# Stored data for newform 4006.2.a.f, downloaded from the LMFDB on 18 April 2024. {"label": "4006.2.a.f", "space_label": "4006.2.a", "level": 4006, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170410918, "dim": 31, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [613, -11039, 34514, 251421, -780901, -3040295, 4546681, 18954284, -4349615, -51329230, -15186792, 71818562, 43652878, -56002609, -50650076, 23364629, 33188263, -3098579, -13287611, -1671302, 3257527, 965971, -451828, -227304, 23766, 28185, 1963, -1710, -333, 28, 13, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16024, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 31.988071049724923, "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": [4006, 1, [5], [1]], "inner_twist_count": 1, "level_primes": [2, 2003], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 31, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [2003, -1]], "trace_display": [31, -13, -23, -18], "traces": [31, 31, -13, 31, -23, -13, -18, 31, 20, -23, -32, -13, -8, -18, -14, 31, -30, 20, -38, -23, -16, -32, -24, -13, 40, -8, -28, -18, -7, -14, -32, 31, -9, -30, -14, 20, 11, -38, -9, -23, -76, -16, -33, -32, -40, -24, -96, -13, 15, 40, -55, -8, -28, -28, -52, -18, -21, -7, -72, -14, -9, -32, -54, 31, -38, -9, -4, -30, -17, -14, -61, 20, -62, 11, -63, -38, -9, -9, -30, -23, -13, -76, -90, -16, 26, -33, -34, -32, -99, -40, -47, -24, -6, -96, -24, -13, -46, 15, -48, 40, -31, -55, -20, -8, 10, -28, 28, -28, 12, -52, -39, -18, -1, -21, -46, -7, -20, -72, -68, -14, 41, -9, 69, -32, -54, -54, -22, 31, 13, -38, -59, -9, 35, -4, 19, -30, -68, -17, -90, -14, 33, -61, -56, 20, -25, -62, -5, 11, 34, -63, -50, -38, 4, -9, -5, -9, 20, -30, -39, -23, -30, -13, -51, -76, 80, -90, -59, -16, -1, 26, -59, -33, -10, -34, -125, -32, -26, -99, 15, -40, -27, -47, -8, -24, -76, -6, 53, -96, -46, -24, -35, -13, -34, -46, 18, 15, -33, -48, -51, 40, -33, -31, -77, -55, 104, -20, -61, -8, -68, 10, -7, -28, 108, 28, -34, -28, 12, 12, 43, -52, -76, -39, -23, -18, 95, -1, -50, -21, 37, -46, 45, -7, 1, -20, -6, -72, 102, -68, -20, -14, -100, 41, 48, -9, 27, 69, -24, -32, 41, -54, -79, -54, 123, -22, 67, 31, 8, 13, 8, -38, 45, -59, -36, -9, 20, 35, 39, -4, -77, 19, -58, -30, 34, -68, 2, -17, 88, -90, 26, -14, -55, 33, -133, -61, 199, -56, 16, 20, 73, -25, -14, -62, 46, -5, 77, 11, 23, 34, -109, -63, 29, -50, 2, -38, 27, 4, 32, -9, 155, -5, -107, -9, 29, 20, 196, -30, 16, -39, 46, -23, 16, -30, 37, -13, 198, -51, -10, -76, 76, 80, 19, -90, 60, -59, -10, -16, 85, -1, 7, 26, -92, -59, -84, -33, 123, -10, -63, -34, -13, -125, 100, -32, -13, -26, -15, -99, 