# Stored data for newform 4031.2.a.b, downloaded from the LMFDB on 23 April 2024. {"label": "4031.2.a.b", "space_label": "4031.2.a", "level": 4031, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660928959, "dim": 59, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [83, -9507, 101714, 520613, -9053202, 3966712, 243068149, -434282476, -3111232034, 7473504953, 23584644351, -65378195942, -121136192812, 359173093507, 461016553433, -1362469348430, -1374231929278, 3764425561928, 3295042936776, -7837727168126, -6401929412793, 12592876149821, 10079540084690, -15891008825404, -12864014959656, 15959988976000, 13342359900423, -12882299120248, -11293682637796, 8410956485268, 7838134125079, -4456024908834, -4479071279024, 1914105250289, 2114084578007, -662618674758, -825562266125, 182152709942, 266719961108, -38488265762, -71146324248, 5754037558, 15599831316, -431808895, -2791005592, -48366925, 402916477, 22452255, -46165271, -4095853, 4096812, 480449, -271237, -38552, 12599, 2065, -366, -67, 5, 1]]], "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16124, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 32.18769705477812, "level_radical": 4031, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [4031, 1, [3337, 697], [1, 1]], "inner_twist_count": 1, "level_primes": [29, 139], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 59, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[29, -1], [139, -1]], "trace_display": [-5, -6, -5, -10], "traces": [59, -5, -6, 41, -5, -7, -10, -12, 23, -18, -27, -8, -22, -24, -18, 5, -23, 1, -32, -14, -36, -6, -3, -18, -8, -1, -12, -9, 59, -18, -32, -39, -12, -18, -9, 10, -44, 5, -27, -68, -44, -25, -40, -56, -39, -40, -20, -9, -39, -21, -28, -49, -31, -32, -32, -48, -58, -5, 6, -44, -88, 35, -22, -10, -43, -31, -45, -29, -60, -14, -20, -4, -90, -25, 15, -64, -39, -28, -120, 24, -77, -71, -33, -14, -71, -61, -6, -34, -78, -88, -28, -31, -36, -4, -12, -29, -48, -4, -43, -81, -45, -33, 12, 29, -20, -88, 11, -19, -106, 49, 13, -85, -57, -35, 11, 41, 6, -88, 1, -10, -130, 28, 77, -57, -27, -37, -67, -69, -80, 41, -57, -27, 10, 32, 21, -15, -40, 65, 59, 67, -85, -46, 28, -5, -5, -39, -71, -62, -57, 73, -67, 110, -113, -79, -27, -102, -53, 6, -5, -115, -38, 46, -57, -9, -16, -120, 26, -42, -127, 77, -56, -111, -58, -7, 9, -53, -77, -59, -68, 68, -85, 97, -17, -114, -96, 58, -6, 82, -150, -65, -60, 148, -108, 42, -102, -17, -57, 21, -115, 58, -61, -16, -10, -63, -185, -63, -12, -90, -17, 155, -99, -44, -3, -99, 9, -131, -147, -17, 3, -10, -79, -6, -50, -46, -70, -54, 43, -97, -131, -5, 70, -12, -69, -11, -78, 95, -44, 79, 51, 36, -113, 121, -32, -85, -40, -39, -105, 114, -60, 39, -17, -13, -84, 85, -34, 31, 5, 148, -108, -3, 23, 23, -34, -74, -53, 68, -44, -7, -69, 51, -45, -27, 34, -84, -9, -9, -60, -5, 