# Stored data for newform 8003.2.a.c, downloaded from the LMFDB on 25 April 2024. {"label": "8003.2.a.c", "space_label": "8003.2.a", "level": 8003, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007199288303427, "dim": 172, "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": 32012, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 63.90427673763069, "level_radical": 8003, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [8003, 1, [4984, 7103], [1, 1]], "inner_twist_count": 1, "level_primes": [53, 151], "conrey_indexes": [1], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 172, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[53, 1], [151, -1]], "trace_display": [8, 25, 27, 31], "traces": [172, 8, 25, 188, 27, 10, 31, 21, 179, 20, -3, 66, 121, 12, 30, 212, 8, 40, 41, 64, 56, 50, 28, 30, 231, 38, 100, 80, 26, 55, 66, 65, 99, 81, 36, 212, 153, 1, 20, 59, 40, 50, 39, -51, 123, 59, 29, 128, 245, 19, 36, 215, -172, 40, 40, 15, 54, 44, 0, -54, 100, -29, 92, 253, 77, 14, 126, -27, 47, 72, 38, 65, 185, 48, 75, 38, 120, 75, 79, 43, 232, 110, 90, 158, 115, 68, 61, 15, -36, -6, 33, 139, 103, -24, -45, 34, 159, -36, 27, 228, 119, 90, 146, 115, 73, -8, 64, 157, 151, -23, 85, 198, 22, -7, 148, 28, 344, 145, -27, -10, 237, 100, 77, 213, 132, 97, 131, 82, 17, 103, -2, 77, 252, -18, 136, 224, 61, 89, 64, 86, 125, 29, 31, 122, 232, -30, 156, 125, 33, -121, 172, 61, -7, 90, 36, -70, 377, -50, -25, 180, 55, 156, 116, 131, 194, 16, 22, -126, 313, 34, 90, 60, 195, -151, 56, -120, 115, 176, 42, 330, 303, 48, 99, 201, 153, -69, 142, 49, 134, 182, -16, 373, 164, -61, -125, 292, 80, 109, 73, 85, -52, 326, 14, -189, 150, -129, 92, 524, 30, -60, 53, -188, 285, -24, 35, 0, 204, 15, -116, -79, -45, 91, 266, 11, 216, -28, 11, 241, 243, 201, 43, 273, 34, -10, 26, -17, 224, -140, 62, -104, 88, 22, 280, 108, 192, -191, 64, -151, -65, 74, -92, 87, 360, -40, 114, 166, 178, 194, 122, 154, 168, 238, 52, -150, -27, 10, -96, 395, 171, -233, 198, -23, 41, -61, 32, -104, 420, -14, 214, -83, -76, -86, 288, 167, 294, 179, 125, -43, 322, -54, 147, 386, 227, 44, -24, 82, 306, 266, -4, -112, 118, 8, -238, 168, 28, 91, 233, 344, -20, -140, -46, -45, 282, 62, 24, 86, 194, -10, 93, 42, 146, 77, 82, 460, 382, -127, -35, 283, -148, 2, 91, 240, 415, 242, 18, 458, 207, 193, -86, -81, 184, 95, 239, 97, 160, -10, -69, 162, 425, 4, 90, -93, 224, -215, 190, -128, 195, -30, -7, -89, 409, -55, -60, 29, 105, 15, 64, 170, 107, -179, -31, 52, 328, -81, 79, -142, -2, -173, 81, -351, 259, -112, 141, -385, 213, -146, -229, 335, 84, 29, 91, -83, 80, -54, 54, -126, 640, -152, -111, 222, 122, -104, 140, 341, 139, -183, -92, 129, 136, -1, 131, 241, 42, 269, 3, 60, -42, 19, 134, 215, 307, -49, -5, -21, -28, -95, 49, 28, 42, 273, -206, 300, 311, -140, -36, 283, 240, -319, 