# Stored data for newform 8018.2.a.d, downloaded from the LMFDB on 19 April 2024. {"label": "8018.2.a.d", "space_label": "8018.2.a", "level": 8018, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915673938, "dim": 30, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [5806, -16055, -187677, 389570, 1412694, -2439940, -5310714, 7391961, 12176542, -13031041, -18532907, 14438012, 19509892, -10327445, -14484744, 4681708, 7629374, -1194868, -2834921, 63566, 728897, 63982, -124502, -22931, 12977, 3693, -658, -301, 0, 10, 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": 30, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [19, -1], [211, 1]], "trace_display": [30, -10, -12, -15], "traces": [30, 30, -10, 30, -12, -10, -15, 30, 10, -12, -17, -10, -19, -15, -8, 30, -18, 10, 30, -12, -14, -17, -15, -10, -4, -19, -37, -15, -37, -8, -11, 30, 6, -18, -4, 10, -46, 30, 0, -12, -28, -14, -61, -17, -14, -15, -4, -10, -1, -4, -8, -19, -19, -37, -17, -15, -10, -37, -6, -8, -32, -11, -24, 30, -24, 6, -44, -18, -2, -4, 10, 10, -58, -46, -42, 30, -32, 0, -42, -12, -38, -28, -25, -14, -48, -61, -15, -17, -39, -14, -21, -15, -45, -4, -12, -10, -33, -1, -38, -4, -27, -8, -26, -19, -41, -19, -44, -37, -20, -17, 31, -15, -53, -10, -21, -37, -35, -6, -50, -8, -33, -32, -29, -11, -6, -24, -61, 30, 29, -24, -41, 6, -15, -44, 32, -18, -28, -2, -75, -4, -9, 10, -31, 10, -35, -58, 25, -46, -45, -42, -56, 30, -45, -32, -37, 0, -91, -42, 6, -12, -43, -38, -85, -28, 3, -25, 10, -14, -15, -48, 10, -61, -18, -15, -16, -17, -116, -39, -38, -14, -75, -21, -56, -15, -7, -45, -12, -4, -44, -12, 14, -10, -86, -33, -31, -1, -77, -38, -34, -4, -7, -27, -13, -8, 9, -26, -1, -19, -17, -41, -30, -19, -64, -44, -9, -37, -14, -20, -33, -17, -78, 31, -2, -15, 44, -53, -61, -10, -55, -21, 25, -37, -93, -35, -93, -6, -12, -50, 52, -8, -27, -33, 29, -32, -14, -29, -19, -11, -58, -6, 16, -24, -179, -61, 58, 30, -46, 29, -40, -24, 3, -41, 62, 6, -57, -15, -38, -44, -57, 32, -102, -18, -40, -28, -13, -2, -49, -75, 79, -4, 53, -9, -55, 10, -8, -31, -28, 10, -68, -35, -50, -58, -16, 25, -98, -46, 29, -45, 26, -42, -25, -56, -85, 30, -58, -45, 2, -32, -147, -37, -3, 0, -113, -91, 123, -42, 0, 6, 47, -12, 44, -43, -18, -38, -60, -85, -3, -28, -34, 3, -34, -25, -107, 10, 24, -14, -113, -15, 105, -48, -11, 10, -36, -61, -58, -18, -59, -15, 52, -16, 83, -17, 58, -116, 15, -39, 168, -38, 103, -14, 30, -75, -20, -21, 25, -56, -122, -15, 10, -7, -49, -45, -80, -12, 146, -4, 17, -44, -101, -12, -36, 14, 97, -10, -135, -86, -40, -33, 56, -31, 