16, -34, -111, -131, 1, 34, -34, -51, -36, -49, -176, -18, -32, -113, -56, 43, -67, 30, 35, 60, 5, 66, -134, 57, -32, -13, -112, 28, 26, 43, -17, -76, -18, 72, -128, 132, -12, -238, 2, 92, -27, 120, -115, -126, 40, -94, -82, 163, 25, -58, -57, 13, -63, 59, -6, -68, 46, 125, -87, 13, 34, -103, -9, 107, 43, -51, -83, 35, 123, -8, -109, 74, -120, 17, -3, 170, 7, -27, 83, 36, -82, 0, -283, 86, -96, -160, 11, 45, -21, -25, -11, 136, 42, -50, -173, 154, -24, -37, -22, 119, -156, -107, 104, -98, 55, -20, -213, -26, 21, -116, -201, 97, -85, 25, -72, 69, 66, 16, -28, -42, 82, -125, -13, 75, -48, -130, 81, -24, -6, 11, -198, 111, 79, 181, 122, 77, -74, 138, -6, 117, -17, 166, -203, 1, 70, -240, -104, 4, -103, 240, -15, 28, -53, -11, -108, -43, -18, -170, -8, 4, -15, 188, -53, 35, 60, 75, -120, -50, -44, 35, -20, -214, -133, 209, 180, 45, 41, 8, -226, 141, 4, 159, -24, 91, -6, 5, 150, -13, 88, 5, -112, 170, 71, 3, 8, 268, -113, 48, -200, 141, -24, -41, -176, 138, 125, -181, -25, 287, 115, 154, -44, 44, -16, 108, -23, -13, -72, -188, 44, 5, -114, 132, -96, 180, 16, 41, -196, -17, 238, -132, 63, 146, -8, 76, -98, -169, 131, -44, -21, 116, -93, 129, 19, 1, -17, -160, -98, 105, 135, 258, -184, 56, 87, 98, -142, 171, -128, 136, -102, 34, 53, 231, -35, 57, -5, 223, -47, 105, 19, 173, -43, 145, -32, 125, -190, -13, 126, 41, 125, 233, -74, 174, 76, -147, -135, -30, 158, -47, 74, 150, -175, 299, -234, 44, 49, -62, 105, -52, -97, -99, 262, -14, 80, 112, -44, 16, -46, -31, 287, 54, -140, 48, -106, 233, -9, 123, -197, -89, 135, 84, 37, 163, -268, 255, -11, -16, 39, 275, 81, 36, -36, 98, -47, -54, -59, 168, 214, 176, 13, 120, -43, -185, -32, -90, 113, -1, -223, 351, 228, 26, 33, 70, 95, 94, 77, -190, 144, 153, 24, -6, -116, -208, -115, 102, -78, 231, 168, -18, 130, 201, -299, 43, -10, 233, -113, 121, -50, 223, 7, 145, 34, 218, -96, 17, 70, -42, 55, 185, -3, 142, -159, -11, 92, 23, -56, 313, 210, -200, 60, -134, -120, 287, -122, 60, 124, 64, -78, 283, 127, -89, 50, 281, 1, 61, 126, 12, -5, -18, -108, -30, 25, 185, -62, 221, 60, 124, 55, 127, 94, 228, -184, 193, -208, -71, 77, 160, 37, -23, 101, 206, 5, 292, -122, 179, 94, 37, -8, 447, -162, 239, -205, 35, 236, 489, -142, 198, 139, -138, -38, 158, -22, -278, 47, 118, 111, 395, -294, 56, 210, -13, 16, 149, -85, 262, -48, -1, 59, 38, -261, -79, 63, 352, -67, 199, 76, 46, 92, 165, 49, 625, -404, -62, 180, 38, 20, 92, -24, 123, -102, -55, -19, 181, -205, 237, -12, 8, -98, 212, 118, 116, -14, 471, 86, 184, -71, 37, 107, -60, 165, 137, -113, 390, 26, -138, 92, -80, -10, 30, 141, 0, -143, 154, 30, -9, 147, -107, 20, 138, -137, 286, 365, 38, 95, 484, -98, -136, -106, 183, -69, 73, 128, 102, 22, 116, 72, -7, 11, 254, 55, 278, 62, 289, 59, 221, -192, -152, 175, 222, 33, 357, -407, 35, 222, 70, 16, 133, 247, -207, 156, 278, -7, 358, -44, 