58, 142, 78, 330, 79, 85, 252, -125, -2, 476, -36, -404, 197, -155, 25, 116, 143, -118, 302, -227, 90, 71, 136, -112, 128, 24, -94, 34, 157, 61, 197, -175, -9, 380, -33, -102, -26, -481, -179, 120, -22, -210, 134, 105, 150, 18, 289, -41, 316, 84, 347, -425, -104, -29, 487, 3, 255, 330, 25, 59, 69, 285, 231, 319, 23, 55, 145, -415, -120, 204, 319, 411, -72, -47, 93, 57, -199, 19, 443, -51, 18, 380, -164, -433, 217, -304, 351, 81, 17, -87, 262, -20, -117, 503, 209, -78, -41, -223, -87, 74, -234, -283, 231, 161, -121, 125, -165, -108, -52, 82, 227, -60, -118, 27, 342, -139, 49, -92, 292, -56, 89, 263, 64, -4, 73, -90, 737, -404, 284, -88, -30, 8, -35, -213, 583, -205, -12, 89, 348, -78, 158, 35, 161, -731, 3, -133, 74, 108, 98, -127, 296, -515, -160, 18, 200, -710, 186, -127, 305, -57, -130, -84, 177, -110, 222, 188, 32, 51, 287, 21, -17, 142, -219, -263, 630, -194, 4, 486, 22, -370, -32, -11, 90, 178, 109, -385, 462, 178, -313, 323, -56, -351, 169, -158, 49, 105, -256, -66, 687, -136, -39, 230, -10, 41, 185, -291, -13, -81, 93, 39, 144, -63, -179, 168, 107, 162, 287, 45, 343, 73, -59, 32, 619, -88, 172, -9, -366, -24, 263, 112, 301, -314, -20, -814, 95, -327, 43, 368, 26, -417, 250, -381, 82, -185, 205, -98, 552, -585, -93, -350, -121, -194, -16, 267, 141, -208, -74, -882, 210, -23, -99, -469, -9, -60, 216, -571, 110, 152, -80, 187, 186, 72, 260, 722, 157, -393, 169, 57, 262, 145, 94, 339, 179, 316, -221, 409, -238, -38, -25, 50, 179, 157, -138, 584, 527, -23, -121, 401, 76, 239, 127, -47, -109, -12, -57, 15, 167, -142, 14, 464, -240, -378, -133, -207, -47, 305, 27, -54, 453, 198, -189, 421, 301, -2, 140, -314, 156, 51, 46, 489, 310, -455, -170, 178, 289, 404, 484, -555, 64, -415, 71, -646, 65, -157, -111, 340, 94, -257, 209, 119, 81, 86, 139, -741, 153, -487, -30, 358, 462, 146, 1, -44, -235, -102, 2, 6, 198, -314, 234, 619, -41, -965, 219, 341, 279, 222, -39, -594, 589, 296, 149, 179, 227, -24, -48, -645, 25, -97, -213, 567, 287, -66, -137, 1064, -416, 157, 106, -188, 137, 381, -77, -943, 138, -307, 212, 34, -111, -498, -253, -212, 40, 181, -40, 361, 422, -154, -778, -406, 3, -271, 108, 80, 58, 151, 39, -37, 55, -176, 402, 360, 215, -679, 266, -61, 377, -133, 11, -203, 527, 229, 240, -102, 323, -708, 283, -865, 280, -559, 71, -117, 116, -433, 190, 420, -8, -454, 417, -559, -253, -84, -27, -741, -8, 11, -229, 17, 21, 10, 34, -257, 191, 180, -160, 66, 349, -10, -24, -31, 211, 215, 201, 98, 33, 241, 17, -427, 972, -286, 380, 373, -410, -148, -143, -362, 121, 254, -332, -32, 174, 174, -307, 16, 188, -260, 162, -71, -117, -723, -228, 297, 475, -213, 38, -336, -75, -40, -93, 49, 619, 92, -57, -375, 18, -148, 39, 313, -93, 13, 169, 85, -196, -46, -209, 733, 1079, -473, -639, -351, 124, -15, 152, -164, 5, -42, -44, -322, 367, -228, 