# Stored data for newform 1008.3.cg.l, downloaded from the LMFDB on 23 April 2024.
{"label": "1008.3.cg.l", "space_label": "1008.3.cg", "level": 1008, "weight": 3, "hecke_orbit": 12, "hecke_orbit_code": 49543581681058800, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 451249961597821746, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [441, 126, -9, -6, 1]], [11, [3969, -1134, 261, -18, 1]], [13, [7056, 0, 264, 0, 1]]], "qexp_display": "q+(2+\\beta _{1}+2\\beta _{3})q^{5}+(-1+2\\beta _{1}-\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "cg", "char_is_real": false, "Nk2": 9072, "analytic_conductor": 27.466010647517926, "hecke_ring_index": 3, "level_radical": 42, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.168", "prec": 17}, "analytic_rank_proved": true, "char_values": [1008, 6, [127, 757, 785, 577], [6, 6, 6, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [145, 577], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.041", "prec": 17}, {"__RealLiteral__": 0, "data": "3.879", "prec": 17}, {"__RealLiteral__": 0, "data": "0.819", "prec": 17}, {"__RealLiteral__": 0, "data": "54.958", "prec": 20}, {"__RealLiteral__": 0, "data": "29.849", "prec": 20}, {"__RealLiteral__": 0, "data": "1186.134", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 6, -8], "traces": [0, 4, 0, 0, 0, 6, 0, -8, 0, 0, 0, 18, 0, 0, 0, 0, 0, 30, 0, -6, 0, 0, 0, 30, 0, 4, 0, 0, 0, -48, 0, 42, 0, 0, 0, -42, 0, -62, 0, 0, 0, 0, 0, 8, 0, 0, 0, 174, 0, -20, 0, 0, 0, 78, 0, 0, 0, 0, 0, -78, 0, -42, 0, 0, 0, 84, 0, 58, 0, 0, 0, -24, 0, 318, 0, 0, 0, -126, 0, -110, 0, 0, 0, 0, 0, -36, 0, 0, 0, 378, 0, -24, 0, 0, 0, -30, 0, 0, 0, 0, 0, 54, 0, -306, 0, 0, 0, 66, 0, 70, 0, 0, 0, -240, 0, 306, 0, 0, 0, 90, 0, 44, 0, 0, 0, 0, 0, 616, 0, 0, 0, -486, 0, 30, 0, 0, 0, -150, 0, 0, 0, 0, 0, 252, 0, 72, 0, 0, 0, 66, 0, -226, 0, 0, 0, 804, 0, -378, 0, 0, 0, -294, 0, 130, 0, 0, 0, 0, 0, 148, 0, 0, 0, 162, 0, 124, 0, 0, 0, -294, 0, 0, 0, 0, 0, 390, 0, 342, 0, 0, 0, -318, 0, -122, 0, 0, 0, -192, 0, -894, 0, 0, 0, -48, 0, 252, 0, 0, 0, 0, 0, -472, 0, 0, 0, 156, 0, -942, 0, 0, 0, -132, 0, 0, 0, 0, 0, 270, 0, 474, 0, 0, 0, -54, 0, 198, 0, 0, 0, -144, 0, -66, 0, 0, 0, 378, 0, -60, 0, 0, 0, 0, 0, 324, 0, 0, 0, -522, 0, -926, 0, 0, 0, -402, 0, 0, 0, 0, 0, 690, 0, 102, 0, 0, 0, 108, 0, 122, 0, 0, 0, 288, 0, 282, 0, 0, 0, -456, 0, -380, 0, 0, 0, 0, 0, 1044, 0, 0, 0, -756, 0, -160, 0, 0, 0, -810, 0, 0, 0, 0, 0, 690, 0, 102, 0, 0, 0, -930, 0, -288, 0, 0, 0, -12, 0, 360, 0, 0, 0, -534, 0, 170, 0, 0, 0, 0, 0, -752, 0, 0, 0, -162, 0, -680, 0, 0, 0, -186, 0, 0, 0, 0, 0, 1326, 0, 684, 0, 0, 0, -126, 0, -704, 0, 0, 0, -132, 0, 1254, 0, 0, 0, -246, 0, 2, 0, 0, 0, 0, 0, -1456, 0, 0, 0, 798, 0, 