280, 15, 64, -40, 105, -27, 28, -47, 147, -8, 10, -24, -136, -76, -2, -6, 98, 53, 136, -96, 33, -46, 115, -24, 133, -35, -74, -13, 134, -34, 178, -46, 46, 18, 12, 15, 58, -33, -1, -48, 60, -51, 159, 40, -157, -33, 45, -31, 82, -77, -10, -55, 41, 104, 30, -20, 150, -61, -7, -8, 114, -68, -16, 10, 96, -7, -2, -28, -77, 108, -28, 28, 205, -34, -27, -28, 7, 12, 199, 12, 59, 43, 70, -52, 102, -76, 15, -39, 216, -23, -1, -18, 9, 95, 119, -1, 256, -50, 174, -21, 19, 37, 39, -46, -6, 45, 63, -7, 186, 1, 18, -20, 115, -6, 35, -72, 73, 102, 45, -68, 139, -20, -56, -14, 71, -100, 207, 41, 35, 48, 103, -9, 21, 27, 90, 69, 166, -24, 142, -32, 82, 41, -30, -54, 146, -79, 35, -54, 25, 123, 91, -22, -144, 67, 90, 31, 42, 8, 55, 13, 244, 8, 12, -38, -51, 45, -73, -59, 305, -36, -26, -9, 175, 20, 61, 35, -55, 39, 32, -4, 64, -77, -161, 19, 41, -58, 77, -30, 116, 34, 5, -68, 97, 2, -204, -17, 83, 88, 218, -90, 10, 26, -111, -14, 116, -55, -13, 33, 52, -133, 100, -61, 8, 199, -75, -56, 92, 16, 81, 20, 38, 73, 15, -25, 106, -14, 12, -62, -75, 46, -2, -5, 201, 77, 66, 11, -52, 23, 35, 34, 230, -109, -16, -63, -49, 29, -6, -50, 41, 2, -204, -38, 53, 27, -35, 4, 95, 32, -5, -9, -9, 155, 28, -5, 211, -107, 25, -9, 149, 29, 209, 20, -4, 196, -46, -30, 129, 16, -20, -39, 205, 46, -151, -23, -39, 16, -66, -30, 77, 37, -183, -13, -16, 198, 82, -51, 49, -10, 101, -76, -21, 76, -64, 80, 35, 19, -87, -90, -82, 60, 34, -59, 70, -10, 99, -16, 19, 85, 6, -1, 130, 7, 12, 26, 61, -92, 168, -59, 172, -84, -110, -33, -198, 123, -133, -10, 293, -63, -60, -34, 124, -13, -4, -125, 36, 100, -21, -32, 112, -13, -25, -26, -23, -15, 13, -99, -49, 280, 169, 15, 257, 64, -445, -40, 2, 105, 49, -27, -106, 28, -132, -47, -220, 147, -58, -8, 156, 10, 89, -24, -36, -136, -18, -76, 77, -2, 118, -6, 199, 98, -221, 53, -122, 136, 51, -96, 174, 33, -139, -46, 193, 115, -74, -24, -13, 133, 35, -35, 332, -74, -2, -13, -33, 134, -16, -34, -38, 178, -143, -46, -46, 46, -23, 18, 289, 12, 44, 15, -18, 58, -76, -33, -164, -1, -202, -48, -39, 60, 330, -51, -47, 159, -7, 40, 29, -157, -82, -33, 202, 45, -22, -31, -182, 82, -108, -77, 224, -10, -23, -55, -31, 41, -4, 104, -23, 30, 43, -20, 90, 150, -207, -61, 17, -7, 37, -8, 143, 114, 38, -68, 10, -16, -261, 10, 268, 96, 8, -7, -378, -2, -159, -28, 44, -77, -15, 108, 191, -28, 57, 28, -109, 205, -152, -34, 105, -27, 62, -28, 99, 7, 130, 12, -125, 199, -26, 12, 23, 59, 169, 43, 251, 70, 146, -52, -260, 102, 89, -76, 126, 15, -81, -39, -13, 216, 4, -23, 148, -1, 39, -18, 97, 9, -283, 95, 150, 119, 116, -1, 138, 256, 157, -50, 257, 174, -117, -21, 251, 19, -48, 