# Stored data for newform 1014.3.f.d, downloaded from the LMFDB on 14 June 2025.
{"Nk2": 9126, "analytic_conductor": 27.629498806134105, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 4, "char_parity": -1, "char_values": [1014, 4, [677, 847], [4, 3]], "cm_discs": [], "conrey_index": 577, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[5, [144, -144, 72, -12, 1]], [7, [625, 250, 50, -10, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511142529827830, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 4, -1, 4, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1014.3.f.d", "level": 1014, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 13], "level_radical": 78, "minimal_twist": "78.3.l.a", "nf_label": "4.0.144.1", "prim_orbit_index": 4, "qexp_display": "q+(\\beta_{2}-1)q^{2}+(\\beta_{3}-\\beta_{2}+\\beta_1)q^{3}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1014.3.f", "trace_display": [-4, 0, 12, 10], "trace_hash": 973352868863940821, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.720", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "48.868", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1046.276", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.247", "prec": 17}, "traces": [0, 4, -4, 0, 0, 12, 0, 10, 8, 12, 0, 36, 0, 0, -20, -12, -16, 0, -12, 52, -24, 30, -72, 0, 0, 0, 0, 0, 20, 0, 0, -106, 16, -12, -48, 0, 0, 20, 0, 0, 48, -24, -60, 0, 72, 36, -72, -132, 0, 0, -4, 0, 0, 72, 0, 240, 0, 72, 0, 180, 24, 144, 0, 30, 0, 0, 24, -38, 96, 0, 0, 228, 24, 190, -40, 0, -104, 0, 0, 96, -48, 36, 0, -264, 60, 96, 96, -120, 0, 336, 0, 0, 144, 30, 264, 0, 0, 194, -4, 108, 8, 0, -48, 0, 0, 120, -72, 216, 0, -314, -240, -216, -40, -264, 0, 312, 0, 0, -360, -240, -48, 0, -144, 168, 212, 168, -60, 0, -32, 0, 0, -312, -24, 620, 0, -36, -96, -336, 96, 116, 0, 180, 0, 0, -48, 120, -380, 0, 40, 144, -144, 428, 208, 0, -120, 0, 0, 388, -96, -552, 0, 60, -36, 686, 48, -288, 0, -624, 0, 0, -192, 156, -192, 0, 120, -370, -144, 12, -672, 0, -72, 0, 0, -300, -144, 552, 0, -384, -264, 90, 168, 720, 0, -146, 0, 0, 8, 168, -216, 0, -8, 258, -96, -300, 96, 0, -48, 0, 0, 792, -120, 624, 0, 132, -216, -348, 0, -380, 0, 138, 0, 0, 432, 244, 80, 0, 264, 72, -144, -692, -624, 0, 0, 0, 0, -1152, 360, -84, 0, 336, 48, 116, -188, 0, 0, -288, 0, 0, -424, -312, -336, 0, 60, -744, 116, 0, 64, 0, -60, 0, 0, 0, 312, -624, 0, 768, -620, 240, 76, -24, 0, 854, 0, 0, 672, 108, -192, 0, -116, -318, 0, -636, -360, 0, -456, 0, 0, 720, 48, 388, 0, 426, 380, 156, -300, 1056, 0, -36, 0, 0, 288, 90, -856, 0, -208, 