# Stored data for newform 8018.2.a.e, downloaded from the LMFDB on 18 April 2024. {"label": "8018.2.a.e", "space_label": "8018.2.a", "level": 8018, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543044434, "dim": 32, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [-26, 1, 3952, -4748, -156333, 166922, 2009136, -1127837, -11493777, 2172294, 33485860, 1246064, -54977657, -10309935, 54673879, 16185737, -34575094, -13236554, 14294549, 6622147, -3883898, -2153341, 674737, 464827, -67520, -66151, 2248, 5966, 261, -309, -31, 7, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32072, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 64.0240523406626, "level_radical": 8018, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8018, 1, [2111, 1901], [1, 1]], "inner_twist_count": 1, "level_primes": [2, 19, 211], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 32, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [19, 1], [211, -1]], "trace_display": [32, -7, -6, -5], "traces": [32, 32, -7, 32, -6, -7, -5, 32, 15, -6, -21, -7, -19, -5, -14, 32, -14, 15, -32, -6, -26, -21, -13, -7, -10, -19, -25, -5, -42, -14, -15, 32, -32, -14, -22, 15, -54, -32, -32, -6, -16, -26, -37, -21, -46, -13, -9, -7, -7, -10, -32, -19, -53, -25, -17, -5, 7, -42, -34, -14, -33, -15, 18, 32, -50, -32, -53, -14, -40, -22, -27, 15, -43, -54, 5, -32, -56, -32, -11, -6, -8, -16, -17, -26, -30, -37, 3, -21, -21, -46, -67, -13, -31, -9, 6, -7, -51, -7, -32, -10, -43, -32, -45, -19, -9, -53, -16, -25, -60, -17, 1, -5, -52, 7, -25, -42, 1, -34, 22, -14, -27, -33, -29, -15, -24, 18, -97, 32, -7, -50, -20, -32, 5, -53, -2, -14, -23, -40, 1, -22, -61, -27, 53, 15, 5, -43, -66, -54, -56, 5, -11, -32, -11, -56, -47, -32, -20, -11, 16, -6, -59, -8, -79, -16, -41, -17, -34, -26, -53, -30, -15, -37, -44, 3, -34, -21, 30, -21, -42, -46, -42, -67, 64, -13, -61, -31, -88, -9, -58, 6, 2, -7, -105, -51, 117, -7, -74, -32, 43, -10, -67, -43, -11, -32, -113, -45, -21, -19, 21, -9, 32, -53, -5, -16, 39, -25, -98, -60, -36, -17, -40, 1, -84, -5, -85, -52, 33, 7, 3, -25, 71, -42, -25, 1, -69, -34, 30, 22, -42, -14, -38, -27, -87, -33, -12, -29, 19, -15, -42, -24, -1, 18, 43, -97, 60, 32, -5, -7, -80, -50, -113, -20, -27, -32, -29, 5, 4, -53, -45, -2, 90, -14, 12, -23, -57, -40, -153, 1, -13, -22, -104, -61, -25, -27, 14, 53, 24, 15, -46, 5, 66, -43, -16, -66, 38, -54, -31, -56, -70, 5, -137, -11, 95, -32, -8, -11, -56, -56, 50, -47, 52, -32, -49, -20, -49, -11, -91, 16, 3, -6, 40, -59, 14, -8, -22, -79, 69, -16, -44, -41, -52, -17, -51, -34, 148, -26, -88, -53, -76, -30, -5, -15, 