276, -384, -58, -1059, 129, -382, 207, -465, 70, -553, 624, -695, -301, -310, -167, -205, -83, -569, 177, -511, -41, 495, 17, -60, -166, 61, 272, -373, -350, -272, -32, -206, 206, -59, 813, -316, 57, 341, 260, 49, -81, 172, -120, -456, -309, 192, 231, 270, -444, -40, 147, 34, 182, 626, 16, -16, -345, 275, 97, 23, -77, 15, -171, 248, -486, -401, 246, -476, 125, -306, 31, -483, -141, -64, 190, 25, 442, -296, -248, 153, -541, -504, 318, -164, 74, 732, -28, -328, -134, 420, 262, 175, 140, -1230, 382, -273, -16, 214, -300, -145, 527, -332, 357, 578, 127, -189, 887, -825, -839, -588, 204, -223, -101, -437, -122, -244, 105, -380, 338, -152, 237, 815, -37, -1072, 88, -1014, -56, 468, -254, 463, 337, -328, -127, -503, -123, -339, 527, -539, 302, -360, -61, -888, 136, 60, 158, 344, 386, -80, -395, 427, 304, 423, -131, -635, -155, -530, -183, -175, -19, 257, -164, -22, -617, 207, -293, -423, 468, -326, -534, 549, -254, -850, -257, -508, 176, -238, -74, 333, 342, -50, -301, 407, 76, -417, -49, 77, -5, 142, 52, -439, 366, 296, -283, -658, 48, -460, 182, -369, 587, -497, -36, -122, 1083, -525, 117, 120, 396, -565, -44, -23, 374, -12, 8, -721, -29, -1031, 312, -217, -102, -414, 124, 21, -183, -319, 171, -918, 487, 38, 48, -354, 52, -1501, -28, 202, 203, 176, 20, -815, 496, -1004, -44, 295, -253, -622, 301, 251, -148, -429, -269, -203, 1322, 30, -515, 0, -22, 244, 483, -250, 122, -336, -269, -300, -54, -104, -17, 345, 141, -316, -377, 12, -76, 69, 5, -1115, 266, 119, -377, -801, -265, -263, 588, 120, -397, -152, -520, -30, 630, -134, -229, -443, -61, -369, -236, -192, -285, -337, 39, -351, 763, -289, 27, 8, -213, -524, 291, -528, 43, -353, 77, 112, 181, -550, -107, -85, -170, -205, 36, -558, 485, -356, 34, -1395, 209, -245, -727, 62, 268, -538, 637, -764, -505, -2, -123, -266, 302, -491, -43, -417, -231, 20, -44, 556, -214, -1065, -180, -272, 580, -577, -361, -51, -89, -332, 105, -186, -195, 186, 169, 23, -42, -29, -91, 295, -167, -963, 150, 220, -718, 235, -159, -578, 1138, 589, 179, -769, -386, 358, 35, -94, 245, -705, -27, 860, 49, -560, -360, 39, 441, -763, 16, -330, -366, -38, -149, -571, 512, -316, -208, -100, -599, -1160, -135, -340, -52, 63, 73, 317, 447, 10, -137, -77, 107, -156, -31, -1074, 54, 137, -120, -810, -21, -413, -292, -158, 27, -127, 364, -245, 615, -1317, 4, -205, 496, -294, -347, -239, -109, -700, -198, -495, -2, 369, -120, -1273, 252, -1547, -100, 336, 193, 53, 123, -257, 173, 87, -268, -444, -184, -1046, 46, 89, 134, -1076, -136, 5, -181, -170, -393, -410, 453, -76, 13, -319, -255, -598, -419, -770, 127, -242, -180, -133, -165, 188, -249, 154, -623, -777, 42, -578, 199, -40, -285, -384, 624, -132, 212, 31, -421, -923, 211, -80, 510, -749, 319, -1355, 177, -466, -497, 165, -86, -777, 122, -222, 410, -258, 64, -539, 