# Stored data for newform 4015.2.a.b, downloaded from the LMFDB on 25 April 2024. {"label": "4015.2.a.b", "space_label": "4015.2.a", "level": 4015, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660928943, "dim": 23, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-9, 69, 330, -2661, -2433, 18072, 13175, -48152, -37050, 63814, 54086, -46653, -44845, 19176, 22317, -4008, -6777, 170, 1226, 95, -121, -18, 5, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16060, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 32.05993641154407, "level_radical": 4015, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [4015, 1, [1607, 2191, 881], [1, 1, 1]], "inner_twist_count": 1, "level_primes": [5, 11, 73], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 23, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [11, -1], [73, 1]], "trace_display": [-5, -3, 23, -10], "traces": [23, -5, -3, 15, 23, -15, -10, -12, 8, -5, 23, 4, -19, -5, -3, -1, -26, 5, -34, 15, -26, -5, -4, -23, 23, -13, -3, -28, -36, -15, -24, -19, -3, -4, -10, -14, 4, -15, -34, -12, -74, 7, -15, 15, 8, 3, 1, 29, 1, -5, -47, -23, -6, -11, 23, -20, -19, 22, -17, 4, -59, 38, -21, -18, -19, -15, 12, 5, -8, -5, -34, 21, -23, -9, -3, -53, -10, 23, -62, -1, 7, 24, -8, 46, -26, -11, 1, -12, -77, 5, -6, 47, 0, -32, -34, -53, -21, -3, 8, 15, -62, 46, 10, 1, -26, -74, -13, -24, -76, -5, 9, 7, -26, 45, -4, -70, -25, 38, 16, -23, 23, -22, 7, -55, 23, -36, -37, 6, -69, -13, -61, 4, 16, -40, -3, 47, -31, -70, -39, -28, -12, 40, -19, -15, -36, 5, 35, 51, -59, -15, -66, 45, -24, -5, -24, 4, -1, 61, 29, -19, -77, 41, 22, -51, -3, -27, -19, 62, -42, -4, -43, -4, -24, 32, -10, -1, -45, 21, -65, -14, -54, 15, -36, -49, 4, 84, -26, -41, -74, -15, 61, 81, -1, 65, -34, -56, 12, 5, -10, -12, -66, 20, 3, -22, -74, -51, 5, 44, -34, 7, -119, 8, 19, 58, -15, -22, -14, 21, 3, 15, -35, -71, 57, 15, 8, -40, -12, -45, -87, 3, -26, -28, -60, 92, 1, -68, -19, 47, -105, 29, -56, -5, -37, -6, 1, 123, 56, 40, -50, -5, -11, -10, -4, -16, -47, -43, -67, -50, -109, -23, -46, 29, 44, -23, -6, -40, 60, 144, -59, -11, -36, -27, 33, 26, 23, -88, -49, -48, 28, -20, -46, 123, -11, -81, -19, -13, 70, -45, -31, 22, 37, -15, -29, 119, -17, -31, -3, 36, -80, 4, 11, 65, 116, 50, -59, -97, -49, -28, 21, 38, -11, 86, -3, 25, -21, -65, -8, -4, -36, -18, 9, 64, 66, 26, -19, -14, 57, -36, -74, -15, -70, 22, -12, 124, 12, 19, 76, -33, 56, 5, -24, -63, -116, 84, -8, -29, -24, -53, -76, -5, -7, -19, -64, 151, -34, -52, 29, -42, -55, 21, -19, -53, -3, 91, -23, 26, 96, -40, -158, -9, -71, 4, 108, -4, -3, -78, -76, 114, 