# Stored data for newform 1350.4.c.l, downloaded from the LMFDB on 25 April 2024.
{"label": "1350.4.c.l", "space_label": "1350.4.c", "level": 1350, "weight": 4, "hecke_orbit": 12, "hecke_orbit_code": 49539733407139142, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1836522789309360980, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [484, 0, 1]], [11, [-12, 1]]], "qexp_display": "q+2iq^{2}-4q^{4}+22iq^{7}-8iq^{8}+\\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": "2.016", "prec": 17}, {"__RealLiteral__": 0, "data": "0.131", "prec": 17}, {"__RealLiteral__": 0, "data": "16.422", "prec": 20}, {"__RealLiteral__": 0, "data": "2.526", "prec": 17}, {"__RealLiteral__": 0, "data": "166.739", "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, 24, 0, 0, -88, 0, 32, 0, 0, 314, 0, 0, 0, 0, 0, 0, -152, 0, 0, 132, 0, -50, 0, 0, 420, 0, 0, 0, 0, 0, 0, 1008, 0, 0, -96, 0, -468, 0, 0, -282, 0, 0, 0, 0, 0, 0, 352, 0, 0, -636, 0, 586, 0, 0, -128, 0, 0, 0, 0, 0, 0, 240, 0, 0, 1256, 0, -1256, 0, 0, -1834, 0, 0, 0, 0, 0, 0, -1520, 0, 0, 2544, 0, -1672, 0, 0, 1008, 0, 0, 0, 0, 0, 0, 984, 0, 0, 608, 0, 12, 0, 0, 1814, 0, 0, 0, 0, 0, 0, -528, 0, 0, 4620, 0, -2374, 0, 0, 200, 0, 0, 0, 0, 0, 0, 300, 0, 0, -1288, 0, -1680, 0, 0, -2248, 0, 0, 0, 0, 0, 0, -176, 0, 0, 3216, 0, -4976, 0, 0, -1056, 0, 0, 0, 0, 0, 0, -5148, 0, 0, -4032, 0, 1236, 0, 0, 1506, 0, 0, 0, 0, 0, 0, 384, 0, 0, -8088, 0, -2102, 0, 0, 1872, 0, 0, 0, 0, 0, 0, 5196, 0, 0, 5312, 0, 1128, 0, 0, 9536, 0, 0, 0, 0, 0, 0, -2192, 0, 0, 3768, 0, -2534, 0, 0, -2928, 0, 0, 0, 0, 0, 0, 7980, 0, 0, -1408, 0, -6168, 0, 0, -8662, 0, 0, 0, 0, 0, 0, 2544, 0, 0, 1020, 0, -410, 0, 0, -2344, 0, 0, 0, 0, 0, 0, 9360, 0, 0, -10216, 0, 512, 0, 0, 13816, 0, 0, 0, 0, 0, 0, -13816, 0, 0, -15516, 0, -14690, 0, 0, -6612, 0, 0, 0, 0, 0, 0, -4092, 0, 0, -960, 0, -1824, 0, 0, -12224, 0, 0, 0, 0, 0, 0, -5024, 0, 0, -8892, 0, -16720, 0, 0, 5024, 0, 0, 0, 0, 0, 0, 11508, 0, 0, -11872, 0, 7336, 0, 0, 1584, 0, 0, 0, 0, 0, 0, -12680, 0, 0, 11088, 0, -21080, 0, 0, -1308, 0, 0, 0, 0, 0, 0, -600, 0, 0, 6080, 0, 5220, 0, 0, 13430, 0, 0, 0, 0, 0, 0, -10176, 0, 0, 10956, 0, 35580, 0, 0, 6688, 0, 0, 0, 0, 0, 0, 132, 0, 0, 5040, 0, -4032, 0, 0, 4190, 0, 0, 0, 0, 0, 0, -17480, 0, 0, 4248, 0, 24570, 0, 0, 11772, 0, 0, 0, 0, 0, 0, 19764, 0, 0, -3936, 0, -5808, 0, 0, -11794, 0, 0, 0, 0, 0, 0, -2432, 0, 0, 13704, 0, 646, 0, 0, -48, 0, 0, 0, 0, 0, 0, -20484, 0, 0, 2200, 0, -7256, 0, 0, -8158, 0, 0, 0, 0, 0, 0, 11944, 0, 0, -30156, 0, 12096, 