91, -1, -38, -77, 77, -38, -113, -34, -14, -4, -42, -7, -119, -27, -24, -13, 58, -8, -34, 9, 13, -26, 117, -1, 17, -19, 22, -17, 5, -41, 1, -30, 56, -19, 51, -64, -78, -44, 76, -9, 80, -37, -12, -14, 41, -20, -15, -33, 36, -17, 29, -78, -181, 31, 13, -2, 79, -15, -112, 44, 50, -53, 118, -61, 184, -10, -50, -55, 119, -21, -98, 25, -34, -37, 60, -93, 136, -35, -18, -93, 208, -6, -23, -12, -4, -50, -35, 52, 74, -8, -9, -27, 142, -33, -72, 29, -39, -32, 97, -14, 115, -29, -29, -19, 19, -11, -4, -58, -112, -6, 82, 16, 72, -24, 10, -179, 97, -61, 44, 58, 4, 30, -37, -46, -47, 29, -33, -40, 74, -24, -40, 3, -113, -41, -51, 62, 42, 6, 7, -57, 71, -15, -93, -38, 191, -44, -119, -57, 32, 32, -93, -102, 132, -18, 27, -40, 42, -28, 40, -13, -37, -2, -62, -49, 72, -75, 17, 79, 101, -4, -161, 53, 39, -9, 53, -55, 226, 10, -54, -8, -67, -31, 1, -28, -88, 10, -15, -68, -68, -35, 75, -50, -72, -58, 116, -16, -51, 25, -11, -98, 83, -46, -96, 29, -24, -45, -82, 26, -44, -42, -15, -25, 85, -56, 71, -85, 7, 30, 10, -58, 15, -45, -198, 2, 260, -32, -85, -147, -8, -37, 108, -3, 87, 0, -50, -113, 6, -91, 84, 123, 19, -42, 10, 0, -13, 6, -163, 47, 130, -12, -52, 44, -14, -43, -36, -18, 112, -38, 9, -60, -77, -85, -102, -3, -21, -28, 53, -34, -103, 3, 210, -34, 62, -25, -4, -107, -5, 10, 34, 24, 76, -14, -49, -113, -162, -15, 13, 105, 170, -48, 80, -11, 12, 10, -84, -36, 153, -61, -48, -58, -1, -18, -45, -59, 136, -15, -56, 52, 206, -16, -17, 83, -46, -17, 172, 58, 173, -116, -102, 15, 97, -39, -90, 168, -13, -38, -19, 103, 208, -14, 23, 30, 103, -75, -6, -20, -63, -21, 31, 25, 29, -56, 46, -122, 108, -15, 47, 10, 183, -7, 0, -49, 139, -45, 38, -80, -84, -12, -181, 146, -3, -4, -127, 17, 209, -44, -131, -101, 93, -12, -68, -36, 117, 14, -168, 97, 41, -10, 75, -135, 193, -86, 76, -40, 293, -33, 92, 56, -28, -31, 122, 91, 67, -1, -85, -38, 45, -77, -10, 77, 61, -38, 67, -113, 339, -34, 189, -14, 35, -4, 65, -42, 14, -7, 207, -119, 40, -27, 36, -24, 100, -13, 153, 58, 91, -8, -61, -34, 90, 9, -93, 13, -60, -26, 182, 117, -73, -1, -55, 17, 219, -19, 130, 22, 61, -17, -150, 5, 117, -41, -83, 1, 11, -30, 54, 56, 248, -19, -21, 51, 83, -64, -4, -78, -14, -44, 3, 76, 16, -9, -19, 80, 2, -37, -130, -12, 176, -14, 206, 41, 214, -20, -45, -15, 72, -33, 109, 36, 56, -17, 27, 29, -76, -78, 218, -181, 28, 31, 151, 13, 59, -2, -4, 79, 112, -15, 85, -112, 127, 44, 110, 50, 119, -53, 104, 118, -33, -61, 279, 184, -29, -10, -23, -50, 346, -55, -25, 119, 62, -21, 135, -98, 241, 25, -40, -34, 255, -37, 56, 60, -1, -93, 25, 136, 