756, 0, 0, 0, 18, 0, 0, 0, 0, 0, 30, 0, -222, 0, 0, 0, 234, 0, -612, 0, 0, 0, -1692, 0, 1458, 0, 0, 0, -1422, 0, -504, 0, 0, 0, 0, 0, -16, 0, 0, 0, -228, 0, 510, 0, 0, 0, -366, 0, 0, 0, 0, 0, -198, 0, -126, 0, 0, 0, -342, 0, -198, 0, 0, 0, 240, 0, -252, 0, 0, 0, -1428, 0, -14, 0, 0, 0, 0, 0, 184, 0, 0, 0, 2394, 0, -830, 0, 0, 0, -36, 0, 0, 0, 0, 0, 2154, 0, 540, 0, 0, 0, 756, 0, 482, 0, 0, 0, -48, 0, -504, 0, 0, 0, -672, 0, -46, 0, 0, 0, 0, 0, 972, 0, 0, 0, 1974, 0, 642, 0, 0, 0, -618, 0, 0, 0, 0, 0, -1398, 0, 162, 0, 0, 0, -150, 0, 284, 0, 0, 0, -624, 0, 1566, 0, 0, 0, -1386, 0, -1354, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, -650, 0, 0, 0, -846, 0, 0, 0, 0, 0, 738, 0, 72, 0, 0, 0, 246, 0, -794, 0, 0, 0, 984, 0, -18, 0, 0, 0, -624, 0, -558, 0, 0, 0, 0, 0, -444, 0, 0, 0, 2478, 0, -504, 0, 0, 0, -18, 0, 0, 0, 0, 0, 1428, 0, -1110, 0, 0, 0, 1068, 0, -1498, 0, 0, 0, 2784, 0, 1350, 0, 0, 0, -846, 0, 766, 0, 0, 0, 0, 0, -728, 0, 0, 0, 2508, 0, 1536, 0, 0, 0, -2154, 0, 0, 0, 0, 0, -270, 0, -1602, 0, 0, 0, -714, 0, -558, 0, 0, 0, -72, 0, 1158, 0, 0, 0, 42, 0, -144, 0, 0, 0, 0, 0, 1456, 0, 0, 0, -1098, 0, -984, 0, 0, 0, -798, 0, 0, 0, 0, 0, 1692, 0, 1374, 0, 0, 0, -672, 0, 180, 0, 0, 0, 3768, 0, -102, 0, 0, 0, -1134, 0, 298, 0, 0, 0, 0, 0, 504, 0, 0, 0, -1110, 0, 1074, 0, 0, 0, 240, 0, 0, 0, 0, 0, -84, 0, 174, 0, 0, 0, -1062, 0, -218, 0, 0, 0, 2040, 0, 1206, 0, 0, 0, -1986, 0, -610, 0, 0, 0, 0, 0, 2080, 0, 0, 0, -1482, 0, 586, 0, 0, 0, -132, 0, 0, 0, 0, 0, 462, 0, 2244, 0, 0, 0, -132, 0, -468, 0, 0, 0, 1548, 0, -642, 0, 0, 0, 48, 0, -1020, 0, 0, 0, 0, 0, 1692, 0, 0, 0, 3438, 0, -2646, 0, 0, 0, 1254, 0, 0, 0, 0, 0, 3054, 0, -84, 0, 0, 0, -1014, 0, 322, 0, 0, 0, -2616, 0, 618, 0, 0, 0, -174, 0, 1764, 0, 0, 0, 0, 0, -2500, 0, 0, 0, -1506, 0, -1900, 0, 0, 0, 66, 0, 0, 0, 0, 0, -294, 0, -582, 0, 0, 0, -1050, 0, 1314, 0, 0, 0, -2340, 0, -36, 0, 0, 0, -1932, 0, 1406, 0, 0, 0, 0, 0, 2168, 0, 0, 0, -3498, 0, -2816, 0, 0, 0, -186, 0, 0, 0, 0, 0, 576, 0, 882, 0, 0, 0, -1344, 0, 434, 0, 0, 0, 5112, 0, -3528, 0, 0, 0, 1494, 0, 2126, 0, 0, 0, 0, 0, 2056, 0, 0, 0, -30, 0, -114, 0, 0, 0, -450, 0, 0, 0, 0, 0, 4938, 0, -1260, 0, 0, 0, -66, 0, -1524, 0, 0, 0, -3984, 0, -2466, 0, 0, 0, 1110, 0, 1072, 0, 0, 0, 0, 0, -5192, 0, 0, 0, -966, 0, 1344, 0, 0, 0, -1542, 0, 0, 0, 0, 0, 1902, 0, 3600, 0, 0, 0, 276, 0, -1198, 0, 0, 0, -3564, 0, 2526, 0, 0, 0, -252, 0, -990, 0, 0, 0, 0, 0, -4768, 0, 0, 0, 1482, 0, 0, 0, 0, 0, 198, 0, 0, 0, 0, 0, 1464, 0, 1620, 0, 0, 0, -2490, 0, -622, 0, 0, 0, 1116, 0, 4410, 0, 0, 0, -1446, 0, 162, 0, 0, 0, 0, 0, 496, 0, 0, 0, -4884, 0, 1310, 0, 0, 0, -1170, 0, 0, 0, 0, 0, 252, 0, 1554, 0, 0, 0, 1320, 0, 296, 0, 0, 0, 5088, 0, 2718, 0, 0, 0, -3696, 