# Stored data for newform 8012.2.a.b, downloaded from the LMFDB on 25 April 2024. {"label": "8012.2.a.b", "space_label": "8012.2.a", "level": 8012, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660932940, "dim": 88, "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": 32048, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 63.976142099449845, "level_radical": 4006, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8012, 1, [4007, 5], [1, 1]], "inner_twist_count": 1, "level_primes": [2, 2003], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 88, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [2003, 1]], "trace_display": [0, 19, 0, 44], "traces": [88, 0, 19, 0, 0, 0, 44, 0, 99, 0, 16, 0, -3, 0, 21, 0, 32, 0, 49, 0, 7, 0, 24, 0, 114, 0, 82, 0, 2, 0, 40, 0, 31, 0, 26, 0, 0, 0, 37, 0, 22, 0, 98, 0, 12, 0, 48, 0, 132, 0, 55, 0, -1, 0, 116, 0, 62, 0, 34, 0, 0, 0, 132, 0, 39, 0, 75, 0, 15, 0, 24, 0, 104, 0, 87, 0, 4, 0, 111, 0, 128, 0, 64, 0, 7, 0, 115, 0, 14, 0, 73, 0, -7, 0, 51, 0, 117, 0, 72, 0, -1, 0, 122, 0, 59, 0, 77, 0, 6, 0, 53, 0, 33, 0, 123, 0, -17, 0, 84, 0, 134, 0, 69, 0, 6, 0, 132, 0, 78, 0, 74, 0, 30, 0, 78, 0, 43, 0, 155, 0, 2, 0, 95, 0, 91, 0, 146, 0, 4, 0, 78, 0, 160, 0, 72, 0, -5, 0, 121, 0, 60, 0, 155, 0, 11, 0, 101, 0, 149, 0, 158, 0, 23, 0, 215, 0, 59, 0, 55, 0, -11, 0, 106, 0, 57, 0, 145, 0, 30, 0, 43, 0, 113, 0, 151, 0, -19, 0, 187, 0, 62, 0, 67, 0, -16, 0, 101, 0, 68, 0, 152, 0, 17, 0, 64, 0, 147, 0, 81, 0, -17, 0, 171, 0, 212, 0, 169, 0, -9, 0, 80, 0, 54, 0, 173, 0, 33, 0, 96, 0, 117, 0, 220, 0, -15, 0, 123, 0, 74, 0, 87, 0, 21, 0, 51, 0, 54, 0, 144, 0, 22, 0, 128, 0, 107, 0, 90, 0, 26, 0, 145, 0, 94, 0, 80, 0, -5, 0, 128, 0, 38, 0, 347, 0, -29, 0, 83, 0, 172, 0, 99, 0, 4, 0, 122, 0, 140, 0, 92, 0, 38, 0, 103, 0, -5, 0, 183, 0, -9, 0, 79, 0, 209, 0, 105, 0, -42, 0, 108, 0, 130, 0, 73, 0, -34, 0, 166, 0, 80, 0, 142, 0, -25, 0, 115, 0, 166, 0, 150, 0, -26, 0, 355, 0, 35, 0, 155, 0, 31, 0, 115, 0, 80, 0, 194, 0, -1, 0, 49, 0, 159, 0, 239, 0, -20, 0, 330, 0, 96, 0, 112, 0, 32, 0, 72, 0, 61, 0, 116, 0, 5, 0, 128, 0, 182, 0, 269, 0, 33, 0, 198, 0, 143, 0, 137, 0, 55, 0, 116, 0, 46, 0, 337, 0, -41, 0, 121, 0, 154, 0, 149, 0, -42, 0, 237, 0, 131, 0, 101, 0, -14, 0, 219, 0, 129, 0, 188, 0, 64, 0, 99, 0, 261, 0, 124, 0, -36, 0, 262, 0, 260, 0, 138, 0, 2, 0, 235, 0, 42, 0, 182, 0, 30, 0, 54, 0, 215, 0, 299, 0, 16, 0, 254, 0, 117, 0, 156, 0, 7, 0, 77, 0, 80, 0, 374, 0, 2, 0, 146, 0, 250, 0, 161, 0, -38, 0, 241, 0, 80, 0, 52, 0, 15, 0, 395, 0, 118, 0, 165, 0, -37, 0, 237, 0, 195, 0, 262, 0, -63, 0, 251, 0, 201, 0, 45, 0, -23, 0, 