276, -35, -38, -18, 190, -93, -79, 208, -8, -6, 221, -23, 11, -12, 65, -4, 166, -50, 36, -35, -182, 52, 236, 74, 179, -8, 83, -9, -8, -27, 262, 142, 56, -33, -8, -72, 49, 29, -60, -39, 60, -32, 11, 97, 76, -14, 42, 115, 160, -29, 154, -29, 6, -19, -105, 19, 92, -11, -125, -4, 143, -58, -25, -112, 367, -6, -18, 82, 98, 16, 76, 72, -19, -24, 1, 10, 373, -179, 98, 97, 57, -61, -148, 44, -6, 58, 107, 4, 287, 30, 28, -37, -184, -46, 197, -47, -34, 29, -24, -33, 212, -40, 149, 74, 67, -24, 83, -40, 119, 3, -17, -113, 51, -41, 161, -51, -24, 62, 113, 42, 12, 6, -71, 7, 160, -57, 110, 71, 28, -15, -116, -93, -9, -38, -108, 191, 61, -44, 8, -119, 131, -57, -11, 32, 132, 32, -84, -93, -10, -102, 85, 132, -15, -18, -37, 27, -48, -40, -267, 42, 124, -28, 70, 40, 42, -13, -74, -37, 90, -2, 275, -62, -39, -49, -22, 72, 55, -75, 180, 17, -31, 79, -228, 101, 319, -4, -6, -161, 74, 53, 58, 39, 154, -9, 23, 53, -253, -55, 114, 226, 139, 10, -83, -54, -147, -8, 36, -67, 3, -31, -241, 1, -125, -28, -64, -88, 173, 10, -82, -15, 382, -68, -46, -68, -32, -35, 293, 75, -13, -50, 8, -72, 33, -58, -311, 116, -185, -16, 224, -51, 269, 25, -25, -11, -115, -98, -21, 83, -94, -46, 147, -96, -34, 29, 97, -24, 137, -45, 236, -82, 86, 26, -24, -44, 32, -42, 81, -15, 277, -25, -157, 85, -199, -56, 156, 71, 208, -85, -130, 7, 124, 30, -38, 10, 61, -58, -171, 15, 113, -45, -165, -198, 190, 2, -121, 260, 79, -32, 41, -85, -24, -147, 37, -8, 145, -37, -77, 108, -27, -3, 95, 87, 161, 0, 55, -50, 167, -113, 4, 6, -136, -91, -171, 84, 14, 123, -33, 19, 14, -42, 151, 10, -66, 0, 22, -13, 125, 6, -44, -163, 41, 47, 71, 130, -87, -12, 202, -52, -212, 44, 34, -14, 123, -43, -35, -36, 40, -18, -310, 112, 170, -38, -367, 9, 249, -60, 142, -77, -46, -85, 134, -102, 18, -3, 149, -21, -2, -28, 49, 53, 36, -34, -9, -103, 78, 3, -185, 210, 82, -34, 267, 62, -78, -25, -12, -4, -30, -107, 19, -5, 66, 10, 58, 34, -20, 24, -35, 76, 144, -14, -22, -49, 234, -113, 10, -162, 131, -15, 15, 13, -56, 105, 68, 170, -256, -48, 12, 80, 106, -11, 185, 12, 18, 10, -222, -84, 189, -36, -262, 153, 48, -61, -49, -48, 365, -58, 51, -1, 300, -18, -13, -45, -58, -59, 121, 136, 302, -15, -176, -56, -84, 52, -326, 206, 356, -16, 437, -17, 133, 83, -234, -46, 4, -17, 28, 172, -78, 58, 169, 173, 163, -116, -94, -102, 148, 15, 81, 97, -93, -39, -42, -90, 179, 168, 10, -13, 74, -38, 74, -19, -95, 103, -173, 208, 276, -14, 31, 23, 6, 30, 48, 103, -65, -75, -228, -6, -225, -20, 5, -63, 331, -21, -132, 31, 155, 25, 8, 29, -32, -56, 137, 46, -217, -122, 98, 108, 112, -15, -98, 47, 