37, 40, 39, 91, -46, 252, -6, 44, 45, 130, 63, 116, -7, -201, 186, 71, 1, 242, 18, 57, -20, -1, 115, -12, -6, -47, 35, 57, -72, 85, 73, -157, 102, 131, 45, 81, -68, 234, 139, 18, -20, -39, -56, 26, -14, 317, 71, 241, -100, 235, 207, -19, 41, 33, 35, -234, 48, 243, 103, 69, -9, 26, 21, 125, 27, 133, 90, 66, 69, 11, 166, -1, -24, -110, 142, 161, -32, 215, 82, -8, 41, 251, -30, -275, -54, 5, 146, 92, -79, 439, 35, 19, -54, 60, 25, 36, 123, -22, 91, 97, -22, 285, -144, -73, 67, 98, 90, 95, 31, -299, 42, -53, 8, 96, 55, -50, 13, -134, 244, -7, 8, -80, 12, -181, -38, -21, -51, -264, 45, 362, -73, 19, -59, -94, 305, 64, -36, 269, -26, 32, -9, -33, 175, -159, 20, -3, 61, -144, 35, -32, -55, -29, 39, 68, 32, -116, -4, -96, 64, 87, -77, -94, -161, -48, 19, 159, 41, -154, -58, 139, 77, -41, -30, -49, 116, 11, 34, 235, 5, 46, -68, -161, 97, -126, 2, -51, -204, 130, -17, 120, 83, 61, 88, -94, 218, -162, -90, 46, 10, -111, 26, 228, -111, -87, -14, 98, 116, 28, -55, -112, -13, -309, 33, -47, 52, -119, -133, -96, 100, 137, -61, -227, 8, -219, 199, 286, -75, -304, -56, 116, 92, -6, 16, -248, 81, -32, 20, -132, 38, 17, 73, -84, 15, 65, -25, -184, 106, 40, -14, 282, 12, -185, -62, -104, -75, 14, 46, 116, -2, -56, -5, 22, 201, -374, 77, -133, 66, -83, 11, -27, -52, -36, 23, 111, 35, 93, 34, -183, 230, -273, -109, -25, -16, -156, -63, -86, -49, 90, 29, -126, -6, -75, -50, -348, 41, -179, 2, 41, -204, -136, -38, -67, 53, -263, 27, 166, -35, -50, 4, 56, 95, 124, 32, 2, -5, 49, -9, -49, -9, -19, 155, 131, 28, -12, -5, -348, 211, -36, -107, 199, 25, -122, -9, -259, 149, -70, 29, -157, 209, -75, 20, -206, -4, -484, 196, 353, -46, -251, -30, -208, 129, 59, 16, 204, -20, -54, -39, 146, 205, -145, 46, -117, -151, -150, -23, -286, -39, 44, 16, -104, -66, -269, -30, -159, 77, -44, 37, 7, -183, -74, -13, 45, -16, -354, 198, 22, 82, -10, -51, -225, 49, -135, -10, 75, 101, -142, -76, 172, -21, -73, 76, 1, -64, -417, 80, -81, 35, 100, 19, -43, -87, -131, -90, -67, -82, -294, 60, 35, 34, -165, -59, -25, 70, -127, -10, -17, 99, 108, -16, 103, 19, 4, 85, -246, 6, 300, -1, -181, 130, 179, 7, -71, 12, -273, 26, 19, 61, -120, -92, 0, 168, -307, -59, -52, 172, -43, -84, 237, -110, -142, -33, -28, -198, -431, 123, 207, -133, 8, -10, -190, 293, -65, -63, -325, -60, -268, -34, -97, 124, -332, -13, -75, -4, -214, -125, 206, 36, -19, 100, 171, -21, -162, -32, -187, 112, 121, -13, -169, -25, -97, -26, -150, -23, -461, -15, 119, 13, -134, -99, -49, -49, 189, 280, -69, 169, 15, 15, -224, 257, -51, 64, 168, -445, -324, -40, 98, 2, -158, 105, -75, 49, -220, -27, -52, -106, -42, 28, 69, -132, -144, -47, -390, -220, -205, 