93, 0, -5, 0, 404, 0, -8, 0, 36, 0, 142, 0, 120, 0, -54, 0, 218, 0, 29, 0, -32, 0, -22, 0, 172, 0, -52, 0, 241, 0, -92, 0, -6, 0, 173, 0, 29, 0, -122, 0, 163, 0, -70, 0, 159, 0, -23, 0, 294, 0, 3, 0, 164, 0, -44, 0, -32, 0, 144, 0, 22, 0, -200, 0, 224, 0, -104, 0, 138, 0, -7, 0, 54, 0, 19, 0, 156, 0, -215, 0, -7, 0, 170, 0, 145, 0, -56, 0, 297, 0, -38, 0, -102, 0, -21, 0, 131, 0, -131, 0, 150, 0, -157, 0, 153, 0, 168, 0, 38, 0, -256, 0, 129, 0, 164, 0, -73, 0, -96, 0, 1, 0, -1, 0, 443, 0, -320, 0, 25, 0, 103, 0, -36, 0, -134, 0, 154, 0, 134, 0, -47, 0, -88, 0, 10, 0, -270, 0, 113, 0, -243, 0, -52, 0, 119, 0, 143, 0, -116, 0, 173, 0, -86, 0, -23, 0, -96, 0, -84, 0, -155, 0, 161, 0, -198, 0, -11, 0, 55, 0, 41, 0, -229, 0, 348, 0, -145, 0, -17, 0, -221, 0, 136, 0, 52, 0, -18, 0, -241, 0, -108, 0, 97, 0, 141, 0, -271, 0, 418, 0, -135, 0, 87, 0, -81, 0, -107, 0, -253, 0, 76, 0, -182, 0, 59, 0, 121, 0, -10, 0, -160, 0, 89, 0, -3, 0, -20, 0, -233, 0, 20, 0, -110, 0, 217, 0, -213, 0, 29, 0, 110, 0, 27, 0, -282, 0, 159, 0, -71, 0, -80, 0, -103, 0, 320, 0, -118, 0, 261, 0, -390, 0, -132, 0, 135, 0, -207, 0, -169, 0, 111, 0, -116, 0, 139, 0, -115, 0, -74, 0, -95, 0, 187, 0, -258, 0, -15, 0, 111, 0, -240, 0, -99, 0, 307, 0, -281, 0, -66, 0, -115, 0, -72, 0, -48, 0, 133, 0, -246, 0, -76, 0, 108, 0, 133, 0, -628, 0, 356, 0, -142, 0, -117, 0, -26, 0, -112, 0, -119, 0, 54, 0, -272, 0, -11, 0, -59, 0, 22, 0, -335, 0, 243, 0, 48, 0, -41, 0, -158, 0, -82, 0, -52, 0, 221, 0, -577, 0, 5, 0, 34, 0, -86, 0, -244, 0, 207, 0, -261, 0, -246, 0, -157, 0, -63, 0, -119, 0, 179, 0, -205, 0, -127, 0, 206, 0, -223, 0, -274, 0, 13, 0, -67, 0, 76, 0, -339, 0, 128, 0, -191, 0, 122, 0, -187, 0, -27, 0, 205, 0, -201, 0, -140, 0, 349, 0, -335, 0, 77, 0, -286, 0, -85, 0, -258, 0, 85, 0, -543, 0, -117, 0, 80, 0, 155, 0, -335, 0, 225, 0, -231, 0, -166, 0, -93, 0, -285, 0, -196, 0, 140, 0, -410, 0, 109, 0, 218, 0, -84, 0, -387, 0, 198, 0, -197, 0, -381, 0, -166, 0, -225, 0, -162, 0, 289, 0, -295, 0, -13, 0, -96, 0, 25, 0, -344, 0, 41, 0, -191, 0, -24, 0, -178, 0, 125, 0, -349, 0, 216, 0, -459, 0, -35, 0, 71, 0, 87, 0, -313, 0, 97, 0, -199, 0, -254, 0, -281, 0, -34, 0, -111, 0, 163, 0, -302, 0, -84, 0, 36, 0, -451, 0, -242, 0, 499, 0, -331, 0, -26, 0, -289, 0, 190, 0, -177, 0, 339, 0, -455, 0, -237, 0, 133, 0, 119, 0, -483, 0, 223, 0, -90, 0, 40, 0, -169, 0, 14, 0, -195, 0, 75, 0, -245, 0, -117, 0, -125, 0, -165, 0, -228, 0, 203, 0, -171, 0, -358, 0, -198, 0, -8, 0, -197, 0, 360, 0, -520, 0, -108, 0, 10, 0, -268, 0, -239, 0, 6, 0, -317, 0, -126, 0, -150, 0, 111, 0, -183, 0, 288, 0, -562, 0, -108, 0, 