133, 10, 15, 183, 361, -7, -50, 0, -5, -49, 235, 139, -33, -45, 117, 38, 104, -80, 95, -84, -54, -12, -95, -181, 24, 146, -42, -3, 75, -4, 365, -127, -214, 17, 190, 209, -63, -44, -163, -131, 358, -101, -9, 93, -278, -12, -137, -68, 93, -36, -104, 117, 185, 14, -2, -168, 81, 97, 254, 41, 98, -10, -317, 75, -38, -135, -54, 193, 136, -86, 146, 76, 93, -40, -83, 293, 136, -33, 140, 92, 180, 56, -132, -28, 25, -31, -105, 122, -133, 91, -22, 67, -64, -1, -61, -85, -138, -38, 81, 45, 434, -77, -25, -10, -71, 77, 229, 61, 254, -38, 21, 67, -377, -113, 224, 339, 70, -34, -114, 189, 130, -14, -275, 35, 293, -4, -163, 65, -274, -42, -121, 14, 329, -7, -2, 207, 42, -119, -87, 40, -48, -27, -21, 36, 296, -24, -288, 100, 407, -13, -129, 153, -121, 58, 114, 91, 323, -8, -163, -61, -226, -34, 190, 90, -6, 9, 115, -93, 110, 13, 5, -60, -13, -26, 44, 182, 31, 117, -15, -73, 175, -1, -101, -55, 7, 17, -272, 219, -308, -19, 125, 130, 283, 22, -110, 61, 34, -17, 34, -150, -135, 5, -314, 117, 280, -41, -20, -83, 224, 1, 33, 11, -53, -30, 312, 54, -39, 56, -48, 248, -123, -19, 8, -21, 192, 51, -323, 83, 292, -64, -129, -4, 228, -78, -225, -14, -196, -44, 638, 3, 6, 76, -378, 16, 331, -9, 417, -19, -25, 80, 218, 2, 197, -37, -21, -130, 109, -12, 81, 176, -40, -14, 44, 206, -318, 41, 183, 214, 442, -20, 6, -45, -272, -15, -89, 72, 135, -33, -181, 109, 42, 36, 151, 56, 295, -17, -13, 27, 70, 29, 21, -76, -45, -78, 138, 218, -8, -181, -40, 28, -131, 31, -512, 151, 304, 13, 137, 59, -65, -2, 73, -4, 55, 79, -90, 112, -108, -15, 104, 85, 76, -112, -14, 127, -114, 44, 176, 110, -49, 50, -12, 119, -185, -53, 253, 104, -63, 118, 105, -33, -249, -61, 52, 279, -26, 184, 155, -29, 372, -10, -281, -23, 171, -50, -157, 346, -77, -55, 299, -25, 362, 119, -306, 62, 109, -21, -54, 135, -33, -98, -213, 241, 235, 25, -137, -40, 102, -34, -43, 255, 71, -37, 354, 56, -95, 60, 115, -1, -73, -93, 20, 25, -204, 136, 233, 276, 164, -35, -272, -38, 180, -18, 52, 190, 208, -93, -38, -79, 87, 208, -16, -8, -39, -6, -87, 221, -217, -23, 99, 11, 343, -12, -184, 65, -10, -4, -207, 166, -17, -50, -64, 36, -105, -35, -106, -182, 420, 52, -96, 236, -231, 74, -382, 179, -27, -8, 109, 83, 74, -9, 195, -8, 157, -27, 12, 262, 404, 142, -188, 56, 249, -33, -104, -8, -157, -72, 81, 49, -111, 29, -64, -60, 38, -39, 270, 60, -189, -32, 252, 11, 254, 97, -26, 76, 134, -14, -3, 42, -151, 115, 463, 160, -114, -29, 374, 154, 300, -29, 206, 6, -321, -19, -66, -105, 23, 19, -403, 92, -187, -11, 350, -125, 114, -4, -147, 143, 217, -58, 19, -25, -41, -112, -24, 