# Stored data for newform 1350.4.c.d, downloaded from the LMFDB on 24 April 2024.
{"label": "1350.4.c.d", "space_label": "1350.4.c", "level": 1350, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510936388175174, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 652997523628958774, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [16, 0, 1]], [11, [42, 1]]], "qexp_display": "q+2iq^{2}-4q^{4}+4iq^{7}-8iq^{8}-42q^{11}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 21600, "analytic_conductor": 79.65257850774982, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [1350, 2, [1001, 1027], [2, 1]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [649], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.078", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "17.112", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "171.900", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, -8, 0, 0, 0, 0, 0, 0, -84, 0, 0, -16, 0, 32, 0, 0, -118, 0, 0, 0, 0, 0, 0, -80, 0, 0, 240, 0, 94, 0, 0, -372, 0, 0, 0, 0, 0, 0, -252, 0, 0, 336, 0, 36, 0, 0, 654, 0, 0, 0, 0, 0, 0, 64, 0, 0, -888, 0, 442, 0, 0, -128, 0, 0, 0, 0, 0, 0, -1380, 0, 0, -1048, 0, 472, 0, 0, -1330, 0, 0, 0, 0, 0, 0, 712, 0, 0, -2172, 0, -160, 0, 0, -576, 0, 0, 0, 0, 0, 0, 264, 0, 0, 320, 0, 2964, 0, 0, 3470, 0, 0, 0, 0, 0, 0, -960, 0, 0, -744, 0, 866, 0, 0, -376, 0, 0, 0, 0, 0, 0, 228, 0, 0, -2152, 0, 1488, 0, 0, -4552, 0, 0, 0, 0, 0, 0, 4504, 0, 0, -2796, 0, 5248, 0, 0, 672, 0, 0, 0, 0, 0, 0, 72, 0, 0, 1008, 0, 300, 0, 0, 3594, 0, 0, 0, 0, 0, 0, -1344, 0, 0, -5280, 0, 2146, 0, 0, -144, 0, 0, 0, 0, 0, 0, -2940, 0, 0, 6176, 0, -2616, 0, 0, -1336, 0, 0, 0, 0, 0, 0, 3568, 0, 0, 4956, 0, 9202, 0, 0, 4560, 0, 0, 0, 0, 0, 0, -3720, 0, 0, -256, 0, -5736, 0, 0, -4054, 0, 0, 0, 0, 0, 0, 3552, 0, 0, 12828, 0, 6862, 0, 0, -1768, 0, 0, 0, 0, 0, 0, -14616, 0, 0, 2744, 0, 512, 0, 0, -2096, 0, 0, 0, 0, 0, 0, 944, 0, 0, 1980, 0, 16990, 0, 0, -636, 0, 0, 0, 0, 0, 0, -11040, 0, 0, 5520, 0, 3360, 0, 0, -7472, 0, 0, 0, 0, 0, 0, 4192, 0, 0, 360, 0, 1424, 0, 0, -1888, 0, 0, 0, 0, 0, 0, 16224, 0, 0, -1576, 0, 5320, 0, 0, -10080, 0, 0, 0, 0, 0, 0, 13384, 0, 0, -1152, 0, -16400, 0, 0, 5964, 0, 0, 0, 0, 0, 0, -3948, 0, 0, -2848, 0, 9612, 0, 0, 13502, 0, 0, 0, 0, 0, 0, 8688, 0, 0, -17556, 0, -6756, 0, 0, 640, 0, 0, 0, 0, 0, 0, 5928, 0, 0, 15624, 0, 2304, 0, 0, -58, 0, 0, 0, 0, 0, 0, 18880, 0, 0, 15876, 0, 1674, 0, 0, 3060, 0, 0, 0, 0, 0, 0, 9108, 0, 0, -1056, 0, -1920, 0, 0, -2002, 0, 0, 0, 0, 0, 0, -1280, 0, 0, 3588, 0, -32258, 0, 0, -11856, 0, 0, 0, 0, 0, 0, -26712, 0, 