315, -260, 244, -953, 49, -727, -85, -78, -170, 20, -371, -1294, 469, -78, -108, -73, 500, -897, -156, -1883, 384, 452, 41, -176, 353, -1104, 355, -86, 37, -684, 140, 353, -413, -1085, -333, -2073, -26, 214, -8, 562, 47, -483, 480, -866, -119, -96, -558, -1157, 650, -566, -257, 439, 316, -746, 102, -299, 198, -92, -162, -318, 368, -641, 4, -291, -638, -534, 639, -14, -266, 449, -421, -414, 556, -36, -1343, -191, 119, -932, -40, -259, -398, -647, -201, -708, 587, -478, 173, 621, -109, -55, 100, -403, 303, -706, -505, -862, 229, -487, -349, -262, -621, 174, 50, -309, -286, -326, -155, -504, 552, -1094, -502, 251, -94, -443, -121, -9, 702, 108, -133, 19, 60, -38, 600, -750, 23, -811, 571, -187, 389, 122, -343, -710, 639, -517, -1253, 18, 111, 479, -809, -1088, -151, -425, -66, 516, 371, 325, -274, 392, -455, -478, 222, -735, -390, -352, -152, 35, 504, -565, -649, 21, -3, -663, -12, 451, 346, 585, -183, -342, 781, -203, -964, 205, -56, -673, 263, 430, -220, -267, -576, 903, 76, -567, 99, -515, 342, 31, -370, -1097, -715, 85, 5, -100, 308, -200, -512, -65, 369, -817, 134, -600, -387, -252, -405, -397, -417, -797, -75, 700, 52, -348, 88, -181, -340, -238, -217, -1666, 456, -60, -373, 623, -548, -704, -210, -1094, -215, -197, -99, 823, 401, -1683, -765, -304, -51, -615, -252, -493, 168, -28, -338, -819, 90, -40, -248, 174, -552, -1782, -85, -841, -99, 745, -544, -578, 285, -637, -541, -178, 24, -873, -623, -588, -25, -186, -109, -818, 70, -519, 126, 697, -119, -525, -285, -34, 675, 336, 236, -471, 433, -343, -325, 10, 375, 568, -12, -768, -663, 34, -160, -577, 682, -1242, -79, 427, -318, -1482, -266, -869, 466, 295, -565, -1424, -155, -81, -69, 89, 766, -1364, 91, -652, -1069, -282, -214, 66, 635, -128, 153, 67, -196, 495, 128, -930, 161, -818, -87, -488, 863, -222, 110, -91, -110, -1516, 174, -310, 138, -80, -202, -920, 791, -955, 74, -638, -58, -403, -540, -121, 541, 36, -283, -607, 323, -349, -993, -328, 551, -1485, -36, -278, 286, 685, -520, -1345, 480, -811, -204, -215, -480, -771, 57, -647, -9, -68, 65, -331, 83, -696, -419, -166, -38, 139, 400, -1346, -402, -348, -883, -338, 115, -203, -569, 812, 86, -984, -191, -155, 145, -163, -361, -1324, 433, -9, -809, -1166, -374, -682, 635, -1626, -1105, -592, -334, -212, 346, -1134, -182, -419, -37, -64, -947, -622, 761, 3, 46, -659, 145, -484, -275, -128, 78, -807, 357, -257, 11, -268, 36, 75, 254, -732, -454, -821, -665, -293, -116, 446, 78, -361, -532, -1589, 329, -424, -633, 546, -286, -895, 116, -206, -561, -1504, -538, 747, 40, -697, -409, -2145, -153, -15, 121, -318, -242, -255, -505, -1013, 31, -860, -394, 700, 266, -925, 91, -547, 363, -164, -387, -518, -247, 182, -336, 103, -194, -702, 661, -596, -1496, -552, -449, -100, 383, 226, -1109, 111, -127, -67, -353, -832, -433, -1067, -281, -174, 