0, -278, 0, 0, 0, 0, 0, -1384, 0, 0, 0, 714, 0, -2502, 0, 0, 0, -2178, 0, 0, 0, 0, 0, 834, 0, -162, 0, 0, 0, 504, 0, 2326, 0, 0, 0, -444, 0, 42, 0, 0, 0, 2730, 0, 446, 0, 0, 0, 0, 0, -2484, 0, 0, 0, 1950, 0, -3866, 0, 0, 0, 2634, 0, 0, 0, 0, 0, -354, 0, -4866, 0, 0, 0, 1692, 0, 426, 0, 0, 0, -3000, 0, -4338, 0, 0, 0, -3768, 0, 1310, 0, 0, 0, 0, 0, -180, 0, 0, 0, 2166, 0, 1432, 0, 0, 0, 378, 0, 0, 0, 0, 0, -3066, 0, -4104, 0, 0, 0, 306, 0, 1222, 0, 0, 0, -1476, 0, -900, 0, 0, 0, -1062, 0, 206, 0, 0, 0, 0, 0, 3204, 0, 0, 0, 690, 0, 604, 0, 0, 0, -1302, 0, 0, 0, 0, 0, -756, 0, 2190, 0, 0, 0, 1974, 0, -1296, 0, 0, 0, 192, 0, 1002, 0, 0, 0, 1146, 0, -2772, 0, 0, 0, 0, 0, -2832, 0, 0, 0, 1350, 0, 2304, 0, 0, 0, -1884, 0, 0, 0, 0, 0, -1974, 0, 222, 0, 0, 0, 2634, 0, -2970, 0, 0, 0, -1128, 0, 174, 0, 0, 0, 1890, 0, -2242, 0, 0, 0, 0, 0, 4376, 0, 0, 0, 834, 0, -630, 0, 0, 0, -756, 0, 0, 0, 0, 0, -2418, 0, 2466, 0, 0, 0, -732, 0, 1334, 0, 0, 0, 3852, 0, 1164, 0, 0, 0, 1950, 0, -2148, 0, 0, 0, 0, 0, 3492, 0, 0, 0, -324, 0, -182, 0, 0, 0, 558, 0, 0, 0, 0, 0, -1386, 0, -2016, 0, 0, 0, -1638, 0, -1488, 0, 0, 0, -6216, 0, -2574, 0, 0, 0, -3504, 0, -50, 0, 0, 0, 0, 0, -252, 0, 0, 0, -2556, 0, 3114, 0, 0, 0, 1980, 0, 0, 0, 0, 0, -4086, 0, -7488, 0, 0, 0, -1554, 0, 1944, 0, 0, 0, -3900, 0, 3132, 0, 0, 0, 1392, 0, -1066, 0, 0, 0, 0, 0, 2464, 0, 0, 0, 3534, 0, -1260, 0, 0, 0, 726, 0, 0, 0, 0, 0, -2580, 0, -1374, 0, 0, 0, 4422, 0, 2914, 0, 0, 0, 2796, 0, -1386, 0, 0, 0, -252, 0, -3024, 0, 0, 0, 0, 0, 1640, 0, 0, 0, 3444, 0, 5120, 0, 0, 0, -30, 0, 0, 0, 0, 0, -1062, 0, 1914, 0, 0, 0, -750, 0, -2772, 0, 0, 0, 1128, 0, 150, 0, 0, 0, -588, 0, 1710, 0, 0, 0, 0, 0, 4932, 0, 0, 0, -2508, 0, 5310, 0, 0, 0, 2766, 0, 0, 0, 0, 0, 1008, 0, 3858, 0, 0, 0, -672, 0, -648, 0, 0, 0, -1500, 0, 4182, 0, 0, 0, 732, 0, -86, 0, 0, 0, 0, 0, 1044, 0, 0, 0, -78, 0, -4752, 0, 0, 0, -1146, 0, 0, 0, 0, 0, -6762, 0, -2088, 0, 0, 0, 456, 0, -2450, 0, 0, 0, -3888, 0, -3078, 0, 0, 0, 3510, 0, 452, 0, 0, 0, 0, 0, -4592, 0, 0, 0, -1062, 0, -2502, 0, 0, 0, 1266, 0, 0, 0, 0, 0, 1434, 0, -234, 0, 0, 0, 2706, 0, -550, 0, 0, 0, 168, 0, -2622, 0, 0, 0, 6210, 0, 900, 0, 0, 0, 0, 0, 180, 0, 0, 0, 3798, 0, 1134, 0, 0, 0, -36, 0, 0, 0, 0, 0, 2886, 0, -2646, 0, 0, 0, 2214, 0, -926, 0, 0, 0, 4104, 0, -990, 0, 0, 0, 4176, 0, 2044, 0, 0, 0, 0, 0, 4276, 0, 0, 0, -2424, 0, 1746, 0, 0, 0, -90, 0, 0, 0, 0, 0, -954, 0, 1074, 0, 0, 0, -2988, 0, 2574, 0, 0, 0, 3696, 0, 2736, 0, 0, 0, 2562, 0, -162, 0, 0, 0, 0, 0, -1256, 0, 0, 0, -5130, 0, 804, 0, 0, 0, 5514, 0, 0, 0, 0, 0, -5106, 0, 5586, 0, 0, 0, 252, 0, 4406, 0, 0, 0, -2436, 0, 42, 0, 0, 0, 984, 0, -3514, 0, 0, 0, 0, 0, 1980, 0, 0, 0, -1800, 0, -1512, 0, 0, 0, 1416, 0, 0, 0, 