0, 0, -21636, 0, 0, 0, 0, 0, 0, 11268, 0, 0, 2112, 0, 10344, 0, 0, -14168, 0, 0, 0, 0, 0, 0, -18480, 0, 0, 19512, 0, 23864, 0, 0, 9496, 0, 0, 0, 0, 0, 0, 4548, 0, 0, -23864, 0, -800, 0, 0, 3938, 0, 0, 0, 0, 0, 0, -5616, 0, 0, 24840, 0, -1936, 0, 0, 24636, 0, 0, 0, 0, 0, 0, 37632, 0, 0, -1200, 0, -24960, 0, 0, -3044, 0, 0, 0, 0, 0, 0, 5152, 0, 0, -3384, 0, -11780, 0, 0, 6720, 0, 0, 0, 0, 0, 0, 20724, 0, 0, -12016, 0, 8992, 0, 0, -28880, 0, 0, 0, 0, 0, 0, 21952, 0, 0, 29556, 0, 18262, 0, 0, -44352, 0, 0, 0, 0, 0, 0, 13596, 0, 0, 704, 0, 1332, 0, 0, -7850, 0, 0, 0, 0, 0, 0, -12864, 0, 0, 48156, 0, 45130, 0, 0, 19904, 0, 0, 0, 0, 0, 0, 19152, 0, 0, 11672, 0, 4224, 0, 0, -27856, 0, 0, 0, 0, 0, 0, -13472, 0, 0, -65940, 0, 37210, 0, 0, -11484, 0, 0, 0, 0, 0, 0, -29856, 0, 0, 20592, 0, 65940, 0, 0, -7632, 0, 0, 0, 0, 0, 0, 16128, 0, 0, -3012, 0, -4772, 0, 0, -4944, 0, 0, 0, 0, 0, 0, 7032, 0, 0, 20024, 0, -6024, 0, 0, 58432, 0, 0, 0, 0, 0, 0, -17776, 0, 0, 228, 0, -15062, 0, 0, 144, 0, 0, 0, 0, 0, 0, -48612, 0, 0, -1536, 0, 51288, 0, 0, 54908, 0, 0, 0, 0, 0, 0, 32352, 0, 0, -10668, 0, -24112, 0, 0, 8408, 0, 0, 0, 0, 0, 0, 79800, 0, 0, -9784, 0, -7488, 0, 0, 23198, 0, 0, 0, 0, 0, 0, -46784, 0, 0, -32208, 0, 27322, 0, 0, -10032, 0, 0, 0, 0, 0, 0, -41724, 0, 0, -20784, 0, -45252, 0, 0, 44438, 0, 0, 0, 0, 0, 0, -21248, 0, 0, 158256, 0, 2880, 0, 0, -4512, 0, 0, 0, 0, 0, 0, -67848, 0, 0, 25640, 0, -38144, 0, 0, -52920, 0, 0, 0, 0, 0, 0, 3800, 0, 0, -51744, 0, 44104, 0, 0, 15072, 0, 0, 0, 0, 0, 0, -3828, 0, 0, 8768, 0, 27984, 0, 0, 80084, 0, 0, 0, 0, 0, 0, -15072, 0, 0, 35808, 0, -40066, 0, 0, 10136, 0, 0, 0, 0, 0, 0, 73476, 0, 0, -25784, 0, 11712, 0, 0, -66850, 0, 0, 0, 0, 0, 0, 57592, 0, 0, -22008, 0, -24472, 0, 0, -73476, 0, 0, 0, 0, 0, 0, -25452, 0, 0, -31920, 0, 23124, 0, 0, -112376, 0, 0, 0, 0, 0, 0, 5632, 0, 0, -3300, 0, -630, 0, 0, 24672, 0, 0, 0, 0, 0, 0, 252, 0, 0, 17072, 0, 34648, 0, 0, 32288, 0, 0, 0, 0, 0, 0, -18104, 0, 0, -84384, 0, -44274, 0, 0, -3876, 0, 0, 0, 0, 0, 0, -41676, 0, 0, -10176, 0, -18240, 0, 0, -3344, 0, 0, 0, 0, 0, 0, -4080, 0, 0, -72732, 0, -58332, 0, 0, 1640, 0, 0, 0, 0, 0, 0, -46644, 0, 0, 35072, 0, 9376, 0, 0, 30528, 0, 0, 0, 0, 0, 0, 27720, 0, 0, -88920, 0, 12034, 0, 0, -10560, 0, 0, 0, 0, 0, 0, -20064, 0, 0, -37440, 0, -42804, 0, 0, -64198, 0, 0, 0, 0, 0, 0, 40864, 0, 0, -91320, 0, -2066, 0, 0, -2048, 0, 0, 0, 0, 0, 0, -97140, 0, 0, 12096, 0, -55264, 0, 0, -562, 0, 0, 0, 0, 0, 0, 67192, 0, 0, -121212, 0, -39938, 0, 0, -10500, 