0, -752, 0, -13880, 0, 0, 22298, 0, 0, 0, 0, 0, 0, 8632, 0, 0, -36096, 0, 10584, 0, 0, -12492, 0, 0, 0, 0, 0, 0, -20484, 0, 0, 3840, 0, -1752, 0, 0, -4304, 0, 0, 0, 0, 0, 0, 2976, 0, 0, -30492, 0, -10480, 0, 0, -3464, 0, 0, 0, 0, 0, 0, -33612, 0, 0, 4720, 0, 1504, 0, 0, 10850, 0, 0, 0, 0, 0, 0, -1512, 0, 0, 29448, 0, 9008, 0, 0, 14916, 0, 0, 0, 0, 0, 0, 4116, 0, 0, -912, 0, -7824, 0, 0, 24172, 0, 0, 0, 0, 0, 0, 8608, 0, 0, -27468, 0, -10340, 0, 0, -5952, 0, 0, 0, 0, 0, 0, -14160, 0, 0, -5464, 0, 18208, 0, 0, 7120, 0, 0, 0, 0, 0, 0, -21752, 0, 0, 30744, 0, -29978, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 600, 0, 0, -18016, 0, -33012, 0, 0, -5546, 0, 0, 0, 0, 0, 0, 11184, 0, 0, 36456, 0, -23486, 0, 0, -20992, 0, 0, 0, 0, 0, 0, -5760, 0, 0, 37160, 0, -2688, 0, 0, -42616, 0, 0, 0, 0, 0, 0, 31600, 0, 0, -48732, 0, -38030, 0, 0, 17676, 0, 0, 0, 0, 0, 0, -8832, 0, 0, -288, 0, 21948, 0, 0, 37296, 0, 0, 0, 0, 0, 0, -4032, 0, 0, -56256, 0, -16724, 0, 0, -1200, 0, 0, 0, 0, 0, 0, -18564, 0, 0, -38224, 0, -14376, 0, 0, 12352, 0, 0, 0, 0, 0, 0, -10720, 0, 0, 29640, 0, -45950, 0, 0, 40464, 0, 0, 0, 0, 0, 0, -12900, 0, 0, 5376, 0, -16248, 0, 0, -69076, 0, 0, 0, 0, 0, 0, 21120, 0, 0, -54228, 0, 7136, 0, 0, -8584, 0, 0, 0, 0, 0, 0, 33108, 0, 0, 3824, 0, 576, 0, 0, -10498, 0, 0, 0, 0, 0, 0, -9200, 0, 0, 9120, 0, 55330, 0, 0, -9600, 0, 0, 0, 0, 0, 0, 21168, 0, 0, 11760, 0, -32508, 0, 0, 37238, 0, 0, 0, 0, 0, 0, -24704, 0, 0, 14868, 0, 57960, 0, 0, 10464, 0, 0, 0, 0, 0, 0, -11472, 0, 0, 1088, 0, 5344, 0, 0, -26784, 0, 0, 0, 0, 0, 0, -3760, 0, 0, 10284, 0, -36968, 0, 0, 44016, 0, 0, 0, 0, 0, 0, 50028, 0, 0, -14272, 0, 7104, 0, 0, -73204, 0, 0, 0, 0, 0, 0, -19824, 0, 0, -22152, 0, -19978, 0, 0, -36808, 0, 0, 0, 0, 0, 0, 4716, 0, 0, -3536, 0, -18240, 0, 0, 830, 0, 0, 0, 0, 0, 0, 46000, 0, 0, 55860, 0, -21520, 0, 0, -2124, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 14880, 0, -15396, 0, 0, 5488, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 11280, 0, 137826, 0, 0, 22944, 0, 0, 0, 0, 0, 0, 71136, 0, 0, -17056, 0, 16216, 0, 0, 47408, 0, 0, 0, 0, 0, 0, -13208, 0, 0, 81180, 0, -38586, 0, 0, -7692, 0, 0, 0, 0, 0, 0, 59844, 0, 0, -14208, 0, -29904, 0, 0, 45040, 0, 0, 0, 0, 0, 0, -51312, 0, 0, -1272, 0, -55164, 0, 0, -27448, 0, 0, 0, 0, 0, 0, -49884, 0, 0, -32824, 0, 7072, 0, 0, 91224, 0, 0, 0, 0, 0, 0, -44640, 0, 0, -3204, 0, 44074, 0, 0, 11040, 0, 0, 0, 0, 0, 0, 6720, 0, 0, 58464, 0, 78660, 0, 0, -5518, 0, 0, 0, 0, 0, 0, -10976, 0, 0, 56712, 0, 77854, 0, 0, -2048, 0, 0, 0, 0, 0, 0, 3768, 0, 0, 24192, 0, 8384, 0, 0, 