367, 85, -6, -198, -18, 67, 82, 4, 98, 169, 16, 256, 76, 101, 72, -394, -19, 80, -24, -169, 1, -139, 10, 53, 373, 67, -179, 292, 98, -116, 97, 222, 57, 8, -61, -44, -148, 257, 44, 242, -6, 239, 58, 65, 107, 48, 4, 235, 287, 64, 30, -28, 28, -86, -37, -252, -184, 97, -46, -140, 197, -63, -47, 285, -34, 271, 29, 58, -24, 36, -33, 15, 212, -20, -40, 57, 149, 240, 74, -294, 67, 317, -24, -319, 83, -214, -40, -2, 119, -18, 3, -21, -17, -262, -113, 224, 51, -24, -41, -174, 161, 27, -51, -124, -24, 224, 62, 187, 113, -209, 42, 31, 12, 196, 6, 13, -71, -399, 7, -152, 160, 61, -57, 9, 110, 481, 71, -247, 28, 26, -15, -209, -116, -30, -93, -114, -9, 52, -38, -157, -108, -34, 191, 52, 61, 170, -44, 76, 8, -53, -119, 28, 131, -41, -57, -204, -11, 215, 32, -568, 132, 368, 32, -61, -84, 380, -93, -42, -10, -276, -102, 302, 85, -78, 132, -198, -15, 232, -18, 26, -37, -159, 27, -44, -48, 300, -40, -21, -267, 63, 42, 332, 124, -39, -28, 216, 70, -255, 40, -140, 42, 102, -13, 64, -74, -250, -37, -276, 90, 171, -2, -272, 275, 23, -62, -148, -39, 62, -49, -454, -22, 209, 72, -204, 55, -35, -75, 85, 180, -58, 17, -247, -31, 32, 79, -280, -228, 306, 101, -103, 319, -322, -4, -211, -6, -16, -161, 205, 74, -223, 53, -39, 58, -14, 39, 89, 154, -219, -9, 137, 23, 323, 53, -50, -253, 172, -55, -13, 114, -128, 226, 91, 139, -108, 10, 194, -83, 137, -54, 26, -147, 244, -8, -228, 36, 183, -67, -213, 3, -127, -31, -120, -241, 280, 1, -432, -125, 409, -28, -175, -64, -33, -88, -59, 173, 401, 10, -509, -82, -264, -15, -27, 382, 272, -68, 132, -46, 232, -68, -235, -32, -261, -35, 17, 293, -349, 75, -92, -13, 276, -50, 176, 8, -337, -72, 189, 33, -217, -58, -29, -311, -92, 116, -110, -185, -96, -16, 26, 224, -322, -51, 151, 269, 344, 25, 69, -25, -480, -11, -91, -115, -101, -98, -333, -21, -11, 83, 41, -94, 148, -46, -347, 147, 149, -96, 110, -34, -6, 29, -362, 97, 1, -24, -1, 137, -66, -45, -512, 236, 333, -82, 176, 86, 100, 26, 96, -24, -413, -44, -465, 32, 43, -42, -234, 81, 45, -15, -121, 277, 181, -25, -168, -157, -220, 85, -61, -199, -326, -56, -108, 156, -306, 71, 74, 208, -314, -85, 272, -130, 439, 7, 99, 124, -65, 30, -71, -38, -131, 10, -723, 61, -26, -58, -79, -171, 181, 15, 37, 113, -103, -45, -37, -165, 29, -198, 208, 190, 53, 2, -116, -121, -79, 260, -138, 79, 533, -32, 134, 41, -116, -85, 98, -24, 42, -147, -91, 37, -294, -8, -135, 145, -4, -37, -118, -77, -144, 108, -112, -27, 62, -3, -41, 95, 98, 87, -264, 161, 15, 0, -168, 55, -412, -50, 352, 167, 164, -113, -253, 4, 58, 6, -427, -136, 376, -91, -122, -171, 