# Stored data for newform 1568.3.g.c, downloaded from the LMFDB on 24 April 2024. {"label": "1568.3.g.c", "space_label": "1568.3.g", "level": 1568, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007611621934624, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 879075940226471726, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1, 1]]], "qexp_display": "q-q^{3}-3\\zeta_{6}q^{5}-8q^{9}-17q^{11}-8\\zeta_{6}q^{13}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "g", "char_is_real": true, "Nk2": 14112, "analytic_conductor": 42.72490545169455, "hecke_ring_index": 2, "level_radical": 14, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [1568, 2, [1471, 197, 1473], [1, 1, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [687], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.959", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.513", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "155.759", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c2", "trace_display": [0, -2, 0, 0], "traces": [0, 2, 0, -2, 0, 0, 0, 0, 0, -16, 0, -34, 0, 0, 0, 0, 0, -50, 0, 14, 0, 0, 0, 0, 0, -4, 0, 34, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 52, 0, -28, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -14, 0, 110, 0, 0, 0, 0, 0, -144, 0, -34, 0, 0, 0, 0, 0, 238, 0, 4, 0, 0, 0, 0, 0, 110, 0, -220, 0, 0, 0, 0, 0, 142, 0, 0, 0, 0, 0, 0, 0, -44, 0, 272, 0, 0, 0, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, 244, 0, -54, 0, 0, 0, 0, 0, 336, 0, -52, 0, 0, 0, 0, 0, 28, 0, -34, 0, 0, 0, 0, 0, -290, 0, 164, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 400, 0, 342, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, -46, 0, -112, 0, 0, 0, 0, 0, -110, 0, -178, 0, 0, 0, 0, 0, 90, 0, 850, 0, 0, 0, 0, 0, -146, 0, 144, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, -238, 0, -604, 0, 0, 0, 0, 0, 0, 0, -238, 0, 0, 0, 0, 0, 32, 0, 110, 0, 0, 0, 0, 0, -770, 0, 522, 0, 0, 0, 0, 0, -290, 0, -416, 0, 0, 0, 0, 0, 220, 0, 116, 0, 0, 0, 0, 0, 238, 0, 0, 0, 0, 0, 0, 0, -954, 0, -142, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 148, 0, 926, 0, 0, 0, 0, 0, 672, 0, 44, 0, 0, 0, 0, 0, -578, 0, -144, 0, 0, 0, 0, 0, 234, 0, 548, 0, 0, 0, 0, 0, -818, 0, 0, 0, 0, 0, 0, 0, 130, 0, -350, 0, 0, 0, 0, 0, 0, 0, 590, 0, 0, 0, 0, 0, 52, 0, -244, 0, 0, 0, 0, 0, 54, 0, -754, 0, 0, 0, 0, 0, 1006, 0, 0, 0, 0, 0, 0, 0, -624, 0, -336, 0, 0, 0, 0, 