29, 174, -34, -94, 293, 310, -133, 70, -18, 169, 56, -82, 61, 192, 541, 248, 191, 23, 283, -229, 391, -77, 156, -87, -202, 246, 196, -207, 180, 47, 229, 43, 41, -63, 408, 33, -13, -32, 176, -279, 83, 233, 160, 143, 381, -150, 175, 86, -67, -22, -133, 51, -90, 108, -35, -6, 277, -130, 63, 94, 82, 230, 98, -36, -23, 204, -39, 33, -39, -108, 273, 30, 157, 248, 177, 3, 250, -80, -46, -6, 461, -46, 182, 32, 64, 6, 109, -90, 63, 314, 111, 122, 251, 168, 84, -12, 250, -182, -38, -255, 260, 39, 323, 104, 306, 166, 159, 98, -28, 240, -68, -10, 222, 107, -47, 55, 87, 119, -28, -223, -106, 105, 150, -139, -18, 313, -131, -260, 268, -147, 395, 161, 131, 187, 194, -147, 152, 151, 179, -329, 65, 59, 128, 119, 205, -6, 356, -333, 256, -165, -55, -28, 240, -9, 336, -140, 14, 85, 5, 77, 560, -224, -75, 292, 7, -3, -153, 223, -75, -19, 746, -326, 211, -10, -494, 44, 83, 103, 122, -111, -56, 405, 10, 7, -6, 172, 81, -3, 269, 118, 201, 52, 96, 48, -111, -227, 493, -173, 168, -71, -72, 113, -31, -29, 224, 160, 170, -233, 212, 125, 293, -44, 408, -173, -34, 260, 67, 120, 192, -423, 47, 402, -289, -40, -122, 210, -345, -432, 420, 15, 226, -213, 22, 265, -368, 175, -90, -71, 26, -78, 5, 252, -124, -114, -8, 280, 155, 84, 352, 40, -12, 45, -326, -67, 345, -197, -368, -23, 21, -181, -133, -197, 109, -14, -168, 12, -84, -304, 39, -27, 9, -45, -125, 135, 41, 220, 260, -27, -111, -163, 44, 33, -113, 45, -174, -46, 379, -15, -126, 54, -223, -21, -169, 447, -413, 117, -134, 180, -68, 17, 51, 86, -221, -90, 328, 276, -61, 154, 151, -78, -84, -35, 310, -143, -53, -134, -145, -65, -40, 1, 503, -156, 106, -109, 134, 123, 47, -44, -116, -73, -71, -35, -106, -108, 287, 121, -205, 298, -92, -513, 172, 362, -203, -46, -35, 110, 33, -242, -69, 247, -13, -126, 9, 197, -387, 207, -25, -103, -321, -182, 173, 257, 192, -211, 164, 425, 48, -153, 303, -81, 277, -377, -332, 397, 163, 40, -172, -216, 89, -312, 93, -133, 221, 357, 74, -40, 46, -620, -66, 23, 158, 20, -2, 46, 91, 104, -273, -121, -123, -65, -204, 94, -295, 16, -295, 44, 199, -21, -14, 177, -42, -147, -129, 146, -56, 283, -439, -299, 7, -215, 707, 36, 191, -136, 327, 188, 1, -288, 92, -417, 233, 33, 70, -22, -296, -492, -24, -21, -90, 116, 72, -154, 309, -39, 157, 49, -431, -81, 299, -144, 385, 39, -530, 60, -192, -234, -269, 153, -140, -149, 284, 79, -9, -25, -230, 65, 150, -67, -264, 78, -250, 109, -40, 132, -204, -101, 177, -216, 336, 82, 137, 198, 98, -388, 108, 12, -104, -385, -299, 61, 91, -38, 3, 90, 228, -132, -105, -214, 94, -280, 35, -20, -185, -101, -513, 27, 299, -267, 148, -143, 1, 261, -541, -74, -51, 286, -124, -71, -47, -169, 200, 137, 238, 229, -50, -81, -126, 26, -18, 265, -9, -174, -85, 120, -65, 61, -33, 95, -130, -147, -19, -68, 102, -129, 25, -402, -348, -125, 54, -62, 55, 83, -138, -11, -112, -101, -269, 