56, -37, 56, -44, -1, 3, -61, -34, -25, -21, -104, 30, -55, -21, -78, -42, 2, -46, 32, -42, 53, -67, -17, 64, -34, -13, 20, -61, 79, -31, -102, -88, -24, -9, -1, -58, 16, 6, 90, 2, 40, -7, 165, -105, -44, -51, -64, 117, -69, -7, -44, -74, -95, -32, -10, 43, 26, -10, -74, -67, -47, -43, 106, -11, 58, -32, -4, -113, 86, -45, -127, -21, -35, -19, -50, 21, 43, -9, -74, 32, 156, -53, -5, -5, -22, -16, -48, 39, -42, -25, -129, -98, -1, -60, 13, -36, 44, -17, -6, -40, 129, 1, -75, -84, 146, -5, -92, -85, -14, -52, -67, 33, 28, 7, 14, 3, -21, -25, 47, 71, -54, -42, 72, -25, -74, 1, -22, -69, -35, -34, 5, 30, 10, 22, -79, -42, 118, -14, 63, -38, 28, -27, 96, -87, -124, -33, -19, -12, -121, -29, -95, 19, 169, -15, 34, -42, -58, -24, -42, -1, 84, 18, -62, 43, 4, -97, 24, 60, 38, 32, 25, -5, 83, -7, -37, -80, 152, -50, 91, -113, 75, -20, 175, -27, 34, -32, -59, -29, 59, 5, 1, 4, -71, -53, 109, -45, 68, -2, -43, 90, -5, -14, -3, 12, -146, -23, -42, -57, 42, -40, -32, -153, 80, 1, -88, -13, 85, -22, 211, -104, 54, -61, -31, -25, 56, -27, -74, 14, 28, 53, -13, 24, 138, 15, -65, -46, 180, 5, -129, 66, -54, -43, -60, -16, 40, -66, 15, 38, 114, -54, 1, -31, 10, -56, -38, -70, 214, 5, 32, -137, -137, -11, -57, 95, -32, -32, 132, -8, -35, -11, 33, -56, 18, -56, 77, 50, -21, -47, -4, 52, -5, -32, -60, -49, 32, -20, 52, -49, 30, -11, -7, -91, 217, 16, 31, 3, 5, -6, -114, 40, -5, -59, 4, 14, 38, -8, -91, -22, 233, -79, 26, 69, 43, -16, -84, -44, 76, -41, -26, -52, 154, -17, 22, -51, -23, -34, -4, 148, 114, -26, -225, -88, 268, -53, -25, -76, 32, -30, -198, -5, -47, -15, 28, 56, 19, -37, 136, 56, 57, -44, 123, -1, 16, 3, -30, -61, -52, -34, -8, -25, 54, -21, 30, -104, 5, 30, 52, -55, 19, -21, 144, -78, 1, -42, 57, 2, -120, -46, -165, 32, 84, -42, 55, 53, 121, -67, -108, -17, 23, 64, 52, -34, 230, -13, -103, 20, -52, -61, 32, 79, 33, -31, -68, -102, 228, -88, 145, -24, 59, -9, 199, -1, -87, -58, -172, 16, 303, 6, 16, 90, -101, 2, 170, 40, 167, -7, 96, 165, -139, -105, -87, -44, -31, -51, 160, -64, 16, 117, -168, -69, 194, -7, 41, -44, -61, -74, 233, -95, 209, -32, -81, -10, 21, 43, -60, 26, 101, -10, 75, -74, 180, -67, -111, -47, 328, -43, -117, 106, 64, -11, -133, 58, 125, -32, 37, -4, 134, -113, -79, 86, -58, -45, 158, -127, 161, -21, 91, -35, 13, -19, -4, -50, 73, 21, 162, 43, 67, -9, 138, -74, 131, 32, 92, 156, 54, -53, 151, -5, 1, -5, -6, -22, 46, -16, -16, -48, 40, 39, 211, -42, 94, -25, 152, -129, 175, -98, -98, -1, 76, -60, 141, 13, 140, -36, -224, 44, 288, -17, 88, -6, -1, -40, 62, 129, 171, 1, -57, -75, 253, -84, 9, 146, 34, -5, 41, -92, 123, -85, 62, -14, 