41, 0, -367, 0, -536, 0, 111, 0, 71, 0, 14, 0, -304, 0, 44, 0, -373, 0, 174, 0, -329, 0, 71, 0, -54, 0, -42, 0, -220, 0, 480, 0, -339, 0, 74, 0, -212, 0, -201, 0, 40, 0, 338, 0, -456, 0, -329, 0, 25, 0, 65, 0, -759, 0, 431, 0, -132, 0, -228, 0, -162, 0, -335, 0, -33, 0, -209, 0, -285, 0, -215, 0, 222, 0, 23, 0, -299, 0, 245, 0, -221, 0, -82, 0, -186, 0, -233, 0, -289, 0, 204, 0, -398, 0, -63, 0, 38, 0, 205, 0, -230, 0, 131, 0, -299, 0, -407, 0, -198, 0, 82, 0, -377, 0, 108, 0, -318, 0, 82, 0, 249, 0, -180, 0, -149, 0, 56, 0, -307, 0, 46, 0, -216, 0, 230, 0, -404, 0, 178, 0, -326, 0, -62, 0, 173, 0, -207, 0, -337, 0, 288, 0, -208, 0, -107, 0, -445, 0, -205, 0, -175, 0, 404, 0, -420, 0, -49, 0, 14, 0, 375, 0, -304, 0, 297, 0, -236, 0, -141, 0, -165, 0, -344, 0, -176, 0, 61, 0, -363, 0, 176, 0, -249, 0, 118, 0, -440, 0, 156, 0, -90, 0, -37, 0, -220, 0, -284, 0, -113, 0, 485, 0, -461, 0, -236, 0, -122, 0, 189, 0, -252, 0, 440, 0, -57, 0, -80, 0, -48, 0, -70, 0, -191, 0, 310, 0, -588, 0, -152, 0, 248, 0, -169, 0, -281, 0, 141, 0, -125, 0, 174, 0, -342, 0, -103, 0, -140, 0, 85, 0, -546, 0, -368, 0, 185, 0, -507, 0, -329, 0, 225, 0, -83, 0, 169, 0, -368, 0, 280, 0, -30, 0, -1, 0, -479, 0, -313, 0, 159, 0, -104, 0, -350, 0, 512, 0, -230, 0, 46, 0, -202, 0, -181, 0, -737, 0, 167, 0, -264, 0, -141, 0, -12, 0, 84, 0, -287, 0, 127, 0, -58, 0, -387, 0, -283, 0, -168, 0, -69, 0, 470, 0, -444, 0, 127, 0, -76, 0, -23, 0, -414, 0, 45, 0, -215, 0, -179, 0, -278, 0, 23, 0, -224, 0, 329, 0, -515, 0, -147, 0, 57, 0, -43, 0, -413, 0, -37, 0, -89, 0, -27, 0, -250, 0, -317, 0, -415, 0, 385, 0, -452, 0, 2, 0, 193, 0, -72, 0, -278, 0, 483, 0, -730, 0, -433, 0, -372, 0, -118, 0, 18, 0, 123, 0, -481, 0, -127, 0, 71, 0, 66, 0, -550, 0, 264, 0, -619, 0, -68, 0, -368, 0, 23, 0, -44, 0, 107, 0, -285, 0, -269, 0, -57, 0, -121, 0, -413, 0, 67, 0, -171, 0, -154, 0, -270, 0, -316, 0, -174, 0, 474, 0, -657, 0, -293, 0, 45, 0, -95, 0, -316, 0, 71, 0, -255, 0, -358, 0, -203, 0, 37, 0, -363, 0, 477, 0, -468, 0, -243, 0, -11, 0, -290, 0, -554, 0, 22, 0, -234, 0, -84, 0, -436, 0, -211, 0, -268, 0, 195, 0, -511, 0, -345, 0, 83, 0, -524, 0, -194, 0, 404, 0, -321, 0, 62, 0, -64, 0, -414, 0, -206, 0, -30, 0, -520, 0, 3, 0, -90, 0, -77, 0, -856, 0, 333, 0, -491, 0, -61, 0, -173, 0, -368, 0, -257, 0, 39, 0, -295, 0, -5, 0, -88, 0, 167, 0, -700, 0, 469, 0, -336, 0, -163, 0, -192, 0, -549, 0, -127, 0, 298, 0, -749, 0, -184, 0, -320, 0, -112, 0, -154, 0, 263, 0, -176, 0, -111, 0, -185, 0, -384, 0, -138, 0, 58, 0, -493, 0, -235, 0, 102, 0, -83, 0, -435, 0, 142, 0, -160, 0, -7, 0, -543, 0, 40, 0, -460, 0, 