# Stored data for newform 8042.2.a.a, downloaded from the LMFDB on 19 April 2024. {"label": "8042.2.a.a", "space_label": "8042.2.a", "level": 8042, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33562474, "dim": 67, "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": 32168, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 64.21569330551368, "level_radical": 8042, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8042, 1, [4023], [1]], "inner_twist_count": 1, "level_primes": [2, 4021], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 67, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [4021, -1]], "trace_display": [67, -11, -20, -40], "traces": [67, 67, -11, 67, -20, -11, -40, 67, 24, -20, -13, -11, -51, -40, -31, 67, -34, 24, -33, -20, -39, -13, -43, -11, -9, -51, -29, -40, -63, -31, -43, 67, -49, -34, -20, 24, -77, -33, -40, -20, -50, -39, -56, -13, -48, -43, -48, -11, 1, -9, -18, -51, -91, -29, -58, -40, -65, -63, -17, -31, -45, -43, -67, 67, -65, -49, -112, -34, -57, -20, -75, 24, -79, -77, -5, -33, -85, -40, -80, -20, -77, -50, -22, -39, -134, -56, -49, -13, -77, -48, -17, -43, -97, -48, -73, -11, -87, 1, -44, -9, -88, -18, -84, -51, -28, -91, -35, -29, -125, -58, -36, -40, -85, -65, -26, -63, -91, -17, -54, -31, -62, -45, -56, -43, -48, -67, -149, 67, -30, -65, 20, -49, -84, -112, -52, -34, -95, -57, -4, -20, -85, -75, -36, 24, -49, -79, -1, -77, -154, -5, -132, -33, -73, -85, -1, -40, -77, -80, 16, -20, -71, -77, -64, -50, -19, -22, -54, -39, -54, -134, -9, -56, -62, -49, -72, -13, -96, -77, -17, -48, -50, -17, -113, -43, -61, -97, -32, -48, -51, -73, -101, -11, -222, -87, 97, 1, -89, -44, -37, -9, 16, -88, -8, -18, -126, -84, -47, -51, -70, -28, -57, -91, -40, -35, 1, -29, -91, -125, 15, -58, -117, -36, -93, -40, -121, -85, -1, -65, -40, -26, 43, -63, -126, -91, -19, -17, 26, -54, -86, -31, -54, -62, 22, -45, -32, -56, -82, -43, -43, -48, 44, -67, -218, -149, 9, 67, -114, -30, -17, -65, -87, 20, -120, -49, -58, -84, -3, -112, -88, -52, -43, -34, -5, -95, 9, -57, -150, -4, 23, -20, -117, -85, -49, -75, 26, -36, -12, 24, -89, -49, 68, -79, -83, -1, -74, -77, -46, -154, 108, -5, -65, -132, -50, -33, -29, -73, -75, -85, -29, -1, -60, -40, -17, -77, 81, -80, -125, 16, -81, -20, 5, -71, 2, -77, -65, -64, 56, -50, -74, -19, -55, -22, -63, -54, 50, -39, -139, -54, 132, -134, -43, -9, -143, -56, 26, -62, 47, -49, -86, -72, -43, -13, -80, -96, 66, -77, 96, -17, -99, -48, -66, -50, 54, -17, -83, -113, 13, -43, 60, -61, 172, -97, -225, -32, 34, -48, -29, -51, 38, -73, 23, -101, -34, -11, 28, -222, 9, -87, -107, 97, 34, 1, -164, -89, 92, -44, -101, -37, 177, -9, -66, 16, -96, -88, 121, -8, -45, -18, -9, -126, 128, -84, -39, -47, -65, -51, -65, -70, 149, -28, -97, -57, -28, -91, 80, -40, -20, -35, 58, 1, -18, -29, -41, -91, 147, -125, 10, 15, -33, -58, 27, -117, 66, -36, 4, -93, 158, -40, -140, -121, 134, -85, -20, -1, 98, -65, -227, -40, 132, -26, 0, 43, -192, -63, 126, -126, 165, -91, 30, -19, 111, -17, -142, 26, 23, -54, -78, -86, 41, -31, 15, -54, 140, -62, -125, 22, -154, -45, 107, -32, 78, -56, -11, -82, 172, -43, 7, -43, 49, -48, 