291, -52, 90, -67, -162, 33, -13, 28, 115, 7, 17, 14, -40, 3, 199, -21, 126, -25, -125, 47, -33, 71, 42, -54, 46, -42, 46, 72, 7, -25, 66, -74, 56, 1, 179, -22, 48, -69, 184, -35, 78, -34, 29, 5, -89, 30, -17, 10, 339, 22, -37, -79, 284, -42, -26, 118, 127, -14, -119, 63, 132, -38, 20, 28, -21, -27, 32, 96, 108, -87, 134, -124, 250, -33, 49, -19, 116, -12, 134, -121, 9, -29, 36, -95, 186, 19, 229, 169, -88, -15, 367, 34, -1, -42, -32, -58, 127, -24, 244, -42, -158, -1, 224, 84, 53, 18, -65, -62, 30, 43, -24, 4, -77, -97, 143, 24, -31, 60, -22, 38, 41, 32, 136, 25, 44, -5, 43, 83, 290, -7, -81, -37, 226, -80, -111, 152, 207, -50, -9, 91, 17, -113, 17, 75, 56, -20, -97, 175, 105, -27, 147, 34, -6, -32, -93, -59, -126, -29, -198, 59, 84, 5, 326, 1, 115, 4, 208, -71, 21, -53, 104, 109, -45, -45, 89, 68, 166, -2, 116, -43, -7, 90, -15, -5, -13, -14, 52, -3, 58, 12, 63, -146, 232, -23, -62, -42, 58, -57, 122, 42, -4, -40, 19, -32, 235, -153, 50, 80, 113, 1, 172, -88, 229, -13, -260, 85, 131, -22, 34, 211, 9, -104, 90, 54, -70, -61, -35, -31, 381, -25, -26, 56, -1, -27, 21, -74, 195, 14, 18, 28, -59, 53, 77, -13, -35, 24, 84, 138, -111, 15, -110, -65, 16, -46, 202, 180, 33, 5, -95, -129, 24, 66, 66, -54, 63, -43, 515, -60, 34, -16, -268, 40, 214, -66, -267, 15, 239, 38, -133, 114, 260, -54, -65, 1, -49, -31, -119, 10, 171, -56, -160, -38, -114, -70, -18, 214, 116, 5, -141, 32, 207, -137, 209, -137, 215, -11, 80, -57, -78, 95, -93, -32, 148, -32, 150, 132, -57, -8, 231, -35, 185, -11, -95, 33, -208, -56, 56, 18, -62, -56, -142, 77, 50, 50, -187, -21, 249, -47, -35, -4, -89, 52, 351, -5, 35, -32, -78, -60, -49, -49, -28, 32, 50, -20, -167, 52, 334, -49, -143, 30, 251, -11, -9, -7, -62, -91, -161, 217, 105, 16, 53, 31, 49, 3, -201, 5, 46, -6, -140, -114, 299, 40, -74, -5, 53, -59, -97, 4, 18, 14, 190, 38, 262, -8, -157, -91, -237, -22, -55, 233, -117, -79, 144, 26, 35, 69, -155, 43, 40, -16, 9, -84, -156, -44, -19, 76, 139, -41, 44, -26, 198, -52, -61, 154, -104, -17, 124, 22, -18, -51, -55, -23, -66, -34, -26, -4, 50, 148, -162, 114, 104, -26, -14, -225, 102, -88, 27, 268, 21, -53, 143, -25, 94, -76, -230, 32, 631, -30, -155, -198, -231, -5, -41, -47, 135, -15, 92, 28, -7, 56, 278, 19, 236, -37, 163, 136, -149, 56, -224, 57, 5, -44, 215, 123, 43, -1, 77, 16, 54, 3, 82, -30, 312, -61, 158, -52, -112, -34, -191, -8, 161, -25, -134, 54, 154, -21, -129, 30, 82, -104, -48, 5, 105, 30, -238, 52, 238, -55, -174, 19, -79, -21, -5, 144, 153, -78, -42, 1, 206, -42, 50, 57, 53, 2, -73, -120, -247, -46, 37, -165, 188, 32, 214, 84, -183, -42, 360, 55, 105, 53, -282, 