1, -191, -6, -108, -139, -216, 275, -268, -1, 105, -67, -108, -66, -151, 82, 1, 69, -86, 358, -314, -112, 57, -10, 54, 35, -409, 68, -322, -25, -79, 169, -94, -57, 205, -55, -202, -29, -361, 107, 120, -162, 141, 80, -236, 31, -34, 115, -443, 133, -118, 62, -214, -203, -108, 201, -306, -7, 14, -19, -188, 2, -136, 68, -34, -62, -270, 132, -420, -91, 11, -2, -133, 19, -152, 207, -121, -208, -111, 334, -148, 54, 144, -150, -88, -17, -189, -23, 25, 29, -90, 76, -318, -63, 242, 196, -404, 138, -111, 95, -75, -269, -63, 86, -227, -16, -54, -29, -174, 25, -84, 107, 50, -47, 274, 372, -328, -77, -61, 118, 102, 81, -215, 57, -283, -81, 27, 267, -219, 29, 214, -106, -107, -76, -83, 66, -45, -45, 80, 211, -219, -95, 31, 113, 263, 129, -264, 68, -132, -69, 155, 184, -117, 7, 198, -43, -57, -5, -194, 448, 203, -61, 38, 128, -276, -103, 152, -18, -65, -43, -16, -65, -118, -206, 186, 354, -262, 18, -37, -5, 0, -25, 111, 12, 129, -9, -21, 141, -294, -44, 183, 19, 154, 66, 160, 101, -212, -234, -48, 326, -119, -21, 122, -69, -87, 63, -351, 101, -103, 76, 111, 211, 4, -171, 342, 198, -21, 67, -53, 219, -21, -118, -97, 195, 50, 48, 214, -67, -169, -73, 2, 59, 97, -99, 251, 107, -220, -27, 86, 63, 297, 67, 129, 62, -139, -113, 34, 197, -308, -59, 373, -72, 285, 74, 14, 311, 45, -27, 28, 296, -114, -191, 191, -59, 265, 53, -49, 99, -111, -69, 584, 361, -362, 64, 304, -35, 30, -14, -231, 183, 6, -13, 92, 164, 103, 24, -65, 188, -226, 81, 67, -8, 114, -257, 513, 224, 124, -61, 245, 15, -84, 16, 2, 222, 223, 31, 174, 240, -229, 22, 208, -120, 183, -32, -71, 74, -41, -118, 166, 252, 147, -19, 433, -32, 48, -113, 57, 67, 33, -31, 185, 215, 55, -48, 212, 232, 414, 100, -274, 103, -38, -210, 133, 114, 227, 42, 326, -41, -155, 75, 126, 118, 226, -44, 525, 192, -416, -218, -2, 181, 217, 4, 144, 35, 98, -117, 368, 242, 55, 58, 354, -133, 61, -20, 39, 172, -81, -26, 58, 201, -25, -50, 313, 186, 174, 160, 249, 125, -213, -202, 449, 242, 281, 1, 491, -82, -149, 125, -305, 198, 235, 55, 562, 84, -152, 44, 316, -12, 103, 66, 33, 42, -85, -168, 283, 256, -102, 41, 220, 109, 137, -150, 71, 125, 452, -112, 17, 289, -237, 45, 395, 123, 440, 99, 227, 260, 69, -176, 225, 486, 82, -23, 358, -115, 220, 96, 37, 195, 110, -22, 527, 71, 199, -216, 344, -21, 61, 17, 13, 191, -3, -229, 542, 186, 55, 165, 132, -17, -85, 18, -162, 170, 258, 22, 471, 280, -151, -75, 397, 226, 156, 39, 27, 0, 21, -158, 401, 196, -179, -15, 491, -54, 51, -126, 315, 321, 40, 6, 136, 230, -5, -238, 212, -44, 427, 41, 134, 50, -110, -178, 223, 243, 111, 5, 332, 87, -63, -80, 14, 45, 51, -111, 483, 224, -249, -70, 223, 188, 42, 161, 50, -78, 176, -286, 411, 343, 44, 65, -75, -31, 42, 73, -45, 168, 