0, 0, 0, 0, 0, 0, 99252, 0, 0, 55264, 0, -76608, 0, 0, 20012, 0, 0, 0, 0, 0, 0, 62064, 0, 0, 23484, 0, 58968, 0, 0, 58760, 0, 0, 0, 0, 0, 0, -9504, 0, 0, 22064, 0, 26448, 0, 0, -130592, 0, 0, 0, 0, 0, 0, 80696, 0, 0, 73080, 0, 11808, 0, 0, -16584, 0, 0, 0, 0, 0, 0, -99852, 0, 0, 16368, 0, -85776, 0, 0, 53198, 0, 0, 0, 0, 0, 0, 3840, 0, 0, 67620, 0, -139480, 0, 0, 7296, 0, 0, 0, 0, 0, 0, -72348, 0, 0, -9376, 0, 48896, 0, 0, 92002, 0, 0, 0, 0, 0, 0, 144, 0, 0, -14388, 0, 48394, 0, 0, 107316, 0, 0, 0, 0, 0, 0, -133584, 0, 0, 20096, 0, 32724, 0, 0, 66528, 0, 0, 0, 0, 0, 0, 35568, 0, 0, 21768, 0, -102134, 0, 0, 66880, 0, 0, 0, 0, 0, 0, 57420, 0, 0, -58864, 0, -20096, 0, 0, 702, 0, 0, 0, 0, 0, 0, 30208, 0, 0, 22608, 0, -112520, 0, 0, 15924, 0, 0, 0, 0, 0, 0, 9240, 0, 0, -46032, 0, -111936, 0, 0, 117002, 0, 0, 0, 0, 0, 0, 47488, 0, 0, 105492, 0, 100928, 0, 0, -29344, 0, 0, 0, 0, 0, 0, -25200, 0, 0, 21432, 0, -6336, 0, 0, -22600, 0, 0, 0, 0, 0, 0, 24328, 0, 0, 116280, 0, 118120, 0, 0, -19500, 0, 0, 0, 0, 0, 0, 109656, 0, 0, 50720, 0, -20628, 0, 0, 55440, 0, 0, 0, 0, 0, 0, -44352, 0, 0, -142488, 0, -3350, 0, 0, 84320, 0, 0, 0, 0, 0, 0, -60432, 0, 0, -30888, 0, 5232, 0, 0, -41648, 0, 0, 0, 0, 0, 0, -84632, 0, 0, 37680, 0, -192280, 0, 0, -107304, 0, 0, 0, 0, 0, 0, -151536, 0, 0, 2400, 0, 129972, 0, 0, -95886, 0, 0, 0, 0, 0, 0, -24320, 0, 0, 129492, 0, -102572, 0, 0, -20880, 0, 0, 0, 0, 0, 0, -55632, 0, 0, 211680, 0, -53720, 0, 0, -185998, 0, 0, 0, 0, 0, 0, 197192, 0, 0, -106788, 0, -64890, 0, 0, -43296, 0, 0, 0, 0, 0, 0, -18612, 0, 0, 40704, 0, 11700, 0, 0, -91534, 0, 0, 0, 0, 0, 0, -43824, 0, 0, 205632, 0, 3600, 0, 0, -142320, 0, 0, 0, 0, 0, 0, 41256, 0, 0, 104192, 0, -26752, 0, 0, 178682, 0, 0, 0, 0, 0, 0, 132544, 0, 0, -117192, 0, 86080, 0, 0, -15456, 0, 0, 0, 0, 0, 0, 54084, 0, 0, -528, 0, 105696, 0, 0, -15442, 0, 0, 0, 0, 0, 0, -20160, 0, 0, 11028, 0, -287938, 0, 0, 16128, 0, 0, 0, 0, 0, 0, 189672, 0, 0, -91384, 0, -16760, 0, 0, 7050, 0, 0, 0, 0, 0, 0, -79816, 0, 0, -26976, 0, 67342, 0, 0, 48336, 0, 0, 0, 0, 0, 0, -75348, 0, 0, 69920, 0, 70476, 0, 0, 30758, 0, 0, 0, 0, 0, 0, -16992, 0, 0, 42756, 0, 131384, 0, 0, -98280, 0, 0, 0, 0, 0, 0, -56076, 0, 0, 62336, 0, -47088, 0, 0, 168008, 0, 0, 0, 0, 0, 0, -44536, 0, 0, -237996, 0, 238640, 0, 0, 52092, 0, 0, 0, 0, 0, 0, -148356, 0, 0, -79056, 0, -2112, 0, 0, 82094, 0, 0, 0, 0, 0, 0, 15744, 0, 0, 88224, 0, -1934, 0, 0, 23232, 0, 0, 0, 0, 0, 0, 113784, 0, 0, -238640, 0, 47176, 0, 0, 38592, 0, 0, 0, 0, 0, 0, 