147, 2, -58, 82, -8, -109, 156, -278, 10, -16, 89, 225, -24, -54, -36, -491, -136, 351, -18, -247, -76, 133, 77, -196, -2, 11, 118, 283, -6, -162, 199, -146, 98, 93, -221, -21, 53, 386, -122, -7, 136, -209, 51, -204, -96, -262, 174, -102, 33, 14, -139, -136, -46, -11, 193, -322, 115, -93, -74, -204, -24, 219, -13, 98, 133, 327, 35, -134, -35, -285, 332, -202, -74, -107, -2, -37, -13, 110, -33, -404, 134, -36, -16, -179, -34, -415, -38, -18, 178, -27, -143, -16, -46, -74, -46, 177, 46, 177, -23, -369, 18, -106, 289, 91, 12, -10, 44, -224, 15, -235, -18, -310, 58, 253, -76, -365, -33, 124, -164, -89, -1, 682, -202, -221, -48, -120, -39, -41, 60, -38, 330, -205, -51, -155, -47, 26, 159, 237, -7, -126, 40, -61, 29, -42, -157, -339, -82, -172, -33, -18, 202, -31, 45, 271, -22, 80, -31, 248, -182, -298, 82, 239, -108, 157, -77, -183, 224, -437, -10, -160, -23, -177, -55, -152, -31, 130, 41, -14, -4, -158, 104, 158, -23, 47, 30, 205, 43, -139, -20, 57, 90, 43, 150, 259, -207, -416, -61, -65, 17, -270, -7, 116, 37, -16, -8, -198, 143, 102, 114, -111, 38, -233, -68, 5, 10, -200, -16, 405, -261, -212, 10, -145, 268, -292, 96, -74, 8, 249, -7, -386, -378, -11, -2, 234, -159, 128, -28, 113, 44, -147, -77, 21, -15, 56, 108, 255, 191, -11, -28, -164, 57, 98, 28, 9, -109, -118, 205, 207, -152, -115, -34, 125, 105, -248, -27, -232, 62, -179, -28, 65, 99, 58, 7, 335, 130, -143, 12, 46, -125, -198, 199, 138, -26, 186, 12, -126, 23, -96, 59, -113, 169, -37, 43, 35, 251, -162, 70, 82, 146, -70, -52, -249, -260, -12, 102, 363, 89, -159, -76, -465, 126, -12, 15, 236, -81, -225, -39, -30, -13, -42, 216, 47, 4, -99, -23, -141, 148, -75, -1, -239, 39, -148, -18, 118, 97, -301, 9, -134, -283, -258, 95, 156, 150, -260, 119, -71, 116, 21, -1, -460, 138, 37, 256, 112, 157, 116, -50, -175, 257, -228, 174, 179, -117, 12, -21, -326, 251, 170, 19, -144, -48, 224, 37, 600, 40, 100, 39, 393, 91, -470, -46, -13, 252, 97, -6, 491, 44, 11, 45, 84, 130, 1, 63, -567, 116, 10, -7, -351, -201, -114, 186, 132, 71, -46, 1, -39, 242, 29, 18, -111, 57, 49, -20, 80, -1, -147, 115, 93, -12, -319, -6, -7, -47, 195, 35, 186, 57, 80, -72, -179, 85, 193, 73, 385, -157, 76, 102, -150, 131, -528, 45, 185, 81, -51, -68, 94, 234, -616, 139, 121, 18, -302, -20, -40, -39, 424, -56, 472, 26, -161, -14, 63, 317, -118, 71, 285, 241, -55, -100, 282, 235, -205, 207, 123, -19, -412, 41, 22, 33, -402, 35, 88, -234, -100, 48, 38, 243, 230, 103, -372, 69, -128, -9, -37, 26, 129, 21, 95, 125, -226, 27, -70, 133, -67, 90, -30, 66, 133, 69, -229, 11, 227, 166, 149, -1, 34, -24, 74, -110, -484, 142, 590, 161, -345, -32, 