732, -144, -610, 240, 0, -696, 0, 0, -864, -388, 0, 0, 624, 552, 120, 96, 336, 0, 912, 0, 0, -1372, 210, -96, 0, 288, 370, 528, 60, 1248, 0, -120, 0, 0, 144, 192, -1968, 0, -270, 192, -504, -672, 864, 0, -890, 0, 0, 288, 420, -24, 0, 672, -480, -672, 408, 144, 0, 960, 0, 0, 864, 300, -788, 0, -72, -552, -1200, -60, 528, 0, 120, 0, 0, -180, 134, -336, 0, -720, 648, 0, -120, 292, 0, -388, 0, 0, -480, -8, -912, 0, 372, 216, 286, -172, 1140, 0, -456, 0, 0, 192, 108, 600, 0, -96, -1610, -480, 24, 96, 0, -216, 0, 0, -864, -792, -2880, 0, -602, -624, -396, 144, -624, 0, -390, 0, 0, 696, -936, 0, 0, 380, -360, 628, 360, -276, 0, 480, 0, 0, -648, -432, 1536, 0, -528, -80, 588, -12, -768, 0, -360, 0, 0, 288, -214, 1384, 0, 624, 168, -480, -586, 0, 0, 816, 0, 0, 1100, 1152, -288, 0, 924, 84, 916, 480, 216, 0, -1032, 0, 0, -232, -300, 376, 0, 0, 548, 288, -186, 576, 0, -336, 0, 0, 720, 424, 1800, 0, -604, 336, 288, 336, -1920, 0, -840, 0, 0, -232, 348, 0, 0, -64, 216, 768, 804, 120, 0, 980, 0, 0, 1608, 0, -248, 0, -390, 624, -1152, 48, 52, 0, 540, 0, 0, -480, 312, -152, 0, 24, 264, 72, 430, -1708, 0, 192, 0, 0, -988, -672, 432, 0, -720, 192, 30, 624, -1416, 0, -1032, 0, 0, 0, -288, 1272, 0, 360, -936, 316, 90, 912, 0, 120, 0, 0, 120, -720, 1080, 0, 548, -388, 150, -240, -2880, 0, 1200, 0, 0, -312, -420, 600, 0, -1056, -1032, -80, -1140, 72, 0, -288, 0, 0, -1032, -288, 96, 0, -114, 856, 996, -1128, 136, 0, -300, 0, 0, 288, 290, 1220, 0, -240, 348, 660, 1546, 1392, 0, -312, 0, 0, 668, 864, 984, 0, 624, 0, -998, 192, -636, 0, 1092, 0, 0, -240, 684, -192, 0, -336, -1790, -120, 468, -1824, 0, 72, 0, 0, -1440, 1372, -744, 0, -24, 96, 570, -240, 1368, 0, 674, 0, 0, -1056, 720, -120, 0, -1248, 648, -744, 1596, 240, 0, 1972, 0, 0, -1896, -144, 3100, 0, 192, 1968, -972, -312, -2064, 0, 792, 0, 0, 1008, -442, 1344, 0, -864, 1212, -240, 384, 1780, 0, 740, 0, 0, -2072, -288, 1872, 0, -3060, 24, -958, 1104, 288, 0, -2148, 0, 0, 1344, 576, -816, 0, -144, 1530, 772, -216, -1920, 0, 432, 0, 0, 108, -864, 912, 0, -1246, 788, 888, 288, -1200, 0, 532, 0, 0, 2400, -1548, 120, 0, -528, -792, 768, 1380, -240, 0, 528, 0, 0, 3288, 180, -2544, 0, 1080, 336, 1464, 1440, -520, 0, 288, 0, 0, 0, -3388, 240, 0, -292, 60, 288, 254, 776, 0, -168, 0, 0, 3840, 480, -360, 0, 1452, 912, -1522, -336, 912, 0, -300, 0, 0, -572, -1872, 344, 0, -1140, 864, 16, 1008, 912, 0, -516, 0, 0, -1176, -192, 1680, 0, 1138, -600, -114, -792, 4488, 0, -888, 0, 0, 960, -276, -48, 0, -96, -1284, -960, -672, 432, 0, -960, 0, 0, -1248, 864, -4320, 0, 90, 2880, 804, 