# Stored data for newform 57.3.k.b, downloaded from the LMFDB on 08 June 2024.
{"Nk2": 513, "analytic_conductor": 1.5531375068536923, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 19, "char_degree": 6, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 11, "char_orbit_label": "k", "char_order": 18, "char_parity": -1, "char_values": [57, 18, [20, 40], [18, 17]], "cm_discs": [], "conrey_index": 10, "dim": 24, "has_non_self_twist": 1, "hecke_cutters": [[2, [419904, -1889568, 55357344, 263485872, 430160220, 343344366, 201168309, 139199679, 114261867, 71496894, 26812194, 4744599, -876998, -750729, -216951, -116982, -29940, -1659, 1670, 789, 273, 126, 42, 9, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504286872469561, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 6, -1, 18, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "57.3.k.b", "level": 57, "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": true, "level_primes": [3, 19], "level_radical": 57, "minimal_twist": "57.3.k.b", "prim_orbit_index": 6, "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "2.2.3.c18", "self_twist_discs": [], "self_twist_type": 0, "space_label": "57.3.k", "trace_display": [-9, 0, 0, -9], "traces": [24, -9, 0, -3, 0, 9, -9, 27, 0, -6, 15, -108, -33, 33, -18, -3, -30, 0, -15, 186, 18, -84, -21, 72, 30, 48, 108, 90, -90, 0, -288, -417, 9, 75, 54, 9, 0, -24, 18, 237, -6, -99, -141, 93, -9, 549, 615, 0, -81, 135, -9, -339, -54, -27, -51, 0, 99, 168, 18, 171, -129, -873, -99, 345, -189, -108, 111, -603, -396, -312, -144, -54, 408, 105, 0, 318, 108, 207, 6, -1278, 0, -795, 477, 837, 651, 633, 81, -504, -123, -99, -132, 1203, 198, 0, -72, -126, 309, 339, -45, -1335, 30, -171, 495, 1365, -135, -828, 72, 0, -93, 1332, -189, 1026, 0, -180, -6, -369, -99, -615, -948, -1044, 327, 315, -27, 1185, -228, -108, 138, -510, 189, -81, -1344, 0, -339, 324, 27, -1017, -654, 378, -672, -216, 45, -267, 195, 360, -1089, -1194, -54, 483, 585, 1449, 0, 591, 126, 885, 294, 135, 123, -177, -72, 1584, 1212, 81, 543, -432, -108, 1968, 102, -1872, -441, 0, -90, -588, 273, -1179, 2346, 150, 27, -645, -198, 270, -333, -600, -333, -987, -417, 9, -1593, -1569, 0, 420, 576, -81, -1041, -2088, -108, -1293, 153, 675, 1017, 1746, 810, -432, -39, 1692, -1425, 2196, -153, 0, -348, 414, -330, 2823, 1512, 504, 1971, 81, -666, -2760, -666, 756, -549, 153, 162, -138, -90, 2736, 0, 81, 738, -1413, 72, 1890, 1815, -945, 234, -2403, -45, -1161, -231, -729, 420, -1851, 0, -2163, -2874, 0, -354, -714, 369, -483, 513, -135, 2061, -2055, 540, -1695, -1242, 0, -288, 999, 216, 765, 690, 1827, 0, 2124, -324, -870, 1860, -135, -915, 4530, 108, -1962, -141, -1692, 990, 3600, 270, -885, -3387, -1350, -1851, 0, -1683, 162, 1314, -1251, 2298, 2277, -1044, -69, -1935, -513, -1527, -1113, 135, 3192, -2067, -909, 825, -402, 0, -1380, -516, -99, 81, -2391, 495, -1365, 1293, -675, -168, 900, 837, 5346, 396, 837, -831, 3090, 954, 0, 1191, -648, 1326, 3813, 1773, 3453, 3192, -9, -306, -4677, 207, 480, 3312, 2322, 363, 3054, -1116, 1755, 0, -36, -2706, -3285, -621, -933, -1125, 738, -654, -6525, 27, -3918, 72, 459, 831, -2217, -54, -2304, -2061, 0, -3255, -474, 216, 159, -843, 162, 1431, 303, 270, -4965, -1320, 351, -1062, 1191, 963, -801, 1044, 0, 0, 525, -1872, -4044, -2595, 2250, 3789, -243, 153, 738, 1170, -342, 1467, 6165, -1989, 3456, -2160, -279, 1356, 0, -918, -2166, 465, -558, 2724, 1659, -81, -540, 1584, -1917, 2487, -897, -387, 3045, 1278, 72, -1566, -3936, 0, 2349, -492, 441, -2205, 594, 