69, -171, -39, 83, -71, -553, 10, 317, 226, 260, -598, -288, 380, -169, -140, -255, 276, -165, -123, 185, -80, 130, -284, -113, 103, -610, 294, -300, -55, -276, -9, -21, 216, 80, -322, -130, 156, 18, 79, -57, -64, 363, 81, -33, 29, 203, -679, -420, -47, -134, -193, -336, -323, 99, -197, -157, 40, -141, 81, 141, -28, 113, -345, -60, -179, 113, 95, 53, -45, -436, -288, -221, -251, -206, 321, -398, -68, -69, -30, 89, 18, -295, 95, -55, -20, -261, 56, -469, 288, -49, 217, -224, -139, 157, -166, -61, 90, 82, 186, -365, -314, 83, -310, 555, -222, -344, -15, 53, 362, -431, -27, 509, -189, -430, 213, 42, -50, -209, -31, -13, -364, -217, -30, -33, 20, -146, -211, -5, 222, -663, -125, -274, 343, -239, -92, -27, 356, -250, -431, -16, 47, 180, -479, 239, -147, -361, 264, -32, 188, -390, -534, 224, 226, 459, 66, -358, 37, 42, -119, 286, -378, 78, -227, -260, -248, -260, -193, 29, -106, 329, -303, 221, -42, 135, -129, 163, -32, 129, -241, -330, 239, 256, 3, 368, 87, -269, -5, -442, -114, -557, -152, -372, -220, 28, -97, 315, -39, -212, 278, -205, 248, -183, -138, -121, 18, -48, -75, -679, -21, 61, -66, 149, 181, 779, -269, 370, -122, -224, -23, 5, -332, -528, -233, -229, 43, -272, -191, 371, -154, 359, -294, 237, 124, 15, -58, -266, 46, -147, -96, -509, 276, 44, -98, 95, 329, -40, -211, -91, 149, -8, 40, 183, 373, 333, 52, -272, -234, -166, 182, -213, -45, 113, -385, -5, 95, -663, -34, -272, 49, 124, -253, 305, 252, 319, -130, -253, -376, -384, -204, -737, 91, -183, 147, -81, -126, 513, -313, 26, -149, -209, 44, -53, 6, 35, -454, -295, 95, 295, -87, 430, -4, 54, 238, -313, -250, -256, 521, -459, 55, -222, -288, -195, -134, -235, -74, -282, 24, 196, 44, 72, 221, -44, 72, 24, -75, -542, -16, 382, 245, -99, 81, -64, -212, -72, -218, -90, -240, -421, 132, -139, -56, 221, -430, 47, -101, -391, 89, -104, 193, -153, -88, -453, 21, 59, 302, -54, 206, 185, -287, -222, 327, -450, -217, 104, 314, -743, 78, -85, 244, -165, -303, -275, 36, -284, -235, -533, -63, -365, 187, 35, 374, -221, -647, 569, 24, 72, 436, 183, -22, 196, -21, -237, 16, 444, -173, -706, 151, -32, -379, -389, -258, 94, -117, -108, 54, 285, -268, -218, -22, -167, -526, -517, -99, 339, 119, -90, -136, -71, 65, -177, -69, 208, -63, -122, 15, -96, -135, 13, -24, 134, -67, -256, 14, -238, 140, -402, 184, -10, 139, -475, -86, -9, -353, 204, 222, -78, -86, 162, -206, 124, 58, -74, -410, -298, -349, -638, 523, -310, 235, 272, -124, 190, -51, 95, 114, -129, -43, -50, -36, -526, -166, -33, -28, 241, -49, -5, 516, -37, 31, -351, 467, -68, -364, 29, -84, -475, -581, -459, 0, -182, 1, 317, 341, -44, 112, -31, -15, -112, 10, -146, 28, -622, -204, 322, -46, 80, 74, -48, -202, -9, -471, -707, 339, 186, 30, -226, -213, -397, -102, -393, -68, 357, 326, 230, -45, 461, -477, -24, 85, -89, 123, 410, -152, 