0, -416, 0, 0, 0, 0, 0, 0, 0, 384, 0, 1268, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 34, 0, -774, 0, 0, 0, 0, 0, 238, 0, 912, 0, 0, 0, 0, 0, -290, 0, 290, 0, 0, 0, 0, 0, -164, 0, -604, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 820, 0, -144, 0, 0, 0, 0, 0, 0, 0, -802, 0, 0, 0, 0, 0, -620, 0, -884, 0, 0, 0, 0, 0, 334, 0, -850, 0, 0, 0, 0, 0, -342, 0, -1570, 0, 0, 0, 0, 0, 476, 0, -28, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 34, 0, -844, 0, 0, 0, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, -810, 0, 46, 0, 0, 0, 0, 0, 238, 0, 1674, 0, 0, 0, 0, 0, -50, 0, -1186, 0, 0, 0, 0, 0, 1004, 0, -880, 0, 0, 0, 0, 0, 178, 0, 0, 0, 0, 0, 0, 0, -90, 0, -1324, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, 0, 0, -850, 0, -1474, 0, 0, 0, 0, 0, -242, 0, -1474, 0, 0, 0, 0, 0, 94, 0, 146, 0, 0, 0, 0, 0, 1152, 0, -892, 0, 0, 0, 0, 0, 430, 0, 0, 0, 0, 0, 0, 0, 532, 0, 272, 0, 0, 0, 0, 0, 0, 0, 1392, 0, 0, 0, 0, 0, -236, 0, 1838, 0, 0, 0, 0, 0, -1342, 0, 238, 0, 0, 0, 0, 0, 604, 0, 1728, 0, 0, 0, 0, 0, -2, 0, 1028, 0, 0, 0, 0, 0, -1870, 0, 0, 0, 0, 0, 0, 0, -1904, 0, -1084, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 436, 0, -68, 0, 0, 0, 0, 0, -110, 0, 734, 0, 0, 0, 0, 0, -2544, 0, -994, 0, 0, 0, 0, 0, -1300, 0, 770, 0, 0, 0, 0, 0, -522, 0, 0, 0, 0, 0, 0, 0, 342, 0, 2448, 0, 0, 0, 0, 0, 0, 0, 290, 0, 0, 0, 0, 0, -574, 0, 700, 0, 0, 0, 0, 0, 578, 0, -1426, 0, 0, 0, 0, 0, -54, 0, 1760, 0, 0, 0, 0, 0, -116, 0, -378, 0, 0, 0, 0, 0, 1726, 0, 0, 0, 0, 0, 0, 0, 820, 0, -238, 0, 0, 0, 0, 0, 0, 0, 364, 0, 0, 0, 0, 0, 3222, 0, 62, 0, 0, 0, 0, 0, 624, 0, 954, 0, 0, 0, 0, 0, -1136, 0, -4046, 0, 0, 0, 0, 0, -626, 0, 2276, 0, 0, 0, 0, 0, -196, 0, 0, 0, 0, 0, 0, 0, -68, 0, 1508, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 1298, 0, -148, 0, 0, 0, 0, 0, -926, 0, 90, 0, 0, 0, 0, 0, 1774, 0, 3326, 0, 0, 0, 0, 0, 1098, 0, -672, 0, 0, 0, 0, 0, 352, 0, 0, 0, 0, 0, 0, 0, -1148, 0, -2332, 0, 0, 0, 0, 0, 0, 0, -1870, 0, 0, 0, 0, 0, 144, 0, -912, 0, 0, 0, 0, 0, 2592, 0, -1042, 0, 0, 0, 0, 0, 3740, 0, -234, 0, 0, 0, 0, 0, -548, 0, 0, 0, 0, 0, 0, 0, -1922, 0, 0, 0, 0, 0, 0, 0, -284, 0, 818, 0, 0, 0, 0, 0, 0, 0, 350, 0, 0, 0, 0, 0, -908, 0, 2250, 0, 0, 0, 0, 0, -244, 0, 1040, 0, 0, 0, 0, 0, 350, 0, 3278, 0, 0, 0, 0, 0, -1586, 0, -2414, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, -590, 0, -666, 0, 0, 0, 0, 0, 0, 0, -2750, 0, 0, 