121, -143, -67, 90, -108, -135, -17, 121, 23, 56, 64, -309, 52, -255, -34, 78, 230, 98, -13, 316, -103, -127, 20, -5, -52, 231, -61, -69, 32, 31, 79, -7, 33, 279, -31, -97, -68, -34, -102, -45, 228, 154, -88, 153, 145, -143, -24, 11, 59, -37, -9, -93, 199, -150, -1, -132, -87, 553, -58, -27, -172, -32, 16, 13, 303, 408, 6, 102, 16, 37, 90, 231, -101, -193, 2, 142, 170, -213, 40, 186, 167, 210, -7, -149, 96, 8, 165, -188, -139, -209, -105, 176, -87, 191, -44, -68, -31, 98, -51, 17, 160, -28, -64, -4, 16, 310, 117, -103, -168, -42, -69, 40, 194, 8, -7, -17, 41, 241, -44, -125, -61, 210, -74, 17, 233, -72, -95, -1, 209, 34, -32, -97, -81, 258, -10, -106, 21, 8, 43, 72, -60, 122, 26, 51, 101, -53, -10, 171, 75, 102, -74, -31, 180, -277, -67, 46, -111, -56, -47, 217, 328, 30, -43, -299, -117, -61, 106, -224, 64, -37, -11, 251, -133, -81, 58, -41, 125, 133, -32, -27, 37, 312, -4, -75, 134, 176, -113, 71, -79, 60, 86, 47, -58, 56, -45, -282, 158, 189, -127, -3, 161, 215, -21, -192, 91, 215, -35, 122, 13, -14, -19, 149, -4, -172, -50, 152, 73, 196, 21, 254, 162, -280, 43, 68, 67, 220, -9, -6, 138, -204, -74, 69, 131, -155, 32, -63, 92, 21, 156, -92, 54, 163, -53, -136, 151, 14, -5, 107, 1, -138, -5, 11, -6, 104, -22, 255, 46, 284, -16, -75, -16, 336, -48, 44, 40, -41, 39, -271, 211, 46, -42, -242, 94, 39, -25, 67, 152, 191, -129, -73, 175, 326, -98, -424, -98, 486, -1, -127, 76, -160, -60, 106, 141, -154, 13, 269, 140, 259, -36, 84, -224, 22, 44, -105, 288, -96, -17, -59, 88, 150, -6, -369, -1, 31, -40, 19, 62, -90, 129, -23, 171, 242, 1, 216, -57, -229, -75, -91, 253, -342, -84, -65, 9, 119, 146, -112, 34, 484, -5, 48, 41, 200, -92, -258, 123, 426, -85, -201, 62, -157, -14, -6, 291, -179, -52, 78, 90, 173, -67, -153, -162, 479, 33, -174, -13, 26, 28, -251, 115, 250, 7, -48, 17, -23, 14, 213, -40, 92, 3, 125, 199, -40, -21, -350, 126, 165, -25, -18, -125, 51, 47, 229, -33, 71, 71, 169, 42, 190, -54, 211, 46, -29, -42, -353, 46, 7, 72, 41, 7, 235, -25, -48, 66, 172, -74, 165, 56, -79, 1, -453, 179, 195, -22, -104, 48, -88, -69, 32, 184, 297, -35, 114, 78, -149, -34, 74, 29, 127, 5, 138, -89, 247, 30, 152, -17, 15, 10, 205, 339, 29, 22, 272, -37, 145, -79, 56, 284, -22, -42, 20, -26, -237, 118, 75, 127, 43, -14, -123, -119, 226, 63, -77, 132, -319, -38, 124, 20, -74, 28, -304, -21, 127, -27, 18, 32, 351, 96, 53, 108, 414, -87, 124, 134, 76, -124, -190, 250, 194, -33, -354, 49, 178, -19, 45, 116, 304, -12, -251, 134, 191, -121, -113, 9, 442, -29, -290, 36, -375, -95, 75, 186, 306, 19, -51, 229, 149, 169, 171, -88, 327, -15, -144, 367, -329, 34, 47, -1, 