42, 44, 82, -67, 4, -218, 170, -149, -18, 9, 81, 67, -70, -114, 163, -30, -40, -17, 78, -65, -2, -87, -73, 20, 83, -120, 15, -49, -52, -58, 132, -84, -87, -3, 18, -112, 144, -88, 237, -52, -69, -43, 84, -34, 19, -5, -104, -95, 97, 9, 158, -57, -162, -150, 157, -4, -100, 23, 60, -20, 16, -117, 128, -85, 45, -49, 173, -75, -89, 26, 43, -36, 74, -12, 32, 24, -64, -89, 281, -49, -89, 68, -160, -79, 25, -83, 158, -1, -56, -74, 111, -77, -78, -46, 299, -154, 9, 108, -69, -5, -53, -65, -18, -132, 53, -50, -44, -33, 122, -29, 97, -73, -200, -75, 184, -85, -40, -29, 210, -1, 17, -60, 164, -40, -81, -17, 124, -77, 11, 81, -45, -80, 103, -125, 243, 16, -48, -81, -1, -20, -80, 5, 41, -71, 36, 2, 70, -77, 72, -65, 326, -64, -192, 56, 33, -50, 93, -74, 86, -19, -36, -55, 250, -22, 92, -63, -78, -54, -26, 50, 123, -39, -159, -139, 278, -54, 115, 132, 10, -134, 76, -43, 119, -9, 120, -143, 95, -56, 110, 26, 90, -62, 142, 47, 29, -49, -103, -86, 354, -72, -95, -43, 40, -13, 276, -80, 221, -96, -19, 66, 89, -77, -10, 96, 82, -17, 43, -99, 49, -48, 22, -66, 195, -50, 31, 54, 82, -17, -33, -83, 180, -113, -139, 13, 303, -43, -30, 60, -2, -61, 240, 172, 75, -97, 145, -225, 256, -32, -60, 34, 65, -48, 70, -29, 262, -51, -47, 38, 300, -73, -1, 23, 99, -101, 4, -34, 18, -11, 27, 28, 229, -222, 90, 9, 137, -87, 299, -107, 253, 97, 32, 34, 195, 1, -28, -164, 76, -89, 224, 92, 26, -44, -31, -101, 312, -37, 80, 177, 66, -9, 196, -66, 207, 16, 98, -96, 96, -88, -80, 121, 46, -8, 87, -45, 195, -18, 32, -9, 478, -126, -1, 128, -87, -84, 189, -39, 149, -47, 52, -65, 182, -51, 162, -65, 80, -70, -8, 149, 241, -28, 0, -97, 218, -57, 181, -28, 91, -91, 70, 80, 149, -40, 41, -20, 135, -35, 49, 58, 184, 1, 306, -18, 51, -29, -12, -41, 237, -91, -94, 147, 147, -125, 40, 10, 326, 15, -234, -33, 225, -58, 18, 27, 24, -117, 340, 66, 191, -36, 107, 4, 213, -93, -45, 158, 51, -40, 265, -140, 278, -121, 30, 134, 225, -85, 100, -20, 109, -1, 189, 98, 74, -65, 2, -227, 403, -40, 44, 132, -36, -26, 150, 0, 302, 43, -18, -192, 244, -63, 28, 126, 171, -126, 80, 165, 149, -91, 13, 30, 401, -19, 210, 111, 17, -17, 342, -142, 210, 26, -42, 23, 170, -54, 115, -78, 209, -86, 204, 41, 202, -31, 50, 15, 297, -54, 120, 140, -251, -62, 268, -125, 326, 22, -13, -154, 357, -45, -96, 107, 238, -32, 3, 78, 175, -56, 146, -11, 465, -82, -42, 172, 104, -43, 195, 7, 276, -43, 27, 49, 217, -48, 124, 42, -76, 44, 217, 82, 79, -67, 71, 4, 334, -218, 214, 170, 287, -149, -50, -18, 160, 9, 28, 81, 176, 67, 172, -70, 187, -114, 140, 163, 33, -30, -251, -40, 385, -17, 15, 78, 33, -65, 159, -2, 414, -87, 93, -73, 151, 20, 83, 83, 50, -120, -88, 15, 31, -49, 56, -52, 297, -58, -175, 132, -98, -84, 190, -87, 330, -3, 12, 18, 146, -112, -128, 144, 162, -88, 160, 237, 83, -52, 51, -69, 159, -43, 65, 84, -268, -34, -26, 19, 206, -5, -339, -104, 155, -95, 65, 97, 203, 9, 47, 158, -97, -57, 201, -162, 52, -150, 14, 157, -75, -4, 77, -100, 216, 23, -103, 60, 364, -20, -105, 16, -112, -117, 343, 128, 56, -85, -237, 45, 239, -49, -35, 173, -169, -75, 38, -89, 437, 26, 39, 43, -14, -36, 33, 74, 165, -12, -168, 32, 33, 24, -94, -64, 258, -89, 