330, -240, -482, -124, -225, 7, -440, -287, 69, -235, -52, -27, -923, 106, -432, 394, -209, -300, 167, 547, -29, -147, -611, -19, -160, 75, 398, 327, -202, -110, 586, -155, -231, -122, -6, -101, -569, 139, -654, 59, 2, -333, 32, 3, -261, 57, -201, 1, -551, -60, 0, -76, -950, 262, 88, 275, 617, -424, -24, 154, -147, -47, 46, 181, -236, -278, -38, -1, 269, -85, -199, -114, -313, -80, -120, 243, -55, -47, -14, 526, -546, 291, -141, 209, -126, 531, 64, 63, 148, -729, 25, 196, -24, -403, -563, 169, -513, 242, -318, -156, 174, -392, -141, 102, -146, 311, -227, -20, 14, -20, -254, 118, -434, 44, 275, 91, -251, 98, -154, -163, 395, 296, -739, -160, 132, -5, -246, 131, 11, -255, -227, 265, 80, -18, 212, 337, -4, -107, -309, 9, -28, 69, 121, 121, 241, -147, 132, -72, -611, -168, 48, -227, -324, 216, -95, 410, -158, -176, 485, 63, -124, -569, 454, -29, -3, -90, 156, -248, -169, 243, 234, 36, 344, -229, -3, 381, -191, -309, -353, 165, -209, 21, 11, -206, 142, -302, -95, -54, -382, 93, 14, -54, -683, 153, -25, 294, -1024, -462, -30, 145, 349, 319, -202, 101, 629, 26, -239, 43, 196, -517, -744, 232, -628, -124, -7, -189, -376, -540, 248, 7, 228, 470, -77, 15, 377, -67, -310, 41, 280, -52, 406, 62, -330, -334, -201, 31, -46, 174, -653, -277, 327, -292, 103, 109, -56, 25, -784, 492, -233, -29, 463, 193, -64, 235, -609, 28, -400, -181, -60, 306, 167, 228, -718, 341, -176, -234, 329, 109, -248, -406, 465, 408, 5, -46, -181, 44, 20, 357, 224, -41, -82, -39, -227, -456, -303, 164, 128, -322, 346, -343, -351, 371, -413, -104, 84, 499, -443, -123, 461, 8, -570, -99, -333, 413, -490, 103, -412, 38, 224, 215, -28, -209, -240, -357, -108, 390, -165, -66, 56, 172, 531, 185, -192, -4, 99, -180, -361, 163, -33, -142, -286, 85, -322, 69, 142, -239, -452, 45, 149, -120, 465, -68, -304, 227, 77, -19, 151, 8, -336, 51, -286, -1, -6, -49, -325, -201, -28, -53, -312, -161, -340, 263, -246, 383, 4, -7, -417, 347, 24, -37, -264, -197, -341, 88, 456, 502, 101, -131, 91, -26, 32, -289, -51, -155, -493, -279, -183, 0, -504, -141, 167, 468, -429, 343, 13, 190, 486, -77, 227, -347, -315, -435, 182, 255, 266, 182, -407, 353, -804, 166, 130, -23, -946, -81, -123, 402, -27, -81, -106, -69, 51, 112, -219, -6, -96, 322, -71, 242, -345, -302, -179, 276, 479, 193, -9, 369, -156, -413, -330, -499, 692, -451, -315, 87, -258, 219, -436, 32, 533, -793, 159, -501, 372, 305, 152, -33, 23, -582, -401, 360, 636, 101, -330, -161, -44, -69, -567, -218, -41, -149, -127, -34, 8, 132, -341, 213, 363, 61, -240, 152, 143, 98, 190, 222, -14, 175, -687, -175, 17, -296, 42, 378, 117, -85, 230, 72, -366, -530, 512, 108, -746, 235, -93, 652, -93, -240, 286, -150, 5, -219, 901, 135, 239, -71, 141, -189, -538, 472, -352, 70, 248, -554, -202, 354, -458, -212, -683, -131, -369, -317, 287, -81, 73, -128, -334, 474, -628, 107, -465, 