240, -2164, 0, 1140, 0, 0, 792, 610, -288, 0, 624, -2088, -264, -598, 780, 0, 432, 0, 0, -1344, -696, 480, 0, -2772, 0, 1320, 868, -1152, 0, 948, 0, 0, -1256, 582, -720, 0, 276, 980, 1296, -1188, -960, 0, -12, 0, 0, -1008, 648, 4392, 0, 3890, -1536, 324, -488, -1272, 0, 1200, 0, 0, -1176, -300, 24, 0, 768, 570, -528, -3312, 720, 0, -144, 0, 0, 1608, -288, -4128, 0, -1332, -1384, -3060, -144, 2640, 0, -1542, 0, 0, 960, 2572, 1172, 0, 0, 2064, 816, 1852, -1632, 0, 672, 0, 0, 1056, -1100, 2316, 0, 2004, 288, -1776, -720, 360, 0, -2712, 0, 0, -1832, 864, -960, 0, -216, 2040, -672, -1080, 2064, 0, -96, 0, 0, 648, 232, -1176, 0, -1316, -376, 1488, 312, -792, 0, -1870, 0, 0, -576, 792, 372, 0, -576, -942, -120, -3996, 672, 0, 480, 0, 0, 2208, -720, -5656, 0, -1338, -1800, 660, 624, 2740, 0, -648, 0, 0, -576, -2208, -672, 0, 1920, -2376, -120, 3074, 1680, 0, 1488, 0, 0, -1200, 232, -792, 0, 576, 0, -2956, -1640, 1176, 0, 1992, 0, 0, -1536, 690, -1608, 0, -120, 314, 2736, 936, -1960, 0, -696, 0, 0, 1536, -1608, -1920, 0, 1392, 248, -654, -624, 240, 0, 658, 0, 0, 2304, 2508, -96, 0, -52, 2148, -1536, -396, -1080, 0, 1240, 0, 0, 2640, 480, 2256, 0, -720, 152, 2160, -816, -624, 0, -1152, 0, 0, -144, 3816, -860, 0, 1708, 300, -432, -1204, -384, 0, -2304, 0, 0, -528, 988, -312, 0, 3060, -432, 250, -216, -144, 0, -588, 0, 0, -60, 504, -1248, 0, 1416, 264, 232, -840, 2064, 0, 636, 0, 0, -2436, 0, 4824, 0, -1204, -1272, 504, 1488, 2328, 0, 722, 0, 0, -632, -1092, -180, 0, -912, -1182, -1560, 576, -240, 0, -1096, 0, 0, -5736, -120, -2140, 0, -168, -1080, 0, -96, -1252, 0, 1080, 0, 0, -300, 72, 480, 0, 2880, -1992, -852, -1224, -2400, 0, -760, 0, 0, -2996, 312, 288, 0, -2028, -600, 1608, -2396, -936, 0, 2268, 0, 0, 160, -540, 2280, 0, -72, -1680, -480, 1158, 576, 0, 144, 0, 0, 1860, 1032, -6072, 0, 3262, -96, -1728, -180, 1128, 0, 3264, 0, 0, -1992, -3420, 2256, 0, -136, -108, 416, 1332, 600, 0, -1464, 0, 0, -4776, -288, -3604, 0, -66, -1220, 1800, 1152, -2180, 0, -1008, 0, 0, -1320, 386, -3092, 0, -1392, -2832, 288, -2520, 624, 0, -2880, 0, 0, 4084, -668, 348, 0, -3720, -984, -144, 776, -432, 0, -732, 0, 0, 1996, 1230, -384, 0, 636, 1320, -1248, 540, -2184, 0, -1104, 0, 0, -1776, 240, 1008, 0, 2102, 192, 330, 2064, 432, 0, -3120, 0, 0, 240, 2016, -936, 0, 1824, -1464, -72, -2160, -144, 0, -3216, 0, 0, 312, 1440, 2976, 0, 360, 744, 708, -420, -3360, 0, 48, 0, 0, -1140, -2784, 480, 0, -1368, -840, -576, -2300, -1348, 0, -740, 0, 0, 6864, 1056, -984, 0, 2232, 120, 2694, -960, -576, 0, 2100, 0, 0, 1488, 432, -3192, 0, -240, 1104, -3504, 