38, -53, -11, 76, -34, 172, -10, -214, 16, 15, -93, 23, -49, 101, -36, 106, -62, -14, 50, -132, 116, -1, -145, -70, 45, -118, 7, 47, 4, -73, -113, 24, 61, 146, 28, 274, -8, -44, 34, -15, -50, 46, -68, -21, -4, 50, -26, -133, 140, -110, -34, -11, -140, -23, 93, -4, 1, -110, -60, 15, -49, -12, -70, 16, 80, 213, -77, -194, 24, 87, -16, 5, -74, -197, -55, 127, -6, -40, -37, -13, -45, 47, -75, 7, 24, -131, 0, 34, 127, -116, -68, -32, 57, 107, -15, 17, -34, -150, -18, -6, -56, -53, -82, 47, 109, 15, -21, 41, 36, -77, -26, -3, 28, -71, 107, 4, 8, -118, -92, 39, 69, 15, 47, -3, -83, 111, -62, 3, 114, -131, -126, 46, 10, 10, 96, 1, 10, -229, 1, -106, 108, 1, -68, 148, 3, 101, -26, 12, 4, 29, 39, -74, -47, 214, 96, 117, -13, -99, -92, 147, 1, -24, -69, -33, 102, 106, -76, -157, -87, 59, -55, -5, -9, -76, 53, 108, 9, -66, 122, -82, 59, 7, -47, -9, 4, 70, -26, -122, 30, 91, -181, 45, -17, -23, -50, 175, -4, 81, 46, -126, 186, -70, -125, 189, -6, 12, -25, 70, 44, -4, -139, 38, -102, 92, -135, -11, 16, -153, 71, 148, 194, -23, -42, 123, 85, -44, 23, -58, -93, 27, 58, -22, 60, 199, 89, 47, 7, -20, -163, -101, 165, -55, -151, 29, 132, 50, 23, -53, -19, -5, -147, -36, 35, 225, -22, 116, -37, 91, 164, 22, 39, 6, -131, 164, -20, 52, -69, 179, 25, 41, -17, -13, -149, 195, 7, 159, -61, -115, -8, 124, -49, 4, -77, -125, 208, 130, 16, 21, 253, 74, -15, -40, -59, -133, 58, 14, -3, -8, -12, 246, 68, 47, -22, 38, 66, 201, -31, 157, 188, 85, -26, -70, 119, 3, -21, 145, -39, 130, 97, -205, 178, -28, -91, 204, 130, -18, -12, 126, 155, 23, 88, 40, -182, 35, -172, 267, -19, -191, 127, 187, 124, -15, -63, 170, -97, 141, -36, -15, 48, -95, -55, 5, -23, 295, 100, -53, 35, 52, 12, 9, -134, 51, 70, 327, 116, 337, -59, -39, 124, 5, 3, -15, 25, 182, -2, 179, -66, -44, 104, 94, -8, 45, -178, 211, 93, 209, -24, -73, 40, 31, 24, -5, -34, 154, 60, 288, -24, 65, 116, 226, 47, 4, -34, 32, 60, 27, -1, -69, 74, -63, 16, 61, -69, 21, 83, -45, 29, 61, -15, 142, 109, -19, -146, 138, -23, 195, -77, 36, 268, 18, 6, 41, -126, 128, 80, -9, 22, -17, -2, 128, 256, -51, 22, 48, 64, -135, -3, -220, 94, 212, -120, -27, -49, 279, -154, 247, -19, -53, -25, 84, 47, 62, -89, 167, 109, -50, -42, 121, -10, -47, 97, -4, 49, 1, -6, 98, -43, 218, -88, 23, 12, -4, -35, 348, 87, 218, -24, -113, 53, 51, -62, 32, 28, 111, -122, 180, -10, -4, -5, -54, 105, -1, -189, 144, 70, 24, -45, 108, 90, -198, -117, 21, 7, 134, -39, 260, -65, -169, 241, 216, -9, -14, -113, 24, 172, 21, -54, 188, 129, -65, 8, 15, 168, 137, -8, -107, -36, 98, -11, -59, -27, -49, -163, 233, 20, 46, 4, -37, 82, 325, 25, 84, -97, -3, 