352, 43, 92, 129, -92, -147, 312, -89, 129, -49, 184, 214, -23, -102, -35, 481, -20, 3, 614, -122, 413, 4, -19, 75, 38, -28, 469, 35, -401, -134, 397, 202, 156, 132, 56, 204, -72, -296, 317, 93, 239, -19, 129, -111, 220, 116, 227, 258, 257, 50, 615, 404, -248, 12, 82, 76, 22, 71, 403, -111, 26, -159, 387, 297, -272, 89, 372, -57, -54, -143, 214, 140, 0, -53, 18, 432, -32, -135, 415, 116, 364, 109, 108, 57, -135, -194, 365, 177, 326, 10, 543, 47, -219, 3, -91, 318, 155, -78, 261, 215, 186, -107, 155, 73, 175, 50, -36, 107, -8, -230, 552, 267, 25, 85, 419, -1, 286, -58, -136, 40, 75, -64, 670, 171, -348, 17, 756, 98, 732, 76, 378, 5, -75, -258, 13, 246, -31, -97, 503, -101, 144, -6, 18, 130, 119, 60, 517, 160, -208, -147, 385, 139, 476, 81, -279, 331, -219, -254, 508, 245, 118, 131, 89, -57, -234, -87, 549, -3, 106, -97, 394, 182, 65, -228, 125, 293, 346, 153, -65, 10, 92, -114, 194, 237, -234, 43, 394, -77, 161, 30, 48, 314, -39, -58, 263, 258, -92, -138, 520, -31, 697, 35, -14, 170, -237, -51, 403, 224, 178, 24, 624, -41, -177, 80, 12, 85, 298, -33, 357, 31, 118, 31, 57, -11, 114, 105, 342, 19, 14, -352, 509, 403, -278, 27, 267, 46, 207, -42, 418, 207, 298, 65, 542, 284, -357, -181, 471, 27, 464, 37, 17, 21, 108, -166, 190, 295, 110, 37, 622, -166, 377, -119, 1, 112, 69, -62, 516, -36, 162, -89, 569, 210, 444, 135, -86, 337, 192, -184, 767, 265, 21, -37, 426, -94, 260, 172, 183, 209, 139, -139, 335, 409, 268, -127, 197, 131, 465, -1, 400, -38, 123, -101, 215, 406, -70, 92, 427, -119, 213, 34, 392, 10, 270, -12, 254, 229, -100, -101, 493, 111, 665, 153, -248, 132, 118, -187, 499, 71, 168, -128, 634, 123, 246, 80, 119, 257, 45, 5, 700, 14, 66, -69, 479, 150, -95, 3, 331, -81, 333, -272, 800, 447, 122, -4, 65, -185, 198, -188, 7, 24, 284, 1, 535, 191, -296, 6, 200, 108, 1028, 139, 699, 216, -37, -275, 161, 268, 158, 1, 444, -105, 362, 67, 356, 108, 147, 66, 712, 151, -151, -82, 603, -1, 583, -69, -258, 86, 233, -358, 530, 314, 376, 112, 267, -57, -56, 10, -9, -54, 617, -35, 725, 409, 41, -68, 397, 322, 250, 25, 240, 79, 29, -169, 459, 94, -72, 57, 379, -205, 270, 55, 266, 202, 176, 29, 381, 361, 181, -107, 553, -120, 631, 162, -108, -141, -358, -80, 671, 236, 95, -31, 630, 34, 527, -115, -42, 443, 199, -133, 633, 118, 149, -62, 323, 214, 116, 203, 230, 108, 207, -201, 217, 306, 150, 7, 399, -14, -26, 19, 373, 188, 397, -2, 412, 136, -238, -68, 501, 34, 931, 62, 523, 270, -221, -132, 557, 420, 161, 91, 434, -11, 529, 2, 5, 133, 305, -19, 874, 152, 416, -207, 504, 121, 307, 208, -144, 111, -75, -334, 579, 148, 94, -54, 628, -144, 183, 150, -92, 88, 499, 17, 672, 189, 7, 23, 35, -25, 82, -29, 335, 90, 313, -76, 476, 318, 308, 