372, -3944, 0, -432, 0, 0, 3168, 1896, 5352, 0, -3144, -3100, 1284, -384, 4584, 0, -1800, 0, 0, 1944, 1092, 624, 0, 2064, 1074, 540, 1968, -1584, 0, -384, 0, 0, -4320, -1008, -332, 0, 2592, -1344, 144, -360, 6596, 0, 2190, 0, 0, 480, -70, -768, 0, -1780, -396, 1224, -158, -1480, 0, -1248, 0, 0, -6096, 2072, 720, 0, 1368, -1872, -4416, -840, 1164, 0, -1380, 0, 0, 1916, -828, -2208, 0, -288, -2890, -1344, 1944, 4296, 0, 960, 0, 0, -1656, -1344, 1008, 0, 1680, 816, -24, 96, 936, 0, -1896, 0, 0, -1544, 2316, 432, 0, 1920, 180, 1440, 4080, -864, 0, -2516, 0, 0, 7896, -108, 3428, 0, 0, -912, 4440, -600, 3312, 0, 2058, 0, 0, -1776, -772, -576, 0, 1200, -324, 144, -30, -1064, 0, 1104, 0, 0, -3004, -2400, -864, 0, -1164, -120, -2522, 1920, 4080, 0, -1164, 0, 0, -1536, -2160, -2760, 0, 240, 744, -1056, -1872, -1056, 0, 864, 0, 0, 840, -3288, -5448, 0, -4992, 2544, 3096, -268, -6288, 0, 644, 0, 0, -2928, 2400, -2880, 0, 520, 3012, 1440, 1908, -576, 0, -1296, 0, 0, -576, 0, 5520, 0, 468, -240, -2748, -816, -4656, 0, -2124, 0, 0, -576, 2686, -508, 0, -776, 2556, 780, -576, 336, 0, 1392, 0, 0, 4460, -3840, -1704, 0, -4908, 360, -542, 16, 720, 0, 1884, 0, 0, 3044, -1110, 672, 0, -912, 4114, -744, -912, 600, 0, -432, 0, 0, 3456, 572, 1320, 0, 1560, -344, 36, -384, 2880, 0, 5570, 0, 0, -32, -3492, -2016, 0, -912, 360, -3144, 2820, 1032, 0, 960, 0, 0, -10056, 1176, 2496, 0, -2688, -1680, -828, -216, -528, 0, -714, 0, 0, 228, 3524, 1584, 0, -4488, 5100, 192, 3048, 1776, 0, 3220, 0, 0, 3648, -960, 1008, 0, -3288, 48, 1800, 3312, -900, 0, 4032, 0, 0, 1920, -1560, 1344, 0, -432, 3700, 52, 510, 1920, 0, 2016, 0, 0, 1656, 1248, 4728, 0, -2254, 4320, -1440, 1584, 4560, 0, 3058, 0, 0, -1608, -2316, -480, 0, 2164, -1152, 1204, -6924, -2280, 0, 1248, 0, 0, 11616, -792, 2836, 0, 1224, 288, -960, -432, 192, 0, 270, 0, 0, 528, -7080, 1196, 0, -780, 708, 504, -120, -864, 0, 360, 0, 0, -5664, 1344, 2160, 0, 2052, -480, 3268, 1872, -2496, 0, 3780, 0, 0, -2640, 1224, -1736, 0, 1152, 1056, -760, -438, -1896, 0, 720, 0, 0, -5520, 1256, -4032, 0, 3898, 720, -5184, -1440, 2064, 0, -1180, 0, 0, -2592, 3000, 2376, 0, 960, 1836, 5160, 1416, 24, 0, -2476, 0, 0, 3000, 1008, 1680, 0, 504, -4392, 1812, 864, 5808, 0, -348, 0, 0, -648, 1300, 976, 0, 1272, -876, 1056, -5932, -2400, 0, 160, 0, 0, 4752, 1176, 2736, 0, -120, -24, 5206, 1344, -288, 0, 1428, 0, 0, 1056, 774, 6624, 0, -720, 5380, 1448, -1860, 288, 0, -288, 0, 0, 5616, -1608, -5736, 0, -1846, 4128, -900, 428, -9480, 0, -100, 0, 0, 6120, -2220, 288, 0, -2640, 2586, -1248, 720, 3084, 0, -336, 