# Stored data for newform 22.4.a.c, downloaded from the LMFDB on 25 April 2024. {"label": "22.4.a.c", "space_label": "22.4.a", "level": 22, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007199321849878, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1198126369263750826, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-1, 1]]], "qexp_display": "q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 352, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 1.2980420201262934, "hecke_ring_index": 1, "level_radical": 22, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [22, 1, [13], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 11], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "0.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "1.878", "prec": 17}, {"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "4.643", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [11, -1]], "trace_display": [2, 1, -3, -10], "traces": [0, 1, 2, 1, 4, -3, 2, -10, 8, -26, -6, 11, 4, -16, -20, -3, 16, 42, -52, 116, -12, -10, 22, 189, 8, -116, -32, -53, -40, -120, -6, -163, 32, 11, 84, 30, -104, -409, 232, -16, -24, 468, -20, 110, 44, 78, 378, 144, 16, -243, -232, 42, -64, 90, -106, -33, -80, 116, -240, -453, -12, 20, -326, 260, 64, 48, 22, -97, 168, 189, 60, -465, -208, 848, -818, -116, 464, -110, -32, -742, -48, 649, 936, 438, -40, -126, 220, -120, 88, -273, 156, 160, 756, -163, 288, -348, 32, 761, -486, -286, -464, -1578, 84, 1208, -128, 30, 180, -1446, -212, -1342, -66, -409, -160, 1761, 232, -567, -480, 416, -906, -420, -24, 121, 40, 468, -652, 723, 520, 2132, 128, 110, 96, 1782, 44, -1160, -194, 159, 336, 921, 378, 1442, 120, 144, -930, -176, -416, 360, 1696, -243, -1636, -1806, -232, -1402, 928, -1092, -220, 489, -64, -2947, -1484, 90, -96, -1890, 1298, 332, 1872, -33, 876, 1920, -80, -1941, -252, -3016, 440, 1986, -240, 1160, 176, -453, -546, 111, 312, 899, 320, 20, 1512, 1227, -326, 462, 576, 530, -696, -1509, 64, 20, 1522, 48, -972, 1254, -572, 4688, -928, -97, -3156, 1200, 168, -1404, 2416, -4914, -256, 1276, 60, 4868, 360, -465, -2892, -330, -424, 1630, -2684, 848, -132, -672, -818, -4663, -320, 3016, 3522, -5862, 464, 5051, -1134, -110, -960, -720, 832, -432, -1812, -742, -840, -522, -48, -5632, 242, 2080, 80, 729, 936, -1856, -1304, 438, 1446, -6345, 1040, 2079, 4264, -126, 256, 1494, 220, 4090, 192, 3120, 3564, 1254, 88, -270, -2320, -273, -388, 5442, 318, 2432, 672, 160, 1842, -1276, 756, -1666, 2884, 4238, 240, -3258, 288, -7804, -1860, -348, -352, -4680, -832, -3149, 720, 761, 3392, 12, -486, 1359, -3272, -583, -3612, -3024, -464, -1100, -2804, -1578, 1856, -60, -2184, 5852, -440, 1208, 978, 2652, -128, -7153, -5894, -780, -2968, 6129, 180, -1320, -192, -1446, -3780, 4872, 2596, 1856, 664, -1342, 3744, -1440, -66, -823, 1752, 10634, 3840, 291, -160, 5270, -3882, 1761, -504, -1793, -6032, 5860, 880, -567, 3972, 6576, -480, -6286, 2320, 848, 352, -10701, -906, 1395, -1092, -420, 222, 8328, 624, 6597, 1798, 121, 640, -2544, 40, -3643, 3024, -12168, 2454, -900, -652, -7942, 924, 723, 1152, 1920, 1060, -9331, -1392, 2132, -3018, -7731, 128, 330, 40, -2860, 3044, 1461, 96, 7938, -1944, 1782, 2508, 2226, -1144, -6466, 9376, -1160, -1856, 2010, -194, 2608, -6312, -1947, 2400, -4499, 336, -12622, -2808, 921, 4832, 4530, -9828, -1314, -512, 1442, 2552, 10980, 120, -538, 9736, -3744, 720, -4872, -930, -200, -5784, -176, -660, 5022, -848, -2587, 3260, 360, -5368, 21924, 1696, 704, -264, 6318, -1344, 4203, -1636, 819, -9326, -1806, -640, -933, 6032, 5148, 7044, -1402, -11724, -480, 928, 10316, 10102, -2226, -2268, 132, -220, 7823, -1920, 489, -1440, 723, 1664, 970, -864, -2947, -3624, 1210, -1484, -13456, -1680, -2340, -1044, -7416, -96, 6544, -11264, -1890, 484, -2283, 4160, -7171, 160, 332, 1458, -12264, 1872, -5040, -3712, 858, -2608, 4650, 876, -11860, 2892, 1920, -12690, 15450, 2080, 4734, 4158, -1941, 8528, -17181, -252, -8480, 512, -6148, 2988, -3624, 440, 1584, 8180, 1986, 384, -2763, 