16, 281, 97, -49, 208, -89, 63, 68, -219, -160, 169, -79, 211, 25, 76, -83, 117, 158, 139, -1, -179, -56, 307, -74, -6, 111, -103, -77, -24, -78, 146, -46, -111, 299, 29, -154, -9, 9, 288, 108, 43, -69, 89, -5, -99, -53, 7, -65, -39, -18, -227, -132, 105, 53, 379, -50, -255, -44, 287, -33, 156, 122, 20, -29, 402, 97, 32, -73, -75, -200, 152, -75, -60, 184, 121, -85, -101, -40, 385, -29, -282, 210, 190, -1, -112, 17, -338, -60, 46, 164, -13, -40, -33, -81, 355, -17, 78, 124, -143, -77, -64, 11, 175, 81, 4, -45, 78, -80, 352, 103, -82, -125, -5, 243, -22, 16, -476, -48, 308, -81, -120, -1, -46, -20, 60, -80, 108, 5, -34, 41, 85, -71, -82, 36, 167, 2, 116, 70, 388, -77, -344, 72, 114, -65, -2, 326, -317, -64, 141, -192, 365, 56, -107, 33, 120, -50, 32, 93, 152, -74, -204, 86, 45, -19, 13, -36, 207, -55, -260, 250, -383, -22, 224, 92, 252, -63, -130, -78, 127, -54, -31, -26, 102, 50, -203, 123, -46, -39, -95, -159, 353, -139, -7, 278, 148, -54, -81, 115, 503, 132, -60, 10, -42, -134, 45, 76, -317, -43, 259, 119, 120, -9, -50, 120, 451, -143, -105, 95, -55, -56, 162, 110, 286, 26, -168, 90, -263, -62, 208, 142, -29, 47, 197, 29, 257, -49, -306, -103, 286, -86, 99, 354, -26, -72, -3, -95, 287, -43, -158, 40, 299, -13, -79, 276, 182, -80, -241, 221, 134, -96, -26, -19, 380, 66, 184, 89, -125, -77, 340, -10, 187, 96, -213, 82, 145, -17, 242, 43, -129, -99, -63, 49, 107, -48, -107, 22, 31, -66, 182, 195, 80, -50, -40, 31, 202, 54, -399, 82, 564, -17, -40, -33, 34, -83, 252, 180, 292, -113, -198, -139, 226, 13, 271, 303, -227, -43, -414, -30, 275, 60, -32, -2, 148, -61, -43, 240, -20, 172, 149, 75, 77, -97, -181, 145, 612, -225, -127, 256, -219, -32, 100, -60, 269, 34, 155, 65, 84, -48, 22, 70, -102, -29, -32, 262, 81, -51, -536, -47, 80, 38, 132, 300, -120, -73, 169, -1, 228, 23, -114, 99, 157, -101, -4, 4, 198, -34, 188, 18, 278, -11, -22, 27, 298, 28, 4, 229, -425, -222, 101, 90, 304, 9, -292, 137, 306, -87, -21, 299, 50, -107, 12, 253, 234, 97, 39, 32, 143, 34, 15, 195, 50, 1, 154, -28, 580, -164, -3, 76, 295, -89, -190, 224, 3, 92, 15, 26, -8, -44, -30, -31, 378, -101, 108, 312, 17, -37, -42, 80, 445, 177, -658, 66, -45, -9, 106, 196, -133, -66, 111, 207, 273, 16, 66, 98, 32, -96, -34, 96, 133, -88, 33, -80, 342, 121, 83, 46, 16, -8, 138, 87, -52, -45, 112, 195, 381, -18, -478, 32, 288, -9, 70, 478, -75, -126, 155, -1, 425, 128, 163, -87, 25, -84, -43, 189, 154, -39, -256, 149, 244, -47, -179, 52, 505, -65, -32, 182, -251, -51, 201, 162, 214, -65, -66, 80, 308, -70, -89, -8, -73, 149, 129, 241, 136, -28, -183, 0, 65, -97, 237, 218, -131, -57, 324, 181, 432, -28, -23, 91, 86, -91, 204, 70, 130, 80, 0, 149, 99, -40, -341, 41, 270, -20, -118, 135, 255, -35, 27, 49, 322, 58, -132, 184, 92, 1, -54, 306, -577, -18, -58, 51, 263, -29, 211, -12, 214, -41, -149, 237, 136, -91, -272, -94, 519, 147, 34, 147, -9, -125, 166, 40, -176, 10, 70, 326, 106, 15, -182, -234, 579, -33, -21, 225, -172, -58, 204, 18, 333, 27, -124, 24, 287, -117, 82, 340, 461, 66, -162, 191, 128, -36, -239, 107, 236, 4, 220, 213, -245, -93, 168, -45, 178, 158, -336, 51, 244, -40, -134, 265, -12, -140, 