0, 0, -1980, 0, -3594, 0, 0, 0, -258, 0, 1858, 0, 0, 0, -324, 0, -4482, 0, 0, 0, 2790, 0, 1762, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 1254, 0, -530, 0, 0, 0, 1110, 0, 0, 0, 0, 0, 11022, 0, -1668, 0, 0, 0, 3954, 0, 2422, 0, 0, 0, -2724, 0, -3276, 0, 0, 0, 3990, 0, -444, 0, 0, 0, 0, 0, -7092, 0, 0, 0, -822, 0, 3276, 0, 0, 0, 1530, 0, 0, 0, 0, 0, -4314, 0, 8106, 0, 0, 0, -2094, 0, -1862, 0, 0, 0, 3648, 0, -4770, 0, 0, 0, -3330, 0, 0, 0, 0, 0, 0, 0, -12108, 0, 0, 0, -4632, 0, -534, 0, 0, 0, -1902, 0, 0, 0, 0, 0, 1038, 0, 6552, 0, 0, 0, -1914, 0, 3222, 0, 0, 0, -540, 0, -2232, 0, 0, 0, 3780, 0, 468, 0, 0, 0, 0, 0, 2816, 0, 0, 0, -2196, 0, -3490, 0, 0, 0, -1776, 0, 0, 0, 0, 0, -1122, 0, -4230, 0, 0, 0, 594, 0, 462, 0, 0, 0, -2532, 0, -3708, 0, 0, 0, 7344, 0, 2322, 0, 0, 0, 0, 0, 1000, 0, 0, 0, -3102, 0, 5298, 0, 0, 0, 2802, 0, 0, 0, 0, 0, 1008, 0, 5622, 0, 0, 0, -4710, 0, 2974, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 4, -1, 6, 0]], "char_orbit_index": 59, "prim_orbit_index": 4, "minimal_twist": "14.3.d.a", "char_is_minimal": false, "conrey_index": 145, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 1, 0, 2], [0, 0, 0, 0], [-1, 2, -1, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [9, 9, -1, -1], [0, 0, 0, 0], [-6, -12, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [5, -5, 2, -2], [0, 0, 0, 0], [-2, -1, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -15, -6, 3], [0, 0, 0, 0], [2, 2, 4, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-12, 0, -2, 4], [0, 0, 0, 0], [7, -7, -15, 15], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-28, -35, 0, -7], [0, 0, 0, 0], [0, 31, -16, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, -4, -10, 0], [0, 0, 0, 0], [2, 0, -2, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [58, 29, 0, 1], [0, 0, 0, 0], [15, 40, -6, 16], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [39, 39, 4, 4], [0, 0, 0, 0], [-3, -6, 15, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-13, 13, -25, 25], [0, 0, 0, 0], [-14, -7, 0, -32], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -42, -28, 14], [0, 0, 0, 0], [29, 29, -15, -15], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-6, 0, -10, 20], [0, 0, 0, 0], [53, -53, 16, -16], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-21, 21, -28, 14], [0, 0, 0, 0], [0, 55, -10, 5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [68, 136, 4, 0], [0, 0, 0, 0], [-9, 0, -8, 16], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [126, 63, 0, -24], [0, 0, 0, 0], [18, 48, 32, -20], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-15, -15, -3, -3], [0, 0, 0, 0], [-22, -44, -26, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}