254, 0, -575, 0, -264, 0, 228, 0, -560, 0, -215, 0, 144, 0, -704, 0, -349, 0, -111, 0, 282, 0, -252, 0, 255, 0, -465, 0, -437, 0, 117, 0, -216, 0, -392, 0, 159, 0, -307, 0, -58, 0, -304, 0, -375, 0, -283, 0, 152, 0, -331, 0, 56, 0, 2, 0, 83, 0, -525, 0, 55, 0, -22, 0, -468, 0, -306, 0, -535, 0, -220, 0, 540, 0, -578, 0, 50, 0, -106, 0, -177, 0, -787, 0, 68, 0, -615, 0, -339, 0, -177, 0, -64, 0, -325, 0, 518, 0, -884, 0, -235, 0, 150, 0, -216, 0, -459, 0, -178, 0, -256, 0, -34, 0, -232, 0, -15, 0, -393, 0, -60, 0, -398, 0, -224, 0, 374, 0, -183, 0, -208, 0, 405, 0, -1031, 0, 4, 0, -601, 0, -286, 0, -145, 0, 103, 0, -653, 0, -479, 0, 83, 0, -105, 0, -668, 0, 158, 0, -391, 0, -52, 0, -337, 0, -284, 0, -104, 0, -34, 0, -466, 0, -152, 0, 179, 0, -423, 0, -538, 0, 395, 0, -4, 0, -29, 0, -421, 0, -462, 0, -454, 0, 305, 0, -760, 0, -111, 0, -190, 0, -70, 0, -228, 0, 422, 0, 133, 0, -751, 0, -140, 0, -234, 0, -520, 0, 390, 0, -1278, 0, -112, 0, 374, 0, -616, 0, -396, 0, 178, 0, -171, 0, -88, 0, -338, 0, -398, 0, -195, 0, 242, 0, -532, 0, -387, 0, 61, 0, -27, 0, -383, 0, 339, 0, 17, 0, -49, 0, -334, 0, -308, 0, -383, 0, -110, 0, -465, 0, -276, 0, -77, 0, 495, 0, -398, 0, 265, 0, -732, 0, -190, 0, -137, 0, -735, 0, 300, 0, -154, 0, -265, 0, 316, 0, 44, 0, -200, 0, -434, 0, 472, 0, -360, 0, 263, 0, -397, 0, -764, 0, -107, 0, 150, 0, -206, 0, -271, 0, -92, 0, -28, 0, -380, 0, 15, 0, -25, 0, -165, 0, -165, 0, 76, 0, -220, 0, 595, 0, -461, 0, 67, 0, 279, 0, -469, 0, -265, 0, 112, 0, 187, 0, -124, 0, -224, 0, 33, 0, -175, 0, 497, 0, -203, 0, 129, 0, 304, 0, -328, 0, -280, 0, 28, 0, -426, 0, -28, 0, -241, 0, -83, 0, 211, 0, 373, 0, -645, 0, -371, 0, 111, 0, 30, 0, -456, 0, 149, 0, -55, 0, 4, 0, -253, 0, 189, 0, -318, 0, 125, 0, 211, 0, 158, 0, 47, 0, 287, 0, -572, 0, 224, 0, -317, 0, -553, 0, -24, 0, -637, 0, 394, 0, 440, 0, -552, 0, -29, 0, 0, 0, -313, 0, -417, 0, 278, 0, -282, 0, -111, 0, 1, 0, 273, 0, -45, 0, 282, 0, -671, 0, -415, 0, 167, 0, -121, 0, -126, 0, 438, 0, 127, 0, 270, 0, -387, 0, -290, 0, -380, 0, 381, 0, 12, 0, -603, 0, 111, 0, -446, 0, 57, 0, 402, 0, 142, 0, 256, 0, -498, 0, -102, 0, -9, 0, -55, 0, -277, 0, -252, 0, 322, 0, 168, 0, -193, 0, 253, 0, -348, 0, -133, 0, -209, 0, -334, 0, -65, 0, 303, 0, -359, 0, -117, 0, 318, 0, 10, 0, -227, 0, 127, 0, 301, 0, -82, 0, -117, 0, -333, 0, -57, 0, 897, 0, -868, 0, -9, 0, -43, 0, -37, 0, -175, 0, 65, 0, 143, 0, -536, 0, -190, 0, -312, 0, -385, 0, 74, 0, -182, 0, 304, 0, 227, 0, -9, 0, -286, 0, 37, 0, 428, 0, 198, 0, 70, 0, -118, 0, -210, 0, 253, 0, -128, 0, -682, 0, 279, 0, -211, 0, 154, 0, 739, 0, -409, 0, 213, 0, -267, 