99, -1485, 159, 954, -1836, 1944, 279, 1098, 1200, -27, -1182, 1995, -279, 0, -1806, 3456, 1305, 15, 108, -81, 1473, -576, -2115, -504, -1107, 2148, -801, 2457, -792, 1770, 567, 2286, 0, 1962, 1878, -4923, -27, -3900, 1074, -2115, 1248, -5670, -504, 396, 465, 108, -1191, 2748, 513, -1779, -2541, 0, 2967, -858, -135, -279, 405, 1620, 171, -2010, 819, -123, -1044, 0, 1404, 222, -756, 4389, -1917, 1656, 0, -4635, -2880, 3537, -3435, -1332, 1137, -1227, 0, 639, 1293, 3105, 1863, 252, 162, 2838, -573, -3492, -2343, 0, -324, 4380, 3243, -2700, 345, 171, -117, -3561, 225, -819, -2922, -567, -1053, -384, -933, -1620, -81, 5010, 0, -1380, 5892, 792, 786, 2478, -396, -2964, 864, 837, -198, 1890, 1080, -9945, -2418, -1755, -3102, 132, -288, 0, 2808, -522, -4665, 3429, 3699, 705, 4362, 9, 5058, 5961, 2304, -2481, -1179, -2997, -810, 5922, 297, 1389, 0, 2709, -4278, 969, 2943, -5367, -6315, -252, 918, -2790, -927, 1554, -474, -819, -2700, 2487, 126, 468, -219, 0, -4698, -6156, -36, 5004, -2229, -432, 1047, 2667, -90, 1695, 1428, -3249, -621, -4749, 171, 1581, 2862, -1215, 0, 819, 1926, 3879, -3456, -2628, 852, -4803, -297, 4149, 2613, -3240, -1155, -4896, -216, -10107, -1956, 3591, -1101, 0, 90, 4878, 162, -936, 2250, -10770, 855, 81, 8496, 2673, 1752, 447, -513, -1515, 1878, -576, 1653, 1188, 0, 7110, 2250, 405, 4431, 3390, 675, -1983, 2985, -297, 5154, -3123, 918, 1233, 804, -297, 594, 1224, 1134, 0, -285, 630, 2595, -564, -1026, -3264, -2853, -270, -1413, 5937, 27, -2982, -576, 3528, 2094, -4647, 2394, 84, 0, -1962, -4710, 4329, 2601, 1839, -1350, 2952, -1152, 10611, -63, 2646, -2331, -333, -5280, 198, -657, 1224, -2367, 0, 3519, 1902, 891, -2385, 756, -3888, 2529, 612, -189, 7692, 81, -3330, -6516, -1257, -2556, -5634, -7512, -3942, 0, -3435, -5508, -4857, -234, -1863, -7365, -5196, 324, 5355, 84, 2691, -63, -10188, -5517, 1200, -720, 2385, 4875, 0, -2448, 6126, -951, 2736, -5379, -396, -756, 1197, -1710, 1701, -1302, -1239, -666, -1857, -6615, 675, 2700, 6378, 0, -4179, 7230, 720, 564, 1473, 396, -900, -951, 324, 2514, 1035, -1206, 4572, 1227, 2034, 1806, -3471, -1485, 0, 5856, 8190, 1233, 915, -324, -8919, -5424, 2871, 4149, 147, 450, -1296, 540, 3582, -3948, 4857, 2565, -7698, 0, 5841, 444, 6480, -369, -7818, 996, 1764, 3582, 2979, 3852, 2487, 396, 0, 3924, 1635, 3627, 6348, 6171, 0, -2751, -8166, 360, -966, -8850, -3582, -3645, -4794, -2772, 3543, -1803, 1206, -639, -9099, 1494, 14373, -1140, -612, 0, 1578, -1728, 6498, -3024, -6471, 6918, -1863, 621, -2772, -348, 1926, -2001, -7659, -2754, 4302, -2811, -828, -6369, 0, -207, -7656, -1236, -3726, 3762, 8517, 117, 1806, 6471, -702, 7836, 5919, 1503, -8940, 6867, -153, 1233, 14499, 0, -1095, -462, -3231, 2979, 7353, -2439, -738, 4128, -999, -2286, 5766, 2196, -5058, 4887, -4851, 4176, 975, -27, 0, -183, 1764, -6012, -8511, 315, -4179, -6381, 1350, -9927, -8691, 648, -4464, -270, -4401, -522, -156, -90, -4254, 0, -1710, 5322, -984, 4824, -6753, 3630, 324, -3645, 12852, -909, -3996, -1713, 5328, 102, 1866, 2673, 4287, -135, 0, 5280, 2496, -4113, -8769, -1998, 846, 3414, -2628, -2052, 600, -2061, -3888, 3420, 7740, 81, -11208, -11922, -7965, 0, -9231, 2106, 1122, -6276, -2349, -4392, -9606, -1197, 1935, 1065, -4113, 2226, 765, 1692, -132, 2199, 3438, 6603, 0, -3375, 10170, 6201, 0, -4869, 6486, -1161, 7977, 2142, 5958, 4647, 6627, 918, 3627, -1500, 1323, 9369, -1383, 0, 2268, 3660, 459, -567, 3405, 1737, 13443, -1179, -6372, -930, 2193, -54, 14805], "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}