23990, 0, 0, 0, 0, 0, 0, -47648, 0, 0, 123336, 0, -13010, 0, 0, -17484, 0, 0, 0, 0, 0, 0, -11808, 0, 0, -3776, 0, 10080, 0, 0, -12244, 0, 0, 0, 0, 0, 0, -7920, 0, 0, 3000, 0, 2592, 0, 0, -67960, 0, 0, 0, 0, 0, 0, -3528, 0, 0, -16744, 0, 2544, 0, 0, -3152, 0, 0, 0, 0, 0, 0, 10640, 0, 0, 136008, 0, -11088, 0, 0, 52104, 0, 0, 0, 0, 0, 0, 52392, 0, 0, 44160, 0, 42672, 0, 0, -102106, 0, 0, 0, 0, 0, 0, -22080, 0, 0, -100068, 0, 26768, 0, 0, -13440, 0, 0, 0, 0, 0, 0, 16752, 0, 0, -4264, 0, 29888, 0, 0, -26078, 0, 0, 0, 0, 0, 0, -124488, 0, 0, 11928, 0, 147898, 0, 0, -2484, 0, 0, 0, 0, 0, 0, 24528, 0, 0, -16768, 0, 80748, 0, 0, -30240, 0, 0, 0, 0, 0, 0, -1440, 0, 0, -145740, 0, 7954, 0, 0, -5696, 0, 0, 0, 0, 0, 0, 19224, 0, 0, -97672, 0, 7552, 0, 0, -13338, 0, 0, 0, 0, 0, 0, -10688, 0, 0, 8748, 0, -96176, 0, 0, -34404, 0, 0, 0, 0, 0, 0, 209436, 0, 0, -64896, 0, 17376, 0, 0, 80570, 0, 0, 0, 0, 0, 0, 6304, 0, 0, 9984, 0, 61760, 0, 0, -21280, 0, 0, 0, 0, 0, 0, -11844, 0, 0, -26160, 0, 40320, 0, 0, -66880, 0, 0, 0, 0, 0, 0, -30320, 0, 0, -70200, 0, 103144, 0, 0, -59604, 0, 0, 0, 0, 0, 0, 4932, 0, 0, -53536, 0, -51660, 0, 0, 31248, 0, 0, 0, 0, 0, 0, 4608, 0, 0, -165384, 0, -110126, 0, 0, 65600, 0, 0, 0, 0, 0, 0, 75432, 0, 0, 4320, 0, -23856, 0, 0, 35680, 0, 0, 0, 0, 0, 0, -118832, 0, 0, 81420, 0, 37760, 0, 0, 27048, 0, 0, 0, 0, 0, 0, -92496, 0, 0, 15792, 0, 76620, 0, 0, -35982, 0, 0, 0, 0, 0, 0, 11392, 0, 0, 6120, 0, 95716, 0, 0, -38448, 0, 0, 0, 0, 0, 0, 45600, 0, 0, 46872, 0, -54008, 0, 0, 22658, 0, 0, 0, 0, 0, 0, 61832, 0, 0, -95232, 0, 13950, 0, 0, -2112, 0, 0, 0, 0, 0, 0, 78480, 0, 0, -34752, 0, 1692, 0, 0, -174982, 0, 0, 0, 0, 0, 0, 70224, 0, 0, 143460, 0, -9576, 0, 0, 27024, 0, 0, 0, 0, 0, 0, -63864, 0, 0, 944, 0, -2560, 0, 0, 33314, 0, 0, 0, 0, 0, 0, -108512, 0, 0, -57360, 0, -18176, 0, 0, 90384, 0, 0, 0, 0, 0, 0, 99588, 0, 0, -23712, 0, -55584, 0, 0, 161750, 0, 0, 0, 0, 0, 0, -62496, 0, 0, -176388, 0, 78470, 0, 0, -9216, 0, 0, 0, 0, 0, 0, -170508, 0, 0, -32488, 0, 232, 0, 0, 30738, 0, 0, 0, 0, 0, 0, -27760, 0, 0, 191184, 0, 26950, 0, 0, 35520, 0, 0, 0, 0, 0, 0, 9684, 0, 0, -75520, 0, -89004, 0, 0, -23026, 0, 0, 0, 0, 0, 0, -63504, 0, 0, -99948, 0, 17264, 0, 0, -6696, 0, 0, 0, 0, 0, 0, -115368, 0, 0, 99416, 0, -12240, 0, 0, -151384, 0, 0, 0, 0, 0, 0, -17680, 0, 0, -24984, 0, 93272, 0, 0, 14724, 0, 0, 0, 0, 0, 0, 91764, 0, 0, -36432, 0, -189168, 0, 0, 50342, 0, 0, 0, 0, 0, 0, 4224, 0, 0, -59232, 0, -47222, 0, 0, 7680, 0, 0, 0, 0, 0, 0, -3504, 0, 0, -42008, 0, 8008, 0, 0, 117432, 0, 0, 0, 0, 0, 0, 128584, 0, 0, 287184, 0, 