337, -42, 197, -32, 9, -58, -42, 127, 16, -24, 188, 244, 4, -42, 2, -158, -169, -1, -100, 224, -91, 84, 312, 53, 478, 18, -345, -65, 309, -62, -3, 30, 209, 43, -54, -24, 130, 4, 83, -77, 56, -97, 16, 143, 85, 24, -166, -31, 203, 60, -343, -22, 366, 38, -249, 41, -230, 32, 17, 136, 236, 25, 296, 44, 145, -5, 388, 43, 13, 83, -93, 290, -191, -7, 332, -81, -186, -37, -271, 226, 60, -80, 249, -111, -220, 152, 2, 207, 25, -50, 230, -9, -272, 91, -142, 17, 265, -113, -37, 17, 230, 75, -14, 56, 320, -20, -278, -97, -73, 175, -196, 105, 175, -27, 27, 147, -335, 34, -1, -6, 25, -32, -51, -93, 15, -59, 288, -126, 281, -29, -69, -198, -247, 59, -371, 84, 418, 5, 199, 326, 108, 1, 535, 115, 102, 4, -151, 208, 52, -71, -114, 21, -502, -53, 134, 104, 52, 109, -128, -45, 249, -45, 31, 89, -73, 68, 76, 166, -316, -2, -286, 116, -168, -43, 12, -7, 76, 90, -185, -15, 152, -5, 98, -13, -16, -14, -274, 52, 111, -3, -350, 58, 96, 12, 25, 63, -268, -146, -240, 232, 143, -23, -168, -62, 333, -42, -332, 58, -66, -57, -104, 122, 188, 42, 96, -4, 215, -40, 137, 19, 277, -32, -36, 235, -398, -153, 141, 50, -167, 80, -101, 113, -1, 1, 101, 172, -272, -88, 79, 229, 236, -13, 128, -260, -212, 85, -189, 131, 210, -22, -143, 34, -111, 211, -427, 9, 113, -104, -143, 90, -355, 54, 31, -70, 603, -61, -213, -35, -329, -31, -22, 381, -10, -25, -265, -26, -147, 56, -296, -1, 425, -27, -127, 21, -273, -74, -226, 195, 98, 14, 253, 18, -133, 28, 281, -59, -267, 53, -48, 77, -149, -13, -46, -35, 111, 24, -201, 84, 27, 138, -231, -111, -62, 15, 13, -110, -184, -65, -17, 16, -79, -46, -272, 202, 16, 180, -151, 33, 491, 5, -21, -95, -95, -129, -368, 24, -166, 66, 8, 66, 109, -54, -486, 63, -101, -43, 29, 515, 109, -60, -166, 34, 232, -16, 28, -268, -235, 40, -683, 214, 19, -66, -209, -267, 354, 15, 95, 239, -91, 38, 447, -133, 135, 114, 31, 260, -59, -54, 77, -65, -186, 1, -2, -49, 24, -31, -719, -119, 41, 10, -178, 171, -161, -56, 18, -160, -409, -38, -112, -114, -218, -70, -68, -18, 61, 214, -197, 116, 256, 5, -96, -141, 47, 32, -17, 207, -257, -137, -206, 209, 46, -137, 97, 215, 214, -11, -372, 80, 16, -57, -130, -78, 348, 95, -72, -93, -637, -32, -57, 148, 121, -32, 227, 150, 299, 132, 50, -57, 54, -8, 124, 231, -447, -35, 229, 185, -81, -11, -17, -95, 7, 33, -216, -208, 19, -56, -8, 56, -310, 18, -146, -62, -71, -56, -662, -142, -675, 77, 130, 50, 256, 50, -67, -187, -50, -21, -35, 249, 236, -47, -314, -35, 104, -4, -196, -89, -134, 52, 20, 351, 30, -5, -258, 35, 255, -32, -456, -78, 384, -60, -406, -49, -199, -49, 223, -28, -162, 32, 61, 50, -184, -20, 276, -167, 179, 52, -272, 334, 