37, -18, -26, -42, -96, 257, 178, -41, -116, 140, -45, 109, -74, -11, -149, -53, 19, -15, 95, 254, -36, -291, 61, -87, 1, -172, 64, 81, 127, 174, 121, 160, -1, 28, 235, -12, 49, 65, 53, 36, -8, 280, -34, 229, -144, 116, -77, -56, -91, 46, 67, 251, 12, -128, -5, 146, 22, 5, 144, 116, 58, 358, -10, -35, 132, -39, 107, -12, -6, -205, -52, 161, -66, -122, 34, 51, -6, 20, 14, 47, -176, 9, 3, 80, 144, 50, -66, -22, -28, 5, 0, 73, -74, -49, 78, 56, 121, -51, -115, 372, 163, -32, 5, -106, 63, 256, 45, 44, 58, -41, 89, 236, -34, 65, 62, 72, -244, 7, 73, 498, -172, -82, -119, -53, 71, -123, -75, 8, -133, 214, -13, -214, 19, 106, -21, -110, -137, 58, 213, 173, 6, 339, -15, -115, -41, -3, -14, -22, 59, 227, -26, 196, -14, -383, 72, -292, 8, 21, -139, 52, -38, 76, 3, -282, -356, -203, 126, 15, -190, 80, 174, 85, -35, 50, 319, 68, -121, -71, -62, -123, 54, 264, 57, -645, 93, -30, -60, 15, -181, 46, -132, -49, 8, 125, 37, -240, 92, -40, 112, 173, 10, -37, -12, -43, -108, -103, 78, -45, -34, -41, 183, 1, -87, -251, -43, 54, 195, 3, -71, -33, 6, 40, -26, -259, 34, -14, 35, -28, -72, 160, 44, -124, -60, -74, -53, 1, -34, 92, -26, -49, 134, 176, 1, -115, -13, -48, 39, -68, -62, 3, 126, 186, -19, 324, 42, -24, -20, 47, 109, 373, -222, 129, -105, -355, 28, 84, -76, 29, -98, -358, 120, -194, -56, -285, -153, 168, -189, -5, 10, 91, 116, 99, -37, 79, -160, -49, -33, -6, 9, -326, 89, 157, 1, -189, -74, 63, -370, 123, 63, 7, -299, -74, 56, 3, 217, -113, -13, 40, 26, -123, -26, -169, -50, -184, -46, -60, 8, -5, -102, -115, -61, 45, -11, -192, -132, 247, 166, -10, -109, -183, 162, -221, -4, -48, -8, -143, -134, -16, 199, 121, -115, -69, -47, -70, -103, -79, 158, -43, 18, 202, 16, 68, -67, -90, -25, 68, -54, -50, 157, -92, -143, 2, -109, 10, 50, 38, -229, -23, -34, -81, 92, 238, -46, 24, 65, -288, 16, 29, 27, 202, -117, -5, 44, 38, -10, 263, -196, -23, -169, -216, 164, 90, -6, 47, 33, -339, -122, -40, 23, 130, 49, 75, 60, 4, -80, 79, 70, 144, 13, -22, 161, -24, -59, 26, -54, -273, 42, -11, 200, -46, 7, 68, -36, 22, 43, -247, 10, -27, -188, -1, -58, -55, 33, -43, 46, 263, 117, 26, 120, -99, 98, 86, 23, 126, -54, 190, -193, -88, -44, 407, -300, 37, -49, -36, 34, -4, -16, -48, -95, -268, 90, -17, 28, 56, -37, -61, -99, -20, -105, -102, 129, 158, -46, 62, 67, 6, -58, 123, 342, 140, -77, 308, -11, -72, -30, -260, -69, -81, -102, -27, 83, 39, -19, -269, -197, -169, -16, -13, 419, 92, -24, 132, 70, -24, 357, -151, 167, -45, -61, -307, -149, 30, -31, -233, 96, -69, -165, 22, -47, 4, -79, -147, 37, 147, -28, -71, 96, -15, 115, 134, 16, -20, -29, 164, 8, -79, 47, 119, 