63, 615, -242, 433, -196, 457, 404, 111, -138, 30, 111, 7, -95, 682, 75, 328, 269, 391, 63, -12, -86, 445, 227, 93, 16, 415, 54, 104, 29, -219, 174, 324, -25, 1001, 84, 199, -107, 80, -50, 229, 47, -20, -274, -134, -372, 1128, 328, -102, 77, 298, 61, -39, -118, 286, -102, 377, -81, 318, 215, -231, -57, 637, 283, 445, 81, 326, -27, -153, -267, 228, 219, 52, -29, 63, -214, 445, 106, 103, 107, -140, 76, 126, 83, -32, -66, 348, 45, 390, 45, -129, -80, -73, -211, 574, 219, 57, 95, 567, -31, 198, -113, -134, -263, 543, -129, 622, 264, -437, -68, 30, 132, 557, 69, 45, -155, 109, -184, 677, 117, -354, -7, 127, -198, -192, 43, 623, 57, 183, 5, 223, 194, -8, -448, 383, -203, 308, 61, 95, -38, -42, -128, 511, 276, 676, 103, 419, -152, 217, 18, -248, 65, 6, 43, 717, 16, 92, 65, 323, 118, -75, 206, 111, -186, -230, -354, 294, 262, -210, -18, 180, 37, -27, 5, -147, 0, 232, 25, 366, -111, -282, -12, 285, -129, 192, 9, 312, 21, 105, -141, 313, 294, -38, 44, 562, -183, 179, -19, -241, -154, -119, -66, 529, -160, 74, -101, 501, 212, -43, 234, -242, 48, -371, -326, 303, 119, 681, 21, 170, -122, -375, 69, 86, 87, 262, -63, 603, 351, -76, -101, 232, 103, 93, -76, -54, -111, -165, -211, 192, -4, -289, 171, 324, -342, 525, -198, 114, 21, -120, -67, 37, 53, -126, -219, 117, 21, 460, 118, -95, 97, -184, -195, -69, -50, 26, -48, 729, -214, -290, 67, 183, 169, 169, 73, 810, -2, -553, -59, 26, -97, 57, 99, 130, -251, 225, -107, 707, 220, 101, 27, -204, -86, -79, -63, -194, -297, 339, -67, 452, -129, -193, -62, 210, 139, 120, 113, 190, -34, -98, -197, 46, 308, 49, 59, 459, -373, 7, 72, -132, -285, -30, -74, 239, -14, 239, -311, 438, -45, 105, 27, -232, -28, -219, -296, 55, 114, 127, 191, 181, -191, -322, 59, 261, -265, -270, -53, 490, 49, -181, -99, 238, 111, 160, 69, 280, -584, 86, -361, 219, 362, -44, -64, -248, -304, 637, 35, -73, -30, 218, 14, 448, 231, -107, -183, 213, -6, 159, 13, 388, -92, -473, -164, 161, -103, 340, -24, 428, 65, -276, -188, -562, 226, 302, -81, 329, -67, 151, 8, 134, -114, 227, 257, -67, -513, -95, -224, 895, -124, -772, 61, 41, -245, 55, -15, 232, 84, 67, -16, 377, -2, -550, -222, 201, -223, 318, -31, 133, -174, -201, -240, -284, 229, -193, -22, 314, -208, 231, 120, -33, -183, -107, 32, 95, 71, -596, -74, 474, 41, 124, 118, -119, -166, -272, -252, 740, -147, 284, 19, -39, -433, -174, 32, 202, -48, 246, 113, 68, -57, 208, -67, 32, -33, 160, 31, 212, -185, -118, -215, 115, -55, -398, 48, 476, -212, -470, -232, 365, -414, -183, -100, 158, 274, -289, -103, 486, 38, 522, 210, -279, -133, -441, -114, 391, -227, 126, -42, 525, -326, -51, 41, -78, 155, -84, -75, 50, -126, -354, -118, 174, -226, -38, 44, -6, -525, -343, -192, 184, 