0, 18, 0, 7, 0, 143, 0, -197, 0, -264, 0, 372, 0, -315, 0, -23, 0, 426, 0, -421, 0, 80, 0, 74, 0, 16, 0, 41, 0, -235, 0, 250, 0, -51, 0, 279, 0, -44, 0, -584, 0, 51, 0, 79, 0, 96, 0, -184, 0, -473, 0, 186, 0, 639, 0, -413, 0, -123, 0, 119, 0, -145, 0, -261, 0, 459, 0, -259, 0, -66, 0, 132, 0, 295, 0, -322, 0, 353, 0, -1038, 0, -171, 0, 442, 0, -41, 0, 23, 0, -6, 0, 460, 0, 49, 0, 76, 0, 35, 0, 217, 0, 179, 0, 62, 0, -35, 0, 334, 0, -358, 0, -107, 0, 229, 0, 600, 0, -447, 0, -160, 0, -132, 0, 278, 0, 73, 0, -475, 0, -320, 0, 122, 0, 319, 0, -149, 0, 521, 0, -210, 0, 67, 0, -153, 0, -1261, 0, 260, 0, 222, 0, 257, 0, 98, 0, 100, 0, 564, 0, -339, 0, 322, 0, 552, 0, -658, 0, -345, 0, -632, 0, 579, 0, 559, 0, -401, 0, -293, 0, 347, 0, 339, 0, -276, 0, 371, 0, -94, 0, -319, 0, 22, 0, -113, 0, -77, 0, 212, 0, -226, 0, 37, 0, 522, 0, -347, 0, -38, 0, -233, 0, 638, 0, 582, 0, -17, 0, -391, 0, -741, 0, 9, 0, -104, 0, 345, 0, 460, 0, -136, 0, 53, 0, 411, 0, -267, 0, -480, 0, -161, 0, -245, 0, 53, 0, 482, 0, -183, 0, -160, 0, 348, 0, -42, 0, -78, 0, 277, 0, 101, 0, 131, 0, -46, 0, -56, 0, 131, 0, 201, 0, -367, 0, -197, 0, -4, 0, -252, 0, -564, 0, 223, 0, 446, 0, -4, 0, -174, 0, -529, 0, 424, 0, 736, 0, 4, 0, 81, 0, 7, 0, 149, 0, -70, 0, 286, 0, -307, 0, -362, 0, 122, 0, 292, 0, -51, 0, 603, 0, -202, 0, -53, 0, 594, 0, 4, 0, -532, 0, 349, 0, 511, 0, -203, 0, -161, 0, -6, 0, 179, 0, 417, 0, -42, 0, -164, 0, 161, 0, -561, 0, 545, 0, 609, 0, -31, 0, 452, 0, -589, 0, 99, 0, 280, 0, 41, 0, 6, 0, -579, 0, 635, 0, -173, 0, -44, 0, 419, 0, -137, 0, 5, 0, 27, 0, -51, 0, -163, 0, 280, 0, -59, 0, 150, 0, 588, 0, -468, 0, -456, 0, 455, 0, 244, 0, 130, 0, 25, 0, -26, 0, 170, 0, 528, 0, -36, 0, -343, 0, -33, 0, 137, 0, 486, 0, 40, 0, 133, 0, -526, 0, 125, 0, 175, 0, 371, 0, 690, 0, -471, 0, 269, 0, 480, 0, -436, 0, -407, 0, -290, 0, 717, 0, -278, 0, -162, 0, -480, 0, 77, 0, 344, 0, -149, 0, 207, 0, 470, 0, 83, 0, -180, 0, 659, 0, 60, 0, 285, 0, -46, 0, -551, 0, 414, 0, 291, 0, -149, 0, -518, 0, 559, 0, 594, 0, -21, 0, 294, 0, 197, 0, 235, 0, -68, 0, -17, 0, 221, 0, 53, 0, 198, 0, 149, 0, 416, 0, -135, 0, -392, 0, 882, 0, -53, 0, -239, 0, -68, 0, -467, 0, 436, 0, 474, 0, -561, 0, -80, 0, 262, 0, -222, 0, -23, 0, 123, 0, 198, 0, -37, 0, 2, 0, 649, 0, -74, 0, 190, 0, -287, 0, -425, 0, 436, 0, 100, 0, 36, 0, -99, 0, 1197, 0, -162, 0, 22, 0, 167, 0, -197, 0, 313, 0, -205, 0, 24, 0, 482, 0, -411, 0, 309, 0, -6, 0, 87, 0, 34, 0, -312, 0, -25, 0, 436, 0, 428, 0, -605, 0, -77, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "8012.2.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}