390, 278, 208, -121, -111, 30, -23, 134, 345, 225, 44, -85, -78, 100, 513, -20, -486, 109, 207, -1, 40, 189, 60, 98, 4, 74, 101, -65, -18, 2, 400, -227, 9, 403, -126, -40, -52, 44, 357, 132, -116, -36, 110, -26, 272, 150, -297, 0, 135, 302, 251, 43, -411, -18, 374, -192, 221, 244, 101, -63, 11, 28, 405, 126, 151, 171, -79, -126, 415, 80, -300, 165, -294, 149, -23, -91, 14, 13, 137, 30, 140, 401, -11, -19, 368, 210, 358, 111, -134, 17, 17, -17, -172, 342, -114, -142, -159, 210, 408, 26, 32, -42, 273, 23, -29, 170, -362, -54, -42, 115, 302, -78, -7, 209, 199, -86, -227, 204, 254, 41, 166, 202, 255, -31, 46, 50, 453, 15, 67, 297, -105, -54, 70, 120, 478, 140, -291, -251, 77, -62, 288, 268, 294, -125, 42, 326, 193, 22, -65, -13, -52, -154, 199, 357, 100, -45, 376, -96, 368, 107, -702, 238, 200, -32, -189, 3, -238, 78, 401, 175, 334, -56, -223, 146, 267, -11, -27, 465, -221, -82, 236, -42, 534, 172, 10, 104, 109, -43, 130, 195, -106, 7, 125, 276, 246, -43, -204, 27, 618, 49, -11, 217, -190, -48, 285, 124, 55, 42, -36, -76, 98, 44, 123, 217, 150, 82, -33, 79, 168, -67, -191, 71, 484, 4, 188, 334, -599, -218, -274, 214, 559, 170, -81, 287, 124, -149, 10, -50, 227, -18, 77, 160, -168, 9, 90, 28, 24, 81, -37, 176, -194, 67, 275, 172, 234, -70, -408, 187, 14, -114, 422, 140, -123, 163, 28, 33, 301, -30, -403, -251, 360, -40, 68, 385, 173, -17, -506, 15, 397, 78, 173, 33, 360, -65, -159, 159, -272, -2, -218, 414, 20, -87, 26, 93, 292, -73, 121, 151, -284, 20, -148, 83, 230, 83, -167, 50, -163, -120, 94, -88, 173, 15, 110, 31, 281, -49, -114, 56, 222, -52, -27, 297, -122, -58, 42, -175, -85, 132, -120, -98, 280, -84, -128, 190, 72, -87, 46, 330, 428, -3, -345, 12, 190, 18, -71, 146, -490, -112, 263, -128, 380, 144, 36, 162, 43, -88, -116, 160, -425, 237, -143, 83, 237, -52, -35, 51, 98, -69, 21, 159, -51, -43, -181, 65, 362, 84, -571, -268, -30, -34, 214, -26, 118, 19, 26, 206, 255, -5, -255, -339, 230, -104, 247, 155, -328, -95, -348, 65, 313, 97, -207, 203, -502, 9, -63, 47, 129, 158, 130, -97, -19, -57, -155, 201, 132, -162, -296, 52, 58, -150, 315, 14, 427, 157, -134, -75, -139, -4, 57, 77, -390, -100, -55, 216, 2, 23, -561, -103, 221, 60, -281, 364, 206, -20, -94, -105, -193, 16, -182, -112, -55, -117, -289, 343, 26, 128, -347, 56, 41, -85, -289, -237, 202, 45, 152, 239, -730, -49, 183, -35, 43, 173, -154, -169, 273, -75, 107, 38, -67, -89, -359, 437, 63, 26, -88, 39, 67, 43, -33, -14, -205, -36, -100, 33, 366, 74, -705, 165, -44, -12, 52, -168, -311, 32, -115, 33, -101, 24, 11, -94, -140, -64, -193, 258, -385, -89, -467, 16, 287, 281, -272, 97, -53, -49, -169, 208, -92, -89, -304, 63, 108, 68, -246, -219, -282, -160, -194, 169, -358, -79, -198, 211, 219, 25, 146, 76, -126, -83, -163, 117, -155, 158, 201, 139, -6, -1, -1122, -179, 165, -56, 72, 307, -37, -74, -426, -6, 72, 111, -52, -103, -288, -77, 90, -24, 38, -78, -89, 146, -618, -46, -262, -111, 214, 299, -490, 29, -369, -154, 47, -9, 322, 9, -453, 288, 164, 108, -312, 43, -89, -69, 93, 89, 185, -5, 107, -99, -508, -53, 180, 7, -120, -65, -199, -39, 119, -18, -238, -227, 61, -132, 33, 105, 207, 53, -231, 