6240, -772, 7128, 1160, 2508, -6846, 176, 23554, -540, 11778, -4640, -7488, -546, 4338, -776, 111, 10884, -2673, 636, 19388, 4864, 899, 1344, 4026, 320, 1568, 3684, -520, -2552, -13920, 1512, 7420, -3332, 1227, 5768, -4806, 8476, -1760, 480, 462, -6516, 9972, 576, -5283, -15608, -6490, -3720, -456, -696, 11132, -704, -1509, -9360, -21924, -1664, 11657, -6298, 20, 1440, -4380, 1522, 990, 6784, -1248, 24, -15204, -972, -18908, 2718, 1254, -6544, -4884, -1166, 1260, -7224, 4688, -6048, 22008, -928, 19526, -2200, 2522, -5608, -363, -3156, 4934, 3712, 1200, -120, -2304, -4368, -20608, 11704, -1404, -880, -7038, 2416, 14609, 1956, -10017, 5304, 2730, -256, 12331, -14306, 1276, -11788, -17178, -1560, 15365, -5936, 4868, 12258, -6396, 360, 3888, -2640, 12090, -384, -6753, -2892, 5123, -7560, -330, 9744, 18075, 5192, -4983, 3712, 1630, 1328, 15387, -2684, -5346, 7488, -22048, -2880, 24222, -132, -12967, -1646, -672, 3504, 3480, 21268, -22680, 7680, -4663, 582, 220, -320, 17870, 10540, 6148, -7764, 12978, 3522, -7610, -1008, -5862, -3586, -28488, -12064, -2763, 11720, 5051, 1760, -1440, -1134, 17855, 7944, 2860, 13152, -4326, -960, 19656, -12572, -720, 4640, -31674, 1696, -47444, 704, -432, -21402, 15780, -1812, 371, 2790, 19292, -2184, -30807, -840, 528, 444, -522, 16656, 27069, 1248, -12080, 13194, -5632, 3596, 13920, 242, -20095, 1280, -15443, -5088, 4620, 80, -12220, -7286, 729, 6048, -1067, -24336, -32818, 4908, -1856, -1800, 24396, -1304, 5418, -15884, -11388, 1848, 14460, 1446, -2485, 2304, -6345, 3840, 4206, 2120, -14254, -18662, 2079, -2784, 17232, 4264, 13420, -6036, 3276, -15462, 7248, 256, 25520, 660, 1494, 80, 14994, -5720, 18908, 6088, 4090, 2922, 54288, 192, -5115, 15876, 6360, -3888, 8841, 3564, -35224, 5016, 1254, 4452, -17610, -2288, -320, -12932, -270, 18752, 18609, -2320, 6048, -3712, 7098, 4020, 9328, -388, 5670, 5216, 5442, -12624, 16476, -3894, -2722, 4800, 2432, -8998, -996, 672, 12760, -25244, -4160, -5616, -18402, 1842, -39763, 9664, -1276, 9060, -1248, -19656, -8659, -2628, -1666, -1024, -10206, 2884, -5760, 5104, 8639, 21960, -41271, 240, -9989, -1076, -3258, 19472, 5823, -7488, -1210, 1440, -7804, -9744, -77301, -1860, 2198, -400, 9048, -11568, 27192, -352, 27095, -1320, -4680, 10044, -16008, -1696, -5958, -5174, -3149, 6520, -8162, 720, 1552, -10736, -19786, 43848, -7230, 3392, 22424, 1408, 12, -528, -11427, 12636, 30020, -2688, 1359, 8406, 11958, -3272, -21320, 1638, 7139, -18652, 16704, -3612, -333, -1280, -3024, -1866, 19560, 12064, 3780, 10296, -1100, 14088, -2697, -2804, -13060, -23448, 41028, -960, 10188, 1856, 4818, 20632, -60, 20204, -17820, -4452, -43738, -4536, 5852, 264, 7440, -440, 47444, 15646, -31408, -3840, -16470, 978, -28188, -2880, 2652, 1446, -1386, 3328, 23876, 1940, -7153, -1728, 22218, -5894, 88452, -7248, -1590, 2420, -9909, -2968, -13568, -26912, 6129, -3360, -45858, -4680, 4527, -2088, -1320, -14832, -9210, -192, -3222, 13088, 37596, -22528, -60, -3780, -33352, 968, 4872, -4566, 37665, 8320, -14420, -14342, 1856, 320, -35715, 664, -3003, 2916, 34892, -24528, 5949, 3744, -3762, -10080, -1440, -7424, 20790, 1716, -23560, -5216, -823, 9300, -14064, 1752, 26786, -23720, 21677, 5784], "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": "22.4.a.c", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [2], [1], [4], [-3], [2], [-10], [8], [-26], [-6], [11], [4], [-16], [-20], [-3], [16], [42], [-52], [116], [-12], [-10], [22], [189], [8], [-116], [-32], [-53], [-40], [-120], [-6], [-163], [32], [11], [84], [30], [-104], [-409], [232], [-16], [-24], [468], [-20], [110], [44], [78], [378], [144], [16], [-243], [-232], [42], [-64], [90], [-106], [-33], [-80], [116], [-240], [-453], [-12], [20], [-326], [260], [64], [48], [22], [-97], [168], [189], [60], [-465], [-208], [848], [-818], [-116], [464], [-110], [-32], [-742], [-48], [649], [936], [438], [-40], [-126], [220], [-120], [88], [-273], [156], [160], [756], [-163], [288], [-348], [32], [761], [-486], [-286], [-464]]}