147, 84, 36, 14, 335, 123, -401, -33, 202, 19, -200, 14, -15, -42, 20, 151, -159, 10, -40, -66, 150, 0, -363, 22, -62, -13, 95, 125, 201, 6, -292, -44, -143, -163, -245, 41, -62, 47, -81, 71, 67, 130, 44, -87, -201, -12, 46, 202, 273, -52, 32, -212, 123, 44, 60, 34, -171, -14, -137, 123, -140, -43, -139, -35, 110, -36, 54, 40, -70, -18, -32, -310, -48, 112, -57, 170, 157, -38, -215, -367, -246, 9, -403, 249, 38, -60, -110, 142, -28, -77, 95, -46, -66, -85, 180, 134, -3, -102, -350, 18, 472, -3, -35, 149, -425, -21, -494, -2, 46, -28, 123, 49, -194, 53, -77, 36, 182, -34, 6, -9, -276, -103, -14, 78, 0, 3, -75, -185, -580, 210, 378, 82, -455, -34, -13, 267, -329, 62, 83, -78, 217, -25, -351, -12, -76, -4, -631, -30, 93, -107, -78, 19, 596, -5, -126, 66, -41, 10, 258, 58, 48, 34, -292, -20, -9, 24, -83, -35, -449, 76, -135, 144, -76, -14, -374, -22, 101, -49, 277, 234, 240, -113, -83, 10, -292, -162, 171, 131, -366, -15, 89, 15, -213, 13, -250, -56, 97, 105, -101, 68, -166, 170, -31, -256, 168, -48, -4, 12, 7, 80, 176, 106, -615, -11, -23, 185, 329, 12, 30, 18, -178, 10, -608, -222, -129, -84, -240, 189, 19, -36, -321, -262, 193, 153, -93, 48, 110, -61, -93, -49, -35, -48, -123, 365, 116, -58, -130, 51, 134, -1, -388, 300, 210, -18, 315, -13, 290, -45, -449, -58, 45, -59, -135, 121, -246, 136, -243, 302, 132, -15, -67, -176, -664, -56, -161, -84, 128, 52, 25, -326, -32, 206, -327, 356, -107, -16, -515, 437, -243, -17, 25, 133, 281, 83, 111, -234, -724, -46, 46, 4, 265, -17, -739, 28, -218, 172, 343, -78, 95, 58, -577, 169, -563, 173, -142, 163, -45, -116, 131, -94, -337, -102, -317, 148, -62, 15, -157, 81, 232, 97, -320, -93, 92, -39, 277, -42, -96, -90, -110, 179, 38, 168, -543, 10, -144, -13, -7, 74, -165, -38, 178, 74, -197, -19, -56, -95, -117, 103, 424, -173, -30, 208, -302, 276, -420, -14, 91, 31, 465, 23, -103, 6, -294, 30, 64, 48, -162, 103, -534, -65, -229, -75, -145, -228, -259, -6, -405, -225, 238, -20, -83, 5, -45, -63, -210, 331, 91, -21, -165, -132, 84, 31, -715, 155, 551, 25, -42, 8, -193, 29, -180, -32, -249, -56, -4, 137, -240, 46, 54, -217, -111, -122, -37, 98, -216, 108, -49, 112, -87, -15, -37, -98, -3, 47, -185, 133, 253, 10, 254, 15, -224, 183, 227, 361, 300, -7, -37, -50, -176, 0, -528, -5, 38, -49, -324, 235, -323, 139, -66, -33, 23, -45, -56, 117, 276, 38, -183, 104, -91, -80, 213, 95, 267, -84, -187, -54, 14, -12, -233, -95, 239, -181, -194, 24, 149, 146], "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.d", "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}