# Stored data for newform 441.4.e.l, downloaded from the LMFDB on 07 May 2024. {"label": "441.4.e.l", "space_label": "441.4.e", "level": 441, "weight": 4, "hecke_orbit": 12, "hecke_orbit_code": 49539870846091705, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 166530711051855974, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [16, -4, 1]], [5, [324, 18, 1]], [13, [-36, 1]]], "qexp_display": "q+4\\zeta_{6}q^{2}+(-8+8\\zeta_{6})q^{4}-18\\zeta_{6}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 7056, "analytic_conductor": 26.019842312531612, "hecke_ring_index": 1, "level_radical": 21, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 3, [344, 199], [3, 1]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [226, 361], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "1.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.066", "prec": 17}, {"__RealLiteral__": 0, "data": "11.675", "prec": 20}, {"__RealLiteral__": 0, "data": "0.415", "prec": 17}, {"__RealLiteral__": 0, "data": "102.605", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [4, 0, -18, 0], "traces": [0, 2, 4, 0, -8, -18, 0, 0, 0, 0, 72, -50, 0, 72, 0, 0, 64, -126, 0, -72, 288, 0, -400, 14, 0, -199, 144, 0, 0, -316, 0, -36, -256, 0, -1008, 0, 0, 162, 288, 0, 0, -540, 0, -648, -400, 0, -56, 72, 0, 0, -1592, 0, -288, -22, 0, 1800, 0, 0, -632, -468, 0, 792, -288, 0, -1024, -648, 0, -232, -1008, 0, 0, 1468, 0, 180, -648, 0, 1152, 0, 0, -236, 1152, 0, -1080, 72, 0, 4536, -1296, 0, 0, -234, 0, 0, -224, 0, -288, -1296, 0, -936, 0, 0, -1592, 666, 0, -252, 0, 0, -176, 670, 0, -162, 3600, 0, 0, 2780, 0, 252, 1264, 0, -3744, 0, 0, -1169, -3168, 0, -288, 2664, 0, 1832, 0, 0, 2592, -2268, 0, 0, -1856, 0, 0, 806, 0, -5256, 0, 0, 2936, -1800, 0, 2844, 1440, 0, -2592, -2390, 0, -3240, 0, 0, 0, 1296, 0, 3024, 944, 0, 9216, 0, 0, 1784, 2160, 0, 144, -6048, 0, -1802, 9072, 0, 2592, -1566, 0, 0, -6400, 0, 936, 3802, 0, 936, 0, 0, 0, 2916, 0, -6300, -1152, 0, -10368, 482, 0, 810, -1872, 0, 0, 4924, 0, -4536, 0, 0, 5328, 0, 0, 4860, 1008, 0, 2304, 7200, 0, 5832, -176, 0, -2680, 5832, 0, 0, -1296, 0, -7200, -4536, 0, 2160, 0, 0, 5560, 1332, 0, 1620, 2016, 0, 0, 6718, 0, 1296, -3744, 0, 0, 7156, 0, -756, 4676, 0, -12672, 0, 0, -2592, 0, 0, 5328, -13032, 0, -1400, 3664, 0, -4096, 6030, 0, 0, 10368, 0, 9072, 590, 0, 792, 0, 0, -1856, 990, 0, -3420, -16128, 0, 6448, -9950, 0, 2734, -10512, 0, 0, -1196, 0, 3600, -5872, 0, -14400, 0, 0, -10963, -11376, 0, 1440, 15804, 0, 16848, 0, 0, 9560, 504, 0, 0, -25920, 0, 4608, 14256, 0, 20448, 0, 0, 2592, -3888, 0, 5112, 24192, 0, 3776, -10102, 0, 7900, 9216, 0, 0, 18144, 0, -7164, -7136, 0, 0, 0, 0, -5508, -288, 0, -12096, 8352, 0, -18468, -3604, 0, -18144, -1800, 0, 0, 0, 0, 6264, -6494, 0, -20160, 0, 0, -12800, 738, 0, -13212, 3744, 0, 30416, 194, 0, 1675, 1872, 0, 0, -6480, 0, -4752, -896, 0, 23328, 0, 0, 2306, 25200, 0, 0, -11376, 0, -14904, -10368, 0, -1928, 1152, 0, 0, 6480, 0, 3744, 1894, 0, -3528, 0, 0, 9848, -4248, 0, 9216, -36288, 0, -25472, -11650, 0, -1296, 5328, 0, 0, -16200, 0, -7524, -19440, 0, 4032, 0, 0, -648, -9216, 0, 14400, -7704, 0, 20804, 11664, 0, 0, -25074, 0, 0, -10720, 0, -23328, -10390, 0, -22464, 0, 0, -1296, 1008, 0, 14616, 0, 0, -36288, 11938, 0, -4212, 4320, 0, 0, -16372, 0, 13500, -11120, 0, 10656, 0, 0, -2106, -6480, 0, 2016, 18972, 0, -25304, -10112, 0, -26872, 3708, 0, 0, 10368, 0, 0, 16200, 0, 28656, 0, 0, 14312, 8064, 0, 5832, -6048, 0, 18704, 8424, 0, 11664, 0, 0, 0, 19628, 0, 19908, 10368, 0, -4608, 0, 0, 15228, -10656, 0, -26064, -22176, 0, -23976, -2800, 0, -7328, 5814, 0, 0, -32768, 0, -24120, -4536, 0, -7200, 0, 0, 0, 11682, 0, -2988, 