0, 0, 0, -3884, 0, -52, 0, 0, 0, 0, 0, -1952, 0, 1262, 0, 0, 0, 0, 0, -104, 0, -2064, 0, 0, 0, 0, 0, -1586, 0, 432, 0, 0, 0, 0, 0, 754, 0, 0, 0, 0, 0, 0, 0, 244, 0, 116, 0, 0, 0, 0, 0, 0, 0, -1006, 0, 0, 0, 0, 0, 0, 0, 748, 0, 0, 0, 0, 0, -240, 0, 56, 0, 0, 0, 0, 0, 522, 0, 624, 0, 0, 0, 0, 0, -2688, 0, 2564, 0, 0, 0, 0, 0, -1202, 0, 0, 0, 0, 0, 0, 0, 3600, 0, 884, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 770, 0, -3538, 0, 0, 0, 0, 0, 1534, 0, -384, 0, 0, 0, 0, 0, -1268, 0, 850, 0, 0, 0, 0, 0, 3402, 0, -570, 0, 0, 0, 0, 0, 3838, 0, 0, 0, 0, 0, 0, 0, -476, 0, 3428, 0, 0, 0, 0, 0, 0, 0, 2030, 0, 0, 0, 0, 0, 2210, 0, 272, 0, 0, 0, 0, 0, 774, 0, 302, 0, 0, 0, 0, 0, -2882, 0, 4464, 0, 0, 0, 0, 0, 1006, 0, -238, 0, 0, 0, 0, 0, -912, 0, 0, 0, 0, 0, 0, 0, -908, 0, -954, 0, 0, 0, 0, 0, 0, 0, 290, 0, 0, 0, 0, 0, 2320, 0, -1008, 0, 0, 0, 0, 0, -5950, 0, -4148, 0, 0, 0, 0, 0, 1294, 0, -1312, 0, 0, 0, 0, 0, 604, 0, 4292, 0, 0, 0, 0, 0, 918, 0, 0, 0, 0, 0, 0, 0, -238, 0, -100, 0, 0, 0, 0, 0, 0, 0, 2894, 0, 0, 0, 0, 0, 3556, 0, 5006, 0, 0, 0, 0, 0, 1102, 0, -820, 0, 0, 0, 0, 0, -1152, 0, -2866, 0, 0, 0, 0, 0, -2160, 0, -3402, 0, 0, 0, 0, 0, 1630, 0, 0, 0, 0, 0, 0, 0, 802, 0, -1598, 0, 0, 0, 0, 0, 0, 0, 4464, 0, 0, 0, 0, 0, -1386, 0, 620, 0, 0, 0, 0, 0, 884, 0, -4518, 0, 0, 0, 0, 0, 3022, 0, -1392, 0, 0, 0, 0, 0, 2588, 0, -334, 0, 0, 0, 0, 0, -2750, 0, 0, 0, 0, 0, 0, 0, -2106, 0, 1666, 0, 0, 0, 0, 0, 0, 0, -2736, 0, 0, 0, 0, 0, 1570, 0, 234, 0, 0, 0, 0, 0, 94, 0, 5500, 0, 0, 0, 0, 0, -240, 0, -476, 0, 0, 0, 0, 0, 28, 0, -1276, 0, 0, 0, 0, 0, 1822, 0, 0, 0, 0, 0, 0, 0, 578, 0, -240, 0, 0, 0, 0, 0, 0, 0, -3154, 0, 0, 0, 0, 0, -3306, 0, 2558, 0, 0, 0, 0, 0, 1152, 0, 272, 0, 0, 0, 0, 0, 844, 0, -220, 0, 0, 0, 0, 0, 574, 0, -4540, 0, 0, 0, 0, 0, -146, 0, 0, 0, 0, 0, 0, 0, 130, 0, 1892, 0, 0, 0, 0, 0, 0, 0, 4930, 0, 0, 0, 0, 0, -3550, 0, 810, 0, 0, 0, 0, 0, 368, 0, 3134, 0, 0, 0, 0, 0, -2788, 0, -898, 0, 0, 0, 0, 0, 2544, 0, 770, 0, 0, 0, 0, 0, -1674, 0, 0, 0, 0, 0, 0, 0, 3076, 0, -522, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 1186, 0, -2194, 0, 0, 0, 0, 0, -1540, 0, 62, 0, 0, 0, 0, 0, 1962, 0, -1004, 0, 0, 0, 0, 0, 1870, 0, -2448, 0, 0, 0, 0, 0, -4226, 0, 0, 0, 0, 0, 0, 0, -3596, 0, 1424, 0, 0, 0, 0, 0, 0, 0, -4306, 0, 0, 0, 0, 0, -3312, 0, -3394, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 1324, 0, 6042, 0, 0, 0, 0, 0, 1100, 0, 4608, 0, 0, 0, 