85, -147, 97, -40, -17, -114, 101, 309, 159, -31, -188, 80, 57, 153, -3, 10, 22, -251, 60, 36, 153, 64, -290, 173, -80, 47, -344, -154, 148, 4, -193, -3, 315, -221, 11, 44, -31, -59, -252, 65, 65, 42, 156, -75, 116, 45, -299, -70, -284, 50, -139, 393, -67, 143, -59, -366, -357, 141, -39, -97, -221, -19, 26, -181, -49, -205, 20, -157, -126, -28, -1, -165, 110, -8, 21, -112, 95, -288, -350, 38, -12, -67, -483, -21, -11, -416, 192, 46, -131, 86, -98, 40, 122, -45, -3, -102, 27, 83, 53, 25, 126, -206, -19, -211, -21, 240, 39, -484, -32, -65, -128, -146, 119, -15, -8, 4, -361, 500, 109, -4, -138, -184, -255, 25, -36, -53, 29, -103, 121, -18, -119, 200, -58, -4, 9, 5, -10, -235, -18, 64, -307, 177, 53, -140, 66, -159, 35, -556, -33, 26, 71, -81, -4, 495, -19, 135, -6, 51, -109, -14, 120, 416, 207, 151, 57, -169, -283, -74, -59, -36, 305, -108, -10, -315, -74, 32, -532, 195, -57, -15, 25, -102, -31, 282, -70, 24, -54, 14, 197, 22, -66, -273, 36, -176, -12, -121, -46, 376, 16, 124, -57, 45, -190, 227, 12, -11, -26, 63, 4, 19, 141, 34, -24, -410, 76, -220, 93, -164, 92, -33, -92, -56, 9, -5, 56, 176, -222, -72, -123, 5, 255, -268, 220, 235, -24, 132, -284, 112, 45, -63, 119, -223, -48, 30, -116, 4, 128, 21, 54, 84, -128, -261, 201, -217, -8, -8, -1, -306, -165, -29, 118, 169, 203, 205, -24, 152, -180, 61, -128, -53, 29, -46, -29, 38, -76, -224, -31, -258, 29, -5, -97, 23, -113, -59, -7, -207, -390, 459, -51, -19, -277, -18, 41, -38, -64, 102, 356, 169, -130, 151, -77, -309, 302, 156, -34, -152, 56, 42, 135, -52, 7, 41, 90, -146, 29, 249, 42, -342, -247, -42, 139, 431, 22, -45, -55, 53, -106, -218, 302, 21, -28, -18, -80, -51, -19, 2, 178, -36, 136, -53, -186, -149, 172, 131, -3, -257, -224, -472, -4, 91, 85, 8, -146, 97, -23, -27, -245, -86, 0, 26, -118, 97, 267, -285, 96, 308, -19, -243, -203, -40, -373, -147, 133, 277, -158, 61, -299, 62, 62, -9, 310, 50, -148, 192, -71, -358, 86, -206, -42, 4, -102, 127, -37, -384, 108, -147, 82, -143, 40, -4, 195, -110, 343, 139, -3, -192, 261, -146, -199, -78, -43, -193, -233, 185, -76, -502, 375, 157, -414, 114, 93, -4, 76, -292, 38, 382, 208, 13, -309, -53, 63, -64, -24, -222, -11, -88, 54, -12, 0, 76, -29, 47, -263, 32, -34, 19, 135, 197, -2, 172, -271, -145, 39, -284, -10, -540, -27, 44, -315, -214, -203, 255, -57, -51, 16, -1, -173, 71, 56, 15, 90, -32, -201, 189, -93, 127, -45, -439, -158, 23, 278, -124, 485, 114, -49, -191, 155, 21, -322, 101, 7, 14, 29, 177, -36, 11, -155, -160, -65, 106, 3, 2, -285, -200, -62, -100, -154, -18, -47, -14, -59, -17, 6, 60, 50, -147, -63, -130, 125, -132, -54, -492, 