27440, 0, 0, -43908, 0, 0, 0, 0, 0, 0, -220416, 0, 0, 5120, 0, -121644, 0, 0, -166174, 0, 0, 0, 0, 0, 0, -14352, 0, 0, -20268, 0, -106090, 0, 0, 129032, 0, 0, 0, 0, 0, 0, 128148, 0, 0, -6928, 0, 47424, 0, 0, -15016, 0, 0, 0, 0, 0, 0, -147392, 0, 0, 205392, 0, -106560, 0, 0, -107844, 0, 0, 0, 0, 0, 0, -56220, 0, 0, 106848, 0, 182004, 0, 0, 9440, 0, 0, 0, 0, 0, 0, 3008, 0, 0, -75456, 0, -141722, 0, 0, 55520, 0, 0, 0, 0, 0, 0, 165912, 0, 0, 140168, 0, -89192, 0, 0, -242302, 0, 0, 0, 0, 0, 0, 80656, 0, 0, 53040, 0, -3024, 0, 0, 80268, 0, 0, 0, 0, 0, 0, -6360, 0, 0, -34528, 0, 33984, 0, 0, 183038, 0, 0, 0, 0, 0, 0, 144384, 0, 0, 29832, 0, -141566, 0, 0, -42336, 0, 0, 0, 0, 0, 0, 24276, 0, 0, -106096, 0, 49968, 0, 0, 212040, 0, 0, 0, 0, 0, 0, -12600, 0, 0, -41736, 0, -123530, 0, 0, -1824, 0, 0, 0, 0, 0, 0, -15648, 0, 0, 81936, 0, 55200, 0, 0, 95646, 0, 0, 0, 0, 0, 0, -15360, 0, 0, -150948, 0, -228722, 0, 0, 7008, 0, 0, 0, 0, 0, 0, -100800, 0, 0, -51856, 0, 17216, 0, 0, -16378, 0, 0, 0, 0, 0, 0, -4536, 0, 0, 211632, 0, 20774, 0, 0, 20964, 0, 0, 0, 0, 0, 0, 10896, 0, 0, -11904, 0, -104856, 0, 0, -1350, 0, 0, 0, 0, 0, 0, 121968, 0, 0, -15576, 0, -266724, 0, 0, 41920, 0, 0, 0, 0, 0, 0, -255036, 0, 0, 73112, 0, 13856, 0, 0, -10928, 0, 0, 0, 0, 0, 0, 36416, 0, 0, -143760, 0, -45602, 0, 0, -44904, 0, 0, 0, 0, 0, 0, 388284, 0, 0, 134448, 0, 92292, 0, 0, 221760, 0, 0, 0, 0, 0, 0, -18880, 0, 0, -153696, 0, -43504, 0, 0, -6016, 0, 0, 0, 0, 0, 0, -90132, 0, 0, 76328, 0, -43400, 0, 0, -174784, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "270.4.a.e", "char_is_minimal": false, "conrey_index": 649, "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, 2], [0, 0], [-4, 0], [0, 0], [0, 0], [0, 4], [0, -8], [0, 0], [0, 0], [-42, 0], [0, 0], [0, 20], [-8, 0], [0, 0], [16, 0], [0, 93], [0, 0], [-59, 0], [0, 0], [0, 0], [0, -84], [0, -9], [0, 0], [0, 0], [-40, 0], [0, 0], [0, -16], [120, 0], [0, 0], [47, 0], [0, 32], [0, 0], [-186, 0], [0, 0], [0, 0], [0, 262], [0, -118], [0, 0], [0, 0], [-126, 0], [0, 0], [0, -178], [168, 0], [0, 0], [18, 0], [0, 144], [0, 0], [327, 0], [0, 0], [0, 0], [0, -80], [0, -741], [0, 0], [0, 0], [32, 0], [0, 0], [0, 240], [-444, 0], [0, 0], [221, 0], [0, 94], [0, 0], [-64, 0], [0, 0], [0, 0], [0, 538], [0, -372], [0, 0], [0, 0], [-690, 0], [0, 0], [0, -1126], [-524, 0], [0, 0], [236, 0], [0, -168], [0, 0], [-665, 0], [0, 0], [0, 0], [0, -252], [0, -75], [0, 0], [0, 0], [356, 0], [0, 0], [0, 336], [-1086, 0], [0, 0], [-80, 0], [0, 36], [0, 0], [-288, 0], [0, 0], [0, 0], [0, -1544], [0, 654], [0, 0], [0, 0]]}