369, -686, 232, 232, -120, -354, -116, -409, -208, -1, 185, -1579, 589, -1000, -378, 448, -475, -252, -196, -1841, -41, 116, 241, -457, 308, 254, -497, -22, -141, -1469, -166, 327, 704, 248, -149, 180, 229, -672, -420, 709, -580, -970, 694, -911, 38, -931, 273, -218, 252, -510, -995, -21, 50, -321, -374, -738, -30, 323, -641, -2249, 313, -1475, -20, 590, 277, 1226, 177, -103, -209, -485, -108, -574, 439, -376, -195, 879, 155, 369, 680, 100, -95, -252, -307, -401, 656, -651, 196, 75, 733, -616, -325, -1114, -94, 272, 32, 1176, -21, -379, -400, 479, -757, 120, 333, -1320, 343, 362, -655, -909, 705, 12, -320, -77, 690, -296, -135, -59, -102, -16, 200, -1126, -299, -325, -272, 130, -182, -1339, 192, 240, 1084, -44, 64, -366, 497, 64, 48, -604, 169, -108, 446, -510, 129, -54, 131, -494, 504, 858, -159, 390, 107, -60, 137, -1313, 798, -626, 174, 258, 262, -345, 253, 191, 225, -406, 97, 415, -661, -1566, -196, -787, -40, -22, -256, 542, -182, -938, 45, -466, 20, -318, -814, -849, -217, -71, 774, -472, 383, -506, 493, -208, 179, 471, 23, -155, 1544, -538, 437, -903, -835, -192, 317, -322, 25, -43, -519, 132, 193, -106, -850, 303, 157, -1227, 45, 158, -395, -1262, -550, 21, 1083, 264, -564, 7, -702, -50, 728, 545, -4, -293, -168, 673, 16, 363, -839, -563, 305, 735, 41, 399, -704, 25, -345, 640, 1415, -542, -170, -288, 309, 443, 8, -217, -52, -76, -190, 347, 1146, 865, -267, 1221, -212, -1328, 365, 239, 30, -166, -209, 561, 951, -665, -371, -445, -98, 901, -1041, -723, 770, -314, -39, 616, 422, 1120, -437, -11, -321, -1012, 469, -1222, -97, -457, -254, 964, 1284, 87, 21, -541, 213, 1138, 181, 643, 310, 263, -652, -270, -81, 39, -744, 856, 221, 434, -179, 846, 267, 412, -203, 1050, 761, -33, -108, -922, -45, 1616, -524, -750, -849, -570, 543, -673, -391, -284, -579, 51, 424, -244, -51, -882, -117, 689, -275, 239, 146, -286, -363, 577, 132, 105, 638, 430, 45, -114, -199, -926, 440, 284, -151, -131, -322, 116, 114, -766, -229, 755, -346, 354, 317, -1336, 92, -856, -221, -664, 415, 777, -287, -221, -166, -1294, 159, -237, -50, 867, 24, -392, -12, -593, -123, 727, -225, 1128, 265, 58, 296, -680, 264, -948, -435, -777, 797, -157, 410, -1287, 680, 216, -111, -10, 221, -93, 459, 499, 661, -638, 608, 126, 630, -92, -279, 212, -16, 1343, -269, 7, 29, 674, -389, 489, 875, -840, 141, 1199, -396, -1434, -90, -375, 1021, 303, 201, -564, 215, -59, 321, -620, 59, -569, 69, -500, -327, 239, -401, -237, 78, 476, 220, 1306, 24, 713, -602, -459, 542, -349, -248, -223, 530, 160, -257, 892, 291, -678, 810, 35, 414, 164, -368, -1215, 664, 4, 715, 4, 37, -336, -446, 350, 306, -203, -399, -1083, 183, -738, -590, -551, 212, -706, -29, 517, 851, 723, 72, -804, 612, -129, -474, -89, -311, 860, 566, -5, -55, -714, 373, -868, 444, -385, -68, 