147, 215, -78, 82, -418, -8, 61, 41, -153, 251, -443, -30, 11, -275, 156, -54, 51, 5, 31, 146, 213, 92, -319, -79, -227, 439, 15, 35, -181, 19, 10, -54, 76, 60, -36, 25, 405, 36, -159, 123, 23, -22, 321, 91, -80, 97, 305, -22, -74, 285, -337, -144, 265, -73, -142, 67, -25, 98, -405, 90, 133, 95, 173, 31, -67, -299, 49, 42, -16, -53, -526, 8, 206, 96, -216, 55, 213, -50, -149, 13, 24, -134, -8, 244, -238, -7, 84, 8, 297, -80, 66, 12, 195, -181, -44, -38, -218, -21, 147, -51, -24, -264, -94, 45, -31, 362, 79, -73, 128, 19, -18, -59, 97, -94, -260, 305, -58, 64, -335, -36, -199, 269, -11, -26, 227, 32, 217, -9, -199, -33, -146, 175, 50, -159, -29, 20, -131, -3, -266, 61, 9, -144, -96, 35, -166, -32, 25, -55, 79, -29, 323, 39, -44, 68, -417, 32, 257, -116, 138, -4, -268, -96, -122, 64, -197, 87, -118, -77, 235, -94, 33, -161, 167, -48, -229, 19, 27, 159, -298, 41, -116, -154, 35, -58, -414, 139, 103, 77, -6, -41, 132, -30, -224, -49, 153, 116, -131, 11, 10, 34, -82, 235, 341, 5, -293, 46, -3, -68, -267, -161, 292, 97, 461, -126, -540, 2, -13, -51, -76, -204, -63, 130, -129, -17, -21, 120, -69, 83, 19, 61, 219, 88, -163, -94, -100, 218, -348, -162, 117, -90, -298, 46, 258, 10, -569, -111, -628, 26, 217, 228, 4, -111, -43, -87, -133, -14, 125, 98, -185, 116, 81, 28, 80, -55, -401, -112, -11, -13, -230, -309, 35, 33, 138, -47, -319, 52, 27, -119, -19, -133, 60, -96, -193, 100, -29, 137, -189, -61, -44, -227, -543, 8, 210, -219, 305, 199, -6, 286, 11, -75, -254, -304, -137, -56, -235, 116, 209, 92, 13, -6, 42, 16, 156, -248, -204, 81, -303, -32, 43, 20, -132, -132, 281, 38, -243, 17, 34, 73, -5, -84, -295, 15, 276, 65, -378, -25, -68, -184, 90, 106, -229, 40, 97, -14, -45, 282, 334, 12, 66, -185, 135, -62, 116, -104, -204, -75, -53, 14, -206, 46, -127, 116, 297, -2, -86, -56, -193, -5, -161, 22, 404, 201, -13, -374, -261, 77, 238, -133, -256, 66, 78, -83, 123, 11, -461, -27, 142, -52, -231, -36, -675, 23, 299, 111, 296, 35, -66, 93, -407, 34, -809, -183, 538, 230, 279, -273, 61, -109, -135, -25, 271, -16, -251, -156, -156, -63, -293, -86, -356, -49, 98, 90, -125, 29, -57, -126, -538, -6, 162, -75, -128, -50, 223, -348, 234, 41, 25, -179, 120, 2, -221, 41, -13, -204, -211, -136, 413, -38, 64, -67, 47, 53, 47, -263, -288, 27, -421, 166, 44, -35, -103, -50, -144, 4, -66, 56, 167, 95, -104, 124, 121, 32, -316, 2, -85, -5, 395, 49, -179, -9, -504, -49, 6, -9, -438, -19, 177, 155, -115, 131, 10, 28, 118, -12, -355, -5, 27, -348, 70, 211, 282, -36, 487, -107, -53, 199, 183, 25, 284, -122, -153, -9, 88, -259, -440, 149, -916, -70, 94, 29, -218, -157, -148, 209, 