36288, 0, 4720, -4536, 0, 11971, 1584, 0, 0, -19440, 0, 12060, 0, 0, 7920, 0, 0, -7130, 13680, 0, -32256, 5832, 0, -10976, 6448, 0, 39800, 11376, 0, 0, 21872, 0, 21024, 5746, 0, -23328, 0, 0, -2392, -13068, 0, -25020, 28800, 0, 0, -1130, 0, -16864, -14400, 0, 0, -5572, 0, -2088, 43852, 0, -45504, 0, 0, -1100, 0, 0, 31608, 20520, 0, 5184, 33696, 0, -10368, -3582, 0, 0, 38240, 0, -2016, 7034, 0, 36144, 0, 0, -25920, -21042, 0, 28584, 36864, 0, 114048, 2592, 0, 10910, 40896, 0, 0, 11044, 0, 2412, -5184, 0, -31104, 0, 0, 899, -20448, 0, 24192, -40824, 0, 49352, 0, 0, 40408, -16488, 0, 0, 63200, 0, 0, -27482, 0, 45504, 0, 0, 36288, -14832, 0, -23400, -57312, 0, -28544, 2822, 0, -40824, -17280, 0, 0, 31652, 0, -23832, 22032, 0, 0, 0, 0, -2212, 24192, 0, 16704, -79200, 0, 27540, -36936, 0, 7208, -8334, 0, 0, 0, 0, 7200, -18598, 0, -29016, 0, 0, -20736, -792, 0, 8964, 25056, 0, -51952, 47304, 0, 34020, -40320, 0, 0, -7084, 0, 11664, 25600, 0, 5904, 0, 0, 486, 52848, 0, 0, -1008, 0, 64800, 30416, 0, -776, 26928, 0, 0, 13400, 0, -3744, 31442, 0, -41256, 0, 0, -12960, 40824, 0, -9756, -38016, 0, -7168, -11600, 0, -19064, 23328, 0, 0, 7532, 0, -43020, -9224, 0, 100800, 0, 0, 11664, -4608, 0, -22752, 116640, 0, -68364, -29808, 0, 0, 4734, 0, 0, -7712, 0, -4608, -16848, 0, 60480, 0, 0, 6480, -27702, 0, -7164, 0, 0, 15152, 19440, 0, -36700, -7056, 0, 0, -108864, 0, -22644, -19696, 0, -33984, 0, 0, 28512, -36864, 0, -36288, 60300, 0, -18144, -50944, 0, 46600, 9000, 0, 0, -10368, 0, 0, -11318, 0, 59256, 0, 0, -32400, 32112, 0, 23328, -60192, 0, -77760, 17770, 0, -7868, 0, 0, 0, -71452, 0, 27108, 2592, 0, -36864, 0, 0, 54432, -28800, 0, -15408, 46512, 0, 1150, 41608, 0, -23328, 16218, 0, 0, -2816, 0, 100296, -2268, 0, -70560, 0, 0, 0, 19710, 0, 3888, -93312, 0, -83120, -36634, 0, -28188, -44928, 0, 0, 23600, 0, -8352, 0, 0, 8064, 0, 0, -1226, -58464, 0, 57600, -77076, 0, -74520, -36288, 0, -47752, -26640, 0, 0, -33696, 0, -8640, 5184, 0, -136872, 0, 0, -32744, 5688, 0, -2772, 108000, 0, 0, -8424, 0, 12636, 10656, 0, 0, 67276, 0, -1800, 8424, 0, -25920, 0, 0, -36936, 0, 0, 37944, 52848, 0, -64476, -50608, 0, 40448, 22302, 0, 0, -107488, 0, -14832, -113400, 0, -27648, 0, 0, 10368, -13554, 0, -3780, -59904, 0, 129600, 44878, 0, 6480, 57312, 0, 0, -76724, 0, 8676, -28624, 0, 64512, 0, 0, 28495, -23328, 0, -6048, -29160, 0, 52888, 0, 0, -33696, -17820, 0, 0, 93312, 0, -50688, 34438, 0, 23400, 0, 0, 39256, -26064, 0, -44316, 159264, 0, 41472, -4536, 0, -33696, -9216, 0, 0, 163296, 0, 36072, -60912, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "147.4.a.f", "char_is_minimal": false, "conrey_index": 226, "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, 4], [0, 0], [-8, 8], [0, -18], [0, 0], [0, 0], [0, 0], [0, 0], [72, -72], [-50, 50], [0, 0], [36, 0], [0, 0], [0, 0], [0, 64], [-126, 126], [0, 0], [0, -72], [144, 0], [0, 0], [-200, 0], [0, 14], [0, 0], [-199, 199], [0, 144], [0, 0], [0, 0], [-158, 0], [0, 0], [-36, 36], [-256, 256], [0, 0], [-504, 0], [0, 0], [0, 0], [0, 162], [288, -288], [0, 0], [0, 0], [-270, 0], [0, 0], [-324, 0], [0, -400], [0, 0], [-56, 56], [0, 72], [0, 0], [0, 0], [-796, 0], [0, 0], [-288, 288], [-22, 22], [0, 0], [900, 0], [0, 0], [0, 0], [0, -632], [-468, 468], [0, 0], [0, 792], [-144, 0], [0, 0], [-512, 0], [0, -648], [0, 0], [-232, 232], [0, -1008], [0, 0], [0, 0], [734, 0], [0, 0], [180, -180], [-648, 648], [0, 0], [576, 0], [0, 0], [0, 0], [0, -236], [1152, -1152], [0, 0], [0, -1080], [36, 0], [0, 0], [2268, 0], [0, -1296], [0, 0], [0, 0], [0, -234], [0, 0], [0, 0], [-112, 0], [0, 0], [-288, 288], [-1296, 1296], [0, 0], [-468, 0], [0, 0], [0, 0], [0, -1592]]}