416, -631, 218, 29, 2, -75, -181, -42, -217, -329, -4, 304, -144, -44, -35, -217, -98, 216, 117, 653, -368, -323, -242, -116, -55, 138, -58, 361, -354, 372, 133, -102, -61, 52, 20, 111, -39, -489, -172, 347, 81, 759, 26, -547, -58, -56, -201, 609, 25, 63, 50, -57, -313, -190, -186, -14, -174, 47, -160, 214, -249, -429, -125, 300, 213, -504, 202, 396, -449, -151, -242, 369, -281, -340, -1, 2, -491, -183, 82, 214, 149, 262, -125, -9, 305, -160, -198, -306, -235, 411, -55, -54, -562, -603, -84, 561, 152, 104, -44, 488, -316, -653, 12, -459, -103, -251, -66, 598, -33, 61, -42, 193, 85, -615, 168, -152, -283, 56, -256, 359, 102, 244, -41, 155, -220, -881, -109, -385, -137, 238, 150, 175, -71, -513, -125, 66, -452, 561, 112, 502, -17, -905, -289, -200, 237, -333, -45, 50, -395, 306, -123, 109, -440, -234, -99, 146, -227, 37, -260, 382, -69, -34, 176, -239, -225, -332, -486, 182, -82, -378, 23, 37, -358, -102, 115, 54, -220, -190, -96, 772, -37, -371, -195, -85, -110, -884, 22, -118, -527, -86, -71, 158, -199, -42, 216, 243, -344, -140, 21, -109, -61, 235, -17, -121, -13, -390, -191, 259, 3, 363, 229, 302, -542, -469, -186, 183, -55, -264, -165, 135, -132, 429, 17, -267, 85, -395, -18, 130, 162, 278, -170, -143, -258, 293, -22, -71, -471, -546, -280, 524, 151, -163, 75, -132, -397, -473, -226, 326, -156, 215, -39, 78, -27, -860, 0, 352, -21, -505, 158, 81, -401, -164, -196, 2, 179, 76, 15, -205, -491, -489, 54, -43, -51, -186, 126, 28, -315, -310, -321, 24, -40, -435, -6, -354, -136, -333, -230, 735, 5, 531, 238, 436, -212, -213, 44, -683, -427, -100, -41, 773, -134, -639, -50, 66, 110, 49, 178, 192, -223, -122, -243, -114, -111, -388, -5, 149, -332, -476, -87, 124, 63, -570, 80, -181, -14, -486, -45, 752, -51, 128, 111, -240, -483, -273, -224, 39, 249, -265, 70, -81, -223, -173, -188, -360, -42, -114, -161, 495, -50, -279, 78, -241, -176, 168, 286, 314, -411, -428, -343, 537, -44, -142, -65, 113, 75, -330, 31, -222, -42, 305, -73, 440, 45, -666, -168, -201, -352, 400, -43, -113, -92, -363, -129, 270, 92, -51, 147, 247, -312, 35, 89, 280, -129, -53, 49, -154, -184, -481, -214, 275, 23, -351, 102, 311, 35, -812, -481, 273, 20, 54, -3, 208, -614, -458, 122, -176, -413, 330, -4, 295, 19, -301, -75, 91, -38, 48, 28, -169, -469, -364, -35, 929, 401, -361, 134, -10, -397, -50, -202, -6, -156, -6, -132, -482, -56, 99, -204, -246, 72, -170, 296, -491, -317, -659, -93, -88, -239, -97, 19, 551, -129, -199, 111, -223, -220, -705, -116, 78, -227, -249, -258, 169, -257, -80, -50, -33, -615, -389, -404, 848, 248, 504, -12], "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": "8026.2.a.b", "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}