78, -597, 318, -61, 340, -211, -159, -98, 26, 281, 243, 1, -9, 424, -286, 290, 338, 103, -635, -834, 436, -78, -371, -665, -338, 790, -179, -385, 171, -501, -470, -295, -6, 442, -335, -689, 162, 698, -566, 311, 117, 110, 308, -375, 406, -534, 146, -18, -102, -409, 59, 246, 290, -104, -428, -211, 370, 82, -335, -18, 182, -34, 206, -526, 360, -106, -34, -587, 384, 174, 325, 59, 88, -405, -33, 467, -190, -954, -464, 108, 588, -116, -113, 283, 23, 451, -58, -153, -33, -254, -78, -61, 15, -649, -32, 243, 375, -267, -90, 345, 249, -85, 17, -93, 392, -605, -44, -49, -34, -272, -626, -2, -330, -427, 496, 50, 434, -59, 3, -88, 472, -96, -369, -387, 427, 837, 76, 227, -67, -167, 254, 354, -77, 42, -458, -468, -114, -208, -275, -448, -398, 867, 70, 443, 336, 683, 746, -364, -28, 13, -32, 290, 319, -193, 493, 361, 110, -1042, 34, -571, -5, 665, -13, -10, -50, -179, -143, -98, -318, -316, 54, -307, 513, -259, -275, -81, 543, -31, -440, 309, -159, 721, 61, 583, 4, 27, 577, 533, 140, -310, -79, 1092, -318, -452, 142, -195, 119, -669, -342, 199, -202, -263, 319, 105, 111, 357, -36, 26, -235, 53, -37, 428, 277, -366, -108, 196, 431, -357, 203, 48, 202, 160, -571, -107, 659, 98, -114, -1075, 222, -36, -265, 246, 35, -579, 262, -4, 407, -263, -90, -167, -95, 439, 853, 81, 30, 407, -121, -783, -294, 719, -332, -618, -2, 173, 275, -279, 110, 81, -487, 76, 82, 178, 113, -274, -12, -27, -169, 107, 451, 110, -214, 381, -9, -656, 759, -252, -167, 246, 129, -521, -48, 28, 159, -1, 414, -9, 209, -620, -58, -14, 77, -58, 376, -29, 353, 176, -77, -352, 183, 602, 279, 568, -166, 280, -13, -22, -191, -281, -9, -355, -248, 17, 667, -441, 335, 151, -235, -130, -338, 147, 587, 355, -48, -197, -538, 165, 125, -25, 83, 272, 182, 321, 611, -367, -89, 71, 435, -688, 106, -140, 218, 671, -452, -569, 191, -472, 545, -683, -78, -189, 372, -4, 71, -1216, -143, -163, 372, 433, 425, 368, 35, 764, 177, 546, -93, 97, -737, -643, 533, 152, -3, -362, -29, -351, -113, -138, 375, 459, -7, -152, -43, 525, -273, -1034, 226, 409, 389, 293, 83, 205, -428, -654, -137, -636, 564, -686, -29, 111, -222, 418, 236, -132, -348, 237, 555, 12, 118, -208, 619, -81, 457, -261, 149, 556, -330, 622, 388, -257, -296, 343, -207, 610, -123, -456, -54, -559, 260, -1053, -36, 115, -190, 463, 167, 715, 426, 119, 50, -296, -45, 428, -82, -485, 44, -199, 62, 915, -213, -330, 395, -141, -6, 211, 354, -248, -296, -478, 39, -5, -557, 543, 170, 161, 165, -279, 137, -120, 683, -33, 205, -245, -72, 857, 183, 510, 74, 596, 535, 401, -148, -443, -125, 714, -703, -524, 188, 309, -430, -155, -204, -186, -36, 124, -95, 399, 388, -252, 12, -483, -218, -26, 136, 209, 182, 202, 136, -155, 227, -712, -163, 416], "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": "4031.2.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}