0, 0, -6600, -960, 4792, 0, -60, -1172, -2928, -144, -5520, 0, -1902, 0, 0, -1632, -1582, -3704, 0, 1632, 4020, -1512, 820, -1344, 0, -1728, 0, 0, -5232, -1056, -3888, 0, 4548, -2316, 3010, -2304, 2376, 0, -3000, 0, 0, 3552, 2352, 1440, 0, -360, -4566, -1848, -3630, 5424, 0, -168, 0, 0, 1872, 1832, -1080, 0, -5352, 960, -3972, 240, -8784, 0, -2256, 0, 0, 1344, -720, 2160, 0, -2064, 396, 1560, 8016, 192, 0, 1924, 0, 0, -5880, -648, 6624, 0, 906, 1176, -3324, 600, -868, 0, -1044, 0, 0, -2976, 6600, -624, 0, 792, -2580, 0, 672, 3740, 0, -1096, 0, 0, 6344, 576, -1140, 0, -1728, -372, -3336, -5568, -5784, 0, 10296, 0, 0, 240, -1800, 7992, 0, -672, -5232, 3072, 414, -960, 0, 1080, 0, 0, -792, -2208, 5232, 0, -290, 5656, -426, -848, -600, 0, -3442, 0, 0, -1320, 9072, -1248, 0, -2740, 1560, 1208, 4908, 1296, 0, -672], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 1, 0], [0, 1, -1, 1], [0, 0, -2, 0], [2, 0, -2, -2], [-1, 0, 1, -2], [0, 5, 0, 0], [2, 0, 2, 0], [3, 0, 0, 0], [2, -2, 6, 2], [10, -2, 10, 0], [2, -2, 0, 2], [0, 0, 0, 0], [-5, -5, 5, -5], [0, 0, 0, 6], [-4, 0, 0, 0], [-4, 4, 12, -4], [-3, 0, 3, 0], [19, 0, -19, 12], [-8, 4, -8, 0], [5, 5, 5, 0], [-18, 2, -2, 2], [8, -8, 18, 8], [-2, 4, -2, 0], [-12, 12, 1, -12], [0, 0, 0, 0], [0, 3, -3, 3], [10, 0, -10, 10], [0, -10, 10, -10], [-6, 6, -6, -6], [-24, 0, 24, 5], [4, 0, -4, 0], [-12, 18, -12, 0], [-8, -8, -8, 0], [0, 10, -10, 10], [0, 0, -6, 0], [23, -36, 23, 0], [-12, 12, 26, -12], [0, 0, 0, 0], [12, -4, 4, -4], [8, 0, -8, 28], [-15, -5, 5, -5], [-5, 5, -24, -5], [16, 0, -16, -4], [6, 0, -6, -6], [-26, 16, -26, 0], [-48, 30, -48, 0], [0, -4, 4, -4], [-25, 25, 1, -25], [11, -24, 11, 0], [-12, 12, 12, -12], [0, 0, 0, 0], [18, -46, 46, -46], [-3, 0, 3, -6], [60, -24, 24, -24], [-10, 10, 10, -10], [31, 0, -31, 26], [10, 0, -10, 20], [44, 2, 44, 0], [12, -12, 12, 0], [36, -25, 25, -25], [-5, 5, -53, -5], [0, 15, 0, 0], [0, 0, 8, 0], [0, 0, 0, 0], [6, -18, 18, -18], [12, 0, -12, 43], [24, 8, -8, 8], [-18, 18, -24, -18], [-10, 0, 10, -20], [68, 0, -68, 22], [6, 0, 6, 0], [36, 23, 36, 0], [-10, 36, -36, 36], [-1, 1, 36, -1], [-14, -24, -14, 0], [-40, 40, 30, -40], [0, 0, 0, 0], [24, -7, 7, -7], [-8, 0, 8, 8], [9, 0, 0, 0], [-28, 28, -12, -28], [-92, 0, 92, -52], [20, 0, -20, 10], [24, 0, 24, 0], [29, -10, 29, 0], [-30, 0, 0, 0], [4, -4, 36, 4], [64, 40, 64, 0], [6, -6, 18, 6], [0, 0, 0, 0], [36, -16, 16, -16], [-19, 0, 19, -53], [66, -30, 30, -30], [10, -10, -42, 10], [4, 0, -4, 8], [84, 0, -84, 71], [24, -50, 24, 0], [30, -6, 30, 0], [2, 24, -24, 24]]}