250, -76, -501, 315, -292, 924, 444, -800, -931, -359, -166, 71, 1504, 139, -640, -504, -241, 38, 938, -588, 141, 1588, 799, -1258, 29, -392, -960, 376, -116, -777, 672, -110, -128, 9, -44, 502, 544, -471, 1681, -671, 49, -10, 546, -171, 734, 1280, -91, 124, 844, -489, 265, 546, -170, 692, -104, 8, 462, 287, 519, -299, 755, 272, 1881, 726, -183, -71, 276, 163, -803, 504, 900, -74, -613, -363, 628, 327, -272, -165, -661, -31, 335, -6, -755, -282, -712, -245, 629, -51, 1304, 531, 376, -428, -594, 538, -144, 178, 247, 13, 397, -201, 207, 7, 224, -281, -100, 736, 721, 309, 616, 28, -768, 903, 702, -1061, 538, -117, 595, -722, 1256, -64, 764, -287, 2325, -714, -232, 835, -580, -97, 1372, -481, 81, -132, 1185, 345, -33, -127, 248, -500, -19, 169, -323, 1004, -161, -36, 727, -715, -519, -206, -507, -293, 933, 348, -11, -518, 82, -479, -297, 519, -200, -597, -772, 1020, 1534, -436, 833, 1242, -170, 69, 300, 91, 458, 373, 309, -88, -365, 359, -349, 342, 373, -481, 221, 666, -379, -749, -1579, 471, 1117, -447, -1615, 507, -1598, -36, 1547, 215, 258, 692, -561, -415, -286, 611, -974, 407, 310, -264, 511, 491, 40, -102, -121, 281, 861, -67, 729, 532, 642, -523, -459, 222, 193, -240, 1581, 668, 41, -9, 394, 311, -185, -124, 2153, -533, 168, 64, -894, -77, -265, -228, -1180, 685, 949, 422, -6, -36, 1383, -153, -215, 511, -242, 450, -329, 217, -246, 312, 215, -175, -417, 440, 1392, 1014, 530, 69, 1001, 282, -588, 933, -301, 597, -590, 13, -263, -762, 827, -346, -726, 597, 727, -185, 49, 564, -240, 69, -438, 76, -575, 309, 110, 726, -345, 307, -1129, -190, -123, 504, 1418, -739, -724, -235, -1482, 172, 412, -1188, 700, 370, 30, -322, -1774, 688, -1417, -581, 335, 318, 7, -301, 900, 911, 313, 243, -529, -886, 279, 532, 1182, 649, -107, 701, 213, -158, 2094, -70, 186, -72, 1297, -745, 1408, 282, 359, -414, 1405, -78, -438, -45, 1376, 163, 484, -795, -517, 150, 689, -59, -804, -145, -40, 51, 843, 432, -890, -119, 1078, 41, 242, -160, 771, -305, 219, 968, 566, 452, 796, -784, 1804, 500, 351, 269, 518, 239, 451, 389, 906, -192, -250, 183, 183, 687, 1841, 253, -123, -203, -78, 448, -349, 659, 512, -663, 851, 774, -1519, -561, -329, -53, 890, -603, 183, 213, 202, -40, 2110, 1187, 1010, 463, 395, -18, -483, 306, -979, 567, 842, 362, 1189, 139, -265, 2, 1346, 107, 66, -493, 1053, -415, 592, -498, -477, 835, 1299, -314, 1212, 507, 571, -15, 1378, -57, 1035, -753, 48, 107, -279, -634, -203, 1244, 1128, -524, -579, -1665, 297, 69, 1775, -623, -550, -1387, -15, 50, -1835, 748, -268, -358, 342, -300, 52, 307, 537, -154, 356, -220, 945, 131, 1089, 419, -35, -12, 304, 1024, 391, 113, 1522, 224, -220, 842, -1869, 1658, 679, 259, 634], "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": "8003.2.a.c", "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}