299, -49, -75, -143, -158, 30, 52, 251, -5, -11, 72, -9, -452, -7, 130, -62, 70, -91, 275, -161, -393, 217, -327, 105, -38, 16, -168, 53, -263, 31, -198, 49, 253, 3, 35, -201, 77, 5, -528, 46, 305, -6, 44, -140, -107, -114, 2, 299, -89, 40, -188, -74, 31, -5, -57, 53, 139, -59, -501, -97, -82, 4, -92, 18, 294, 14, 0, 190, -360, 38, 319, 262, -32, -8, -107, -157, -26, -91, 23, -237, -116, -22, -219, -55, 23, 233, -417, -117, -60, -79, -80, 144, -335, 26, 274, 35, -286, 69, -149, -155, -213, 43, 30, 40, -142, -16, -189, 9, -8, -84, -269, -156, -49, -44, -181, -19, 74, 76, -342, 139, 158, -41, -1, 44, 74, -26, -190, 198, -139, -52, -226, -61, 263, 154, -359, -104, -441, -17, -230, 124, 139, 22, 256, -18, 125, -51, -62, -55, -208, -23, -166, -66, -232, -34, 188, -26, -290, -4, -91, 50, 61, 148, -21, -162, 17, 114, -139, 104, 62, -26, 42, -14, -247, -225, -171, 102, -308, -88, -391, 27, 248, 268, -395, 21, 136, -53, -39, 143, -314, -25, -256, 94, 476, -76, -141, -230, -346, 32, -53, 631, -26, -30, 32, -155, -21, -198, -90, -231, 223, -5, -179, -41, -391, -47, -156, 135, 232, -15, -20, 92, 195, 28, 40, -7, -19, 56, -267, 278, -181, 19, -157, 236, -232, -37, 251, 163, -5, 136, 7, -149, -120, 56, 218, -224, 72, 57, 312, 5, -325, -44, -527, 215, -90, 123, -461, 43, -135, -1, 7, 77, 194, 16, -146, 54, 26, 3, -9, 82, 342, -30, -289, 312, -194, -61, 66, 158, -136, -52, -373, -112, 200, -34, 68, -191, -111, -8, -7, 161, -183, -25, -219, -134, -72, 54, 230, 154, -325, -21, -213, -129, 130, 30, -261, 82, 250, -104, 222, -48, -231, 5, -392, 105, 56, 30, -385, -238, 321, 52, -246, 238, -48, -55, 223, -174, -80, 19, -274, -79, -102, -21, 15, -5, 73, 144, -357, 153, 192, -78, -62, -42, 180, 1, -154, 206, -3, -42, -518, 50, 122, 57, 11, 53, -25, 2, -242, -73, 136, -120, -520, -247, 529, -46, -379, 37, -362, -165, -343, 188, -35, 32, 222, 214, -144, 84, 274, -183, -107, -42, -206, 360, -169, 55, 95, 105, 262, 53, -225, -282, 11, 121, 71, -143, 551, -67, -98, 90, 302, -108, -24, -135, -331, -17, -220, 121, 49, 23, -216, 56, 282, 64, -506, -309, 244, 52, 12, -255, -113, -34, -629, 78, 550, 230, -279, 98, -97, -13, 47, 316, -213, -103, -224, -127, 265, 20, -376, -5, 314, -52, -309, 231, -142, -61, -45, -69, 122, 32, 340, 31, -412, 79, -204, -7, 20, 33, -68, 279, 369, -31, 82, -97, -286, -68, 281, -34, 20, -102, -361, -45, -485, 228, 202, 154, 68, -88, 17, 153, -111, 145, -376, -143, -310, -24], "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": "8018.2.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": 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}