161, 115, 116, 54, 262, -145, -195, -1, -58, 15, 40, -289, -145, -43, -93, -64, 18, -70, 457, -241, -36, -247, 45, 19, 113, 101, 376, -118, -211, -247, 23, -49, 7, 199, -57, 104, -270, 47, 219, -426, -36, 172, 4, -32, -99, 244, -106, -73, -135, 322, 163, 28, -113, 84, 47, -315, -15, 24, -110, -161, 72, 68, 61, -86, -26, -538, 58, 146, -120, 272, 6, 72, 28, 128, -401, -41, -141, 274, 450, -305, 263, 42, -8, -552, -161, -244, -74, -44, 49, 86, 149, 88, 34, -140, -117, -173, -165, -15, 167, -148, -210, -24, -50, 104, 200, 21, -193, 46, 61, -660, -86, -407, -68, -106, 67, 6, -155, -21, -301, 81, 17, -7, -4, 482, 36, -229, 60, 50, 136, -236, -1, -225, -26, 166, -10, 107, 96, -133, 105, 205, 210, 65, 140, 232, 4, -138, 387, -110, -121, -109, 301, -199, -34, -234, -187, -235, -80, -11, 101, -59, -295, 347, -140, -56, 255, -8, 83, -23, 70, 9, 268, -76, 93, 246, 12, -601, -417, -4, 20, 199, 52, 311, 1, 109, 26, 5, -61, -110, -2, 500, 102, -128, -60, -431, 68, 6, -10, 15, 57, -24, 293, -56, -49, -254, -236, -225, -428, -12, -221, -385, 68, 70, -70, 127, 310, 64, -244, 16, -66, -163, 126, 205, 80, -127, 80, -158, -37, 213, -248, 20, -154, -117, -77, 274, 138, -252, 58, -194, 62, 17, 3, -87, 24, 281, -441, 172, 8, 87, -133, -179, -264, -22, -16, -83, -305, 5, -27, 5, -42, 174, -115, -277, -74, -13, 9, -67, -329, -197, 339, 52, 24, 130, -55, -51, 85, -393, 32, 127, -241, 43, -122, -3, -6, 95, 5, -307, -67, -40, 388, -68, -221, -112, -37, -4, 210, 44, 70, -13, 188, 52, 187, 181, -45, 30, -319, 41, -34, 47, 286, -28, 308, -342, -75, -46, 184, 277, -90, 7, 96, 48, -247, -294, 24, 151, 220, -75, 14, -131, -119, -436, -155, -39, 0, 143, 243, -52, -51, 34, -123, 8, -181, -47, 127, 19, 186, -583, 86, -116, -124, -37, 19, -76, -68, -141, -12, -345, -11, -32, 88, -325, 300, 58, 57, -5, 203, 169, -28, 107, 155, 304, 146, -335, -15, 218, 57, 17, -353, 17, 103, -30, -166, -413, -34, -22, 29, -183, 161, -150, -191, 130, 24, -54, -18, 107, -14, -117, -117, -6, 86, -12, -84, 217, -56, 462, -268, 21, -211, -53, 131, -260, -217, -191, -82, -395, -23, -183, 3, 47, -10, 41, 118, -128, 109, -370, -205, -299, -254, 15, 136, -153, 114, 191, -21, -239, 391, -364, -300, 41, -35, -106, -64, 211, 36, -268, 154, 133, -58, -77, -244, -71, 131, 272, -26, -43, 45, -207, 132, -3, 723, -34, 57, 31, 28, -11, 17, -16, 117, -71, -306, -138, 83, 15, 107, 323, -113, -187, 164, 4, 114, -3, 253, 82, 8, 107, -325, -328, -80, -118, 237, 4, -12, -280, -92, -40, -402, 220, 136, 39, -130, 166, 616, -342, 69, 44, -12, -389, 166, 15, -11, -393, 428, 351, 47, 325, -105, -45, 98, -3, 331, 