124, -75, -28, 20, -34, -206, 301, -4, 96, -484, -497, 196, 172, 353, -452, -46, 56, -251, 118, -30, -672, -208, 318, 129, 264, 59, -5, 16, 14, 204, -387, -20, 308, -54, 146, -39, -402, 146, 82, 205, -330, -145, 112, 46, 27, -117, 26, -151, 389, -150, -167, -23, -260, -286, 39, -39, 23, 44, -63, 16, -57, -104, 416, -66, -53, -269, 56, -30, -198, -159, -347, 77, 88, -44, -63, 37, -191, 7, 45, -183, -33, -74, -107, -13, -38, 45, -101, -16, 156, -354, -23, 198, 45, 22, 229, 82, 345, -10, -394, -51, -882, -225, 110, 49, -412, -135, 354, -10, 134, 75, -114, 101, -151, -142, 53, -76, -545, 172, -473, -21, 559, -73, 380, 76, 42, 1, -225, -64, 130, -417, -564, 80, 335, -81, 447, 35, 135, 100, 323, 19, -383, -43, 463, -87, -390, -131, 212, -90, 354, -67, 53, -82, 272, -294, -474, 60, 412, 35, 85, 34, -223, -165, 66, -59, -47, -25, -26, 70, 407, -127, -542, -10, 200, -17, -483, 99, 4, 108, -51, -16, -223, 103, -248, 19, -329, 4, 243, 85, 119, -246, 161, 6, 144, 300, 12, -1, -298, -181, 243, 130, -328, 179, 97, 7, -102, -71, -592, 12, -73, -273, 92, 26, -139, 19, 298, 61, -4, -120, 27, -92, -40, 0, 71, 168, -5, -307, -270, -59, 200, -52, -450, 172, 11, -43, -528, -84, -112, 237, -64, -110, -324, -142, 609, -33, -48, -28, 295, -198, 111, -431, -268, 123, -27, 207, -273, -133, 17, 8, 332, -10, -46, -190, 82, 293, 491, -65, 22, -63, -357, -325, -23, -60, -428, -268, 122, -34, 182, -97, -3, 124, -271, -332, -99, -13, -467, -75, 435, -4, 321, -214, -384, -125, -136, 206, -44, 36, -272, -19, 107, 100, 5, 171, -94, -21, 68, -162, -51, -32, -47, -187, -203, 112, 171, 121, -38, -13, -583, -169, 191, -25, 211, -97, 147, -26, 136, -150, 103, -23, 700, -461, -41, -15, -174, 119, 131, 13, 401, -134, -38, -99, -435, -49, 367, -49, 148, 189, 587, 280, 7, -69, -350, 169, -192, 15, -122, 15, -285, -224, 147, 257, -132, -51, 198, 64, -131, 168, -33, -445, 344, -324, -240, -40, 203, 98, -115, 2, 72, -158, -86, 105, 86, -75, -330, 49, 263, -220, -621, -27, -403, -52, 398, -106, 73, -42, -201, 28, 141, 69, 558, -132, -39, -144, 300, -47, -429, -390, 509, -220, 291, -205, 200, 147, 120, 2, -232, -58, 18, 82, 104, -8, -89, -109, 123, 156, 12, -278, 41, 10, 122, -16, -260, 89, 562, 225, -216, -24, -206, -54, 252, -36, 25, -491, 46, -136, -106, 351, -186, -18, -94, -247, 22, -76, 21, 133, 59, 77, 315, -196, 10, -2, -474, 11, 278, 118, -422, 283, 17, -6, -56, -162, -235, 199, 95, -146, 269, 98, 181, 93, -469, -221, 185, -21, -131, 53, 334, 386, 172, -122, -148, -7, -298, 136], "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": "4006.2.a.f", "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}