44272, 0, 0, -278880, 0, -194104, 0, 0, 85620, 0, 0, 0, 0, 0, 0, -59712, 0, 0, 9728, 0, -59220, 0, 0, -15046, 0, 0, 0, 0, 0, 0, -54816, 0, 0, -10296, 0, 370190, 0, 0, -2584, 0, 0, 0, 0, 0, 0, 399408, 0, 0, 104456, 0, 192, 0, 0, 45464, 0, 0, 0, 0, 0, 0, 86320, 0, 0, 249744, 0, -41976, 0, 0, -68604, 0, 0, 0, 0, 0, 0, 153012, 0, 0, 81936, 0, 26412, 0, 0, -262504, 0, 0, 0, 0, 0, 0, -8800, 0, 0, -158256, 0, 172414, 0, 0, 29024, 0, 0, 0, 0, 0, 0, 115080, 0, 0, -173536, 0, 32632, 0, 0, 10418, 0, 0, 0, 0, 0, 0, -11144, 0, 0, 38676, 0, -61776, 0, 0, 17556, 0, 0, 0, 0, 0, 0, -125628, 0, 0, -47776, 0, 158256, 0, 0, -61114, 0, 0, 0, 0, 0, 0, 120624, 0, 0, 270996, 0, 10354, 0, 0, -48384, 0, 0, 0, 0, 0, 0, -134304, 0, 0, -99472, 0, 86544, 0, 0, 153720, 0, 0, 0, 0, 0, 0, 14832, 0, 0, 15900, 0, -83786, 0, 0, -13200, 0, 0, 0, 0, 0, 0, -274560, 0, 0, -45072, 0, -18240, 0, 0, -129786, 0, 0, 0, 0, 0, 0, -8448, 0, 0, 18072, 0, 95062, 0, 0, -41376, 0, 0, 0, 0, 0, 0, -89964, 0, 0, 13088, 0, 56672, 0, 0, 20702, 0, 0, 0, 0, 0, 0, -235872, 0, 0, -181200, 0, -14650, 0, 0, -53412, 0, 0, 0, 0, 0, 0, -129936, 0, 0, 73920, 0, 52392, 0, 0, 72306, 0, 0, 0, 0, 0, 0, -78048, 0, 0, 154488, 0, 323820, 0, 0, -95456, 0, 0, 0, 0, 0, 0, -156108, 0, 0, 79304, 0, -37984, 0, 0, -132176, 0, 0, 0, 0, 0, 0, 98912, 0, 0, -274008, 0, -7586, 0, 0, 189384, 0, 0, 0, 0, 0, 0, -1884, 0, 0, -18192, 0, -132132, 0, 0, -97056, 0, 0, 0, 0, 0, 0, 95456, 0, 0, -80976, 0, 241472, 0, 0, 3200, 0, 0, 0, 0, 0, 0, -25224, 0, 0, -136864, 0, -15752, 0, 0, -63040, 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.c", "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, 22], [0, -8], [0, 0], [0, 0], [12, 0], [0, 0], [0, 38], [-44, 0], [0, 0], [16, 0], [0, -105], [0, 0], [157, 0], [0, 0], [0, 0], [0, 24], [0, 117], [0, 0], [0, 0], [-76, 0], [0, 0], [0, -88], [66, 0], [0, 0], [-25, 0], [0, 32], [0, 0], [210, 0], [0, 0], [0, 0], [0, -314], [0, 314], [0, 0], [0, 0], [504, 0], [0, 0], [0, 380], [-48, 0], [0, 0], [-234, 0], [0, -252], [0, 0], [-141, 0], [0, 0], [0, 0], [0, -152], [0, -3], [0, 0], [0, 0], [176, 0], [0, 0], [0, 132], [-318, 0], [0, 0], [293, 0], [0, -50], [0, 0], [-64, 0], [0, 0], [0, 0], [0, 322], [0, 420], [0, 0], [0, 0], [120, 0], [0, 0], [0, 44], [628, 0], [0, 0], [-628, 0], [0, 264], [0, 0], [-917, 0], [0, 0], [0, 0], [0, 1008], [0, -309], [0, 0], [0, 0], [-760, 0], [0, 0], [0, -96], [1272, 0], [0, 0], [-836, 0], [0, -468], [0, 0], [504, 0], [0, 0], [0, 0], [0, -1328], [0, -282], [0, 0], [0, 0]]}