360, -170, -227, -83, -222, 241, -441, -87, 111, 27, 41, 158, -80, -62, -548, -204, 283, 154, 3, 240, 200, 35, 129, 114, -127, -39, 98, -83, -131, -26, -135, -14, 61, -126, -244, -2, -187, -146, 46, 115, -28, -233, -420, 10, 362, 323, -113, -95, 10, -108, 13, -60, -432, 96, -8, -428, 2, 88, 1, 16, -587, -74, 92, 10, -63, 94, 259, 223, -229, 184, 114, 28, -140, 1, -262, 150, -535, -91, -106, 88, 217, 109, 24, 108, -68, 29, -508, 147, 1, 425, 27, 331, -55, -68, -130, -19, -705, -30, 148, 283, 169, -115, -272, 3, 339, -29, 47, -62, 101, -131, -284, 254, -78, -26, 180, 269, 14, -105, 12, 295, 110, -353, -234, 4, -324, -137, -127, -137, 29, -8, -218, 114, 194, 39, 65, -36, -284, 123, -74, -56, -391, 99, 220, -47, -131, 382, 249, -240, 214, -182, -5, 228, -540, 96, -281, -158, 140, -90, 117, 268, 73, -37, -199, -13, 247, 220, -185, -134, -99, 45, -179, 263, -6, -92, -32, -13, -365, -60, 147, 98, -374, -332, -105, 1, 98, -198, -32, 105, -24, -4, -210, 158, -164, -69, 123, -52, 188, 363, -33, 16, 359, 154, -84, 102, -194, 56, -5, 1, 106, 127, -176, 147, 323, -76, 548, 10, 40, -413, -157, 149, 167, 11, -441, -87, -4, -241, 4, -50, 59, 356, 34, 272, 170, -55, -66, -149, 356, 147, -5, 400, -584, 202, -60, -9, -338, 310, 196, -56, -76, -11, -411, -49, 215, 53, -171, 33, -405, -205, 108, -36, -10, 382, 15, 9, 229, -215, -180, -309, -66, 110, 300, -4, 401, 122, 81, -52, 156, 82, -82, 101, -163, -409, -16, 59, 492, 204, -165, 189, 7, 98, -539, 311, -77, -47, -463, -127, -30, 117, -9, 145, 68, -211, 322, 4, -43, -10, -360, 57, 70, 66, 14, 4, 51, -26, -302, -67, -91, 133, -122, 207, -471, -173, 282, 30, 282, 78, -50, -104, 91, 63, -221, -6, 106, -181, -25, 34, 121, -109, 45, 144, -333, 125, -112, -17, -362, 163, 175, 245, -23, 224, -487, 656, -222, -50, -186, 65, 117, -152, 175, -46, -34, 33, 33, -4, -225, 545, -372, -459, 81, -32, 29, -450, 26, 46, 512, 297, -321, 280, -126, 631, -61, 44, 44, 186, 346, -392, -528, -103, -70, 65, -367, -33, -23, -125, 191, 463, 443, 45, 189, -81, 15, 400, -212, -6, -344, -86, -475, -27, 12, -4, 545, -33, 454, -25, -40, -280, 331, 106, 70, -128, -338, -23, -93, 44, 281, 60, 183, -213, -4, 80, 311, 571, -111, -139, 147, 141, 144, -72, 38, 44, 32, 391, 252, -102, -32, -29, -486, -59, 92, 239, 327, 21, 133, -135, -68, -355, -276, -9, -11, 122, -39, 271, 121, 16, -10, 329, -196, -167, -153, -36, 206, -21, 163, 71, -440, -151, 559, -145, 148, -70, -27, 74, -34, 194, 208, 304, -327, -405, -23], "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": "4015.2.a.b", "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}