0, 0, 958, 0, 0, 0, 0, 0, 0, 0, -720, 0, -6076, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -2010, 0, -6800, 0, 0, 0, 0, 0, 1474, 0, 994, 0, 0, 0, 0, 0, -3122, 0, -4690, 0, 0, 0, 0, 0, -5814, 0, 242, 0, 0, 0, 0, 0, 1474, 0, 0, 0, 0, 0, 0, 0, 6004, 0, -3868, 0, 0, 0, 0, 0, 0, 0, -94, 0, 0, 0, 0, 0, 1168, 0, -870, 0, 0, 0, 0, 0, 1008, 0, -5362, 0, 0, 0, 0, 0, -2, 0, -2448, 0, 0, 0, 0, 0, 892, 0, -728, 0, 0, 0, 0, 0, -624, 0, 0, 0, 0, 0, 0, 0, 1780, 0, -430, 0, 0, 0, 0, 0, 0, 0, -5074, 0, 0, 0, 0, 0, 578, 0, -1926, 0, 0, 0, 0, 0, -50, 0, -532, 0, 0, 0, 0, 0, -578, 0, -2386, 0, 0, 0, 0, 0, -774, 0, 3250, 0, 0, 0, 0, 0, -476, 0, 0, 0, 0, 0, 0, 0, -1392, 0, 3078, 0, 0, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, -3306, 0, 236, 0, 0, 0, 0, 0, -1838, 0, 782, 0, 0, 0, 0, 0, 1242, 0, 158, 0, 0, 0, 0, 0, -5762, 0, 1342, 0, 0, 0, 0, 0, 1904, 0, 0, 0, 0, 0, 0, 0, -7532, 0, -1482, 0, 0, 0, 0, 0, 0, 0, 4832, 0, 0, 0, 0, 0, -1728, 0, 3470, 0, 0, 0, 0, 0, 6574, 0, 2538, 0, 0, 0, 0, 0, -6100, 0, 2, 0, 0, 0, 0, 0, -1028, 0, -3148, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 6102, 0, 1870, 0, 0, 0, 0, 0, 0, 0, 1350, 0, 0, 0, 0, 0, 1590, 0, -1008, 0, 0, 0, 0, 0, 3026, 0, 4046, 0, 0, 0, 0, 0, 1084, 0, 398, 0, 0, 0, 0, 0, -2502, 0, 2516, 0, 0, 0, 0, 0, -7250, 0, 0, 0, 0, 0, 0, 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, 8, 4, -1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "56.3.k.a", "char_is_minimal": false, "conrey_index": 687, "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], [1, 0], [0, 0], [-1, 0], [0, 0], [0, -3], [0, 0], [0, 0], [0, 0], [-8, 0], [0, 0], [-17, 0], [0, 0], [0, -8], [0, 0], [0, 3], [0, 0], [-25, 0], [0, 0], [7, 0], [0, 0], [0, 0], [0, 0], [0, -3], [0, 0], [-2, 0], [0, 0], [17, 0], [0, 0], [0, 8], [0, 0], [0, 19], [0, 0], [17, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [0, 8], [0, 0], [26, 0], [0, 0], [-14, 0], [0, 0], [0, 24], [0, 0], [0, 29], [0, 0], [0, 0], [0, 0], [25, 0], [0, 0], [0, -53], [0, 0], [0, 51], [0, 0], [-7, 0], [0, 0], [55, 0], [0, 0], [0, 13], [0, 0], [0, 0], [0, 0], [-72, 0], [0, 0], [-17, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [119, 0], [0, 0], [2, 0], [0, 0], [0, 0], [0, 0], [0, -43], [0, 0], [55, 0], [0, 0], [-110, 0], [0, 0], [0, 75], [0, 0], [0, -8], [0, 0], [71, 0], [0, 0], [0, 0], [0, 0], [0, -19], [0, 0], [0, -21], [0, 0], [-22, 0], [0, 0], [136, 0], [0, 0]]}