379, -560, -50, -349, -255, -131, -44, -121, 287, -169, -33, -570, 156, 311, 122, -235, 20, -277, -29, -93, 402, -385, 97, -385, 32, -158, -73, -98, -75, 61, -200, 3, 152, -79, -75, 260, -60, 561, 184, -460, 121, -491, -85, -271, -101, -62, -40, -133, 385, 160, -29, -485, -282, 4, 210, -34, 190, -223, -1, 193, -112, 337, 17, -274, -338, 301, -60, -5, 46, 42, 164, -766, -13, 37, -40, -103, -33, -162, -81, -396, 355, -298, -17, -556, 78, 232, 124, -166, -143, 11, -77, -474, -64, -151, 11, 228, 175, -122, 81, -43, 4, -13, -45, 149, 78, -520, -80, -259, 352, 157, 103, -663, -82, -503, -125, 64, -5, -84, 243, -92, -22, 8, 16, -70, -476, 28, -48, -335, 308, -123, -81, -561, -120, 382, -1, -221, -46, -47, -20, -223, 60, -215, -80, -188, 108, 270, 5, -278, -34, -18, 41, -133, 85, -309, -71, -249, -82, -53, 36, 72, 167, -360, 2, -99, 116, -42, 70, 131, 388, -198, -77, -431, -344, 288, 72, -60, 114, -31, -65, -448, -2, 45, 326, -748, -317, 350, -64, -276, 141, 181, -192, -326, 365, -68, 56, -374, -107, 332, 33, 49, 120, -845, -50, 82, 32, 58, 93, -119, 152, -52, -74, -285, -204, 344, 86, 54, 45, -90, -19, -300, 13, 98, -36, -206, 207, -414, -55, -898, -260, 509, 250, -613, -383, 400, -22, 177, 224, -436, 92, -592, 252, -109, -63, 203, -130, 215, -78, -465, 127, -160, -54, -690, -31, 68, -26, -32, 102, 259, 50, 113, -203, -466, 123, -66, -46, 13, -39, -181, -95, 334, -159, -221, 353, -478, -139, -84, -7, 84, 278, -117, 148, -442, -54, -270, -81, 176, 115, -114, 503, -161, 132, -436, -60, 188, 10, -371, -42, -84, -134, 244, 45, 442, 76, -446, -317, -62, -43, -130, 259, -240, 119, -262, 120, 161, -9, -81, -50, 157, 120, -244, 451, -201, -143, -329, -105, 480, 95, -258, -55, -88, -56, -535, 162, 142, 110, 240, 286, 68, 26, -73, -168, -483, 90, 60, -263, -650, -62, -292, 208, -152, 142, -788, -29, -65, 47, 16, 197, 345, 29, -314, 257, -230, -49, -473, -306, -227, -103, -107, 286, 125, -86, -692, 99, 243, 354, -280, -26, -520, -72, -271, -3, -354, -95, -72, 287, -222, -43, -240, -158, 366, 40, -152, 299, -395, -13, 189, -79, 545, 276, -319, 182, -284, -80, -83, -241, 130, 221, -141, 134, -88, -96, 54, -26, -482, -19, -320, 380, -483, 66, -86, 184, -141, 89, -117, -125, 325, -77, 73, 340, -145, -10, -431, 187, 6, 96, -854, -213, 142, 82, -236, 145, -36, -17, -362, 242, 457, 43, 35, -129, -264, -99, -347, -63, -49, 49, -98, 107, -168, -48, -244, -107, -220, 22, 25, 31, -233, -66, -94, 182, 358, 195, -788, 80, 378, -50, -259, -40, -95, 31, -263, 202, -389, 54, 9, -399, 304, 82, -366, 564, -91, -17, -148, -40, 267, -33, -25, 34, 167, -83, -397, 252, -521, 180, -291, 292, 97, -113, -418, -198, 4, -139, -388, 226, -317, 13, 268, 271, 230, 303, 111, -227, -131, -43, 56, -414, -58, -30, -579, 275, 28, 60, -633, -32, -654, -2, 79, 148, -4, -61, -447, -43, 116, 240, -10, -20, -126, 172, -537, 149, 121, 75, -672, 77, 208, -97, -173, -181, 550, 145, -330, 612, -859, -225, 180, -127, 590, 256, -67, -219, -1023, -32, -190, 100, 84, -60, -2, 269, -137, 34], "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": "8042.2.a.a", "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}