# Stored data for newform 1452.3.e.h, downloaded from the LMFDB on 11 September 2025. {"Nk2": 13068, "analytic_conductor": 39.56413438511511, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 3, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": -1, "char_values": [1452, 2, [727, 485, 1333], [2, 1, 2]], "cm_discs": [], "conrey_index": 485, "dim": 4, "field_disc": 7744, "field_disc_factorization": [[2, 6], [11, 2]], "field_poly": [3, -10, 11, -2, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[5, [1296, 0, 104, 0, 1]], [7, [-88, 0, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525472319833516, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 32, "hecke_ring_index_factorization": [[2, 5]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1452.3.e.h", "level": 1452, "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": false, "level_primes": [2, 3, 11], "level_radical": 66, "minimal_twist": "132.3.e.b", "nf_label": "4.0.7744.1", "prim_orbit_index": 2, "qexp_display": "q+(-1-\\beta _{1})q^{3}+(\\beta _{1}-\\beta _{3})q^{5}+\\beta _{2}q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1452.3.e", "trace_display": [0, -4, 0, 0], "trace_hash": 114650323260656187, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.649", "prec": 17}, {"__RealLiteral__": 0, "data": "0.639", "prec": 17}, {"__RealLiteral__": 0, "data": "65.853", "prec": 20}, {"__RealLiteral__": 0, "data": "37.215", "prec": 20}, {"__RealLiteral__": 0, "data": "1707.141", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 4, 0, -4, 0, 0, 0, 0, 0, -28, 0, 0, 0, -48, 0, 32, 0, 0, 0, 56, 0, 0, 0, 0, 0, -108, 0, 92, 0, 0, 0, 24, 0, 0, 0, 0, 0, 120, 0, 48, 0, 0, 0, 120, 0, -64, 0, 0, 0, 156, 0, 128, 0, 0, 0, 0, 0, -56, 0, 0, 0, 48, 0, 0, 0, 0, 0, 136, 0, -96, 0, 0, 0, 104, 0, 108, 0, 0, 0, 192, 0, 68, 0, 0, 0, 224, 0, -64, 0, 0, 0, 352, 0, -24, 0, 0, 0, -360, 0, 0, 0, 0, 0, 168, 0, -704, 0, 0, 0, -128, 0, -120, 0, 0, 0, -432, 0, 336, 0, 0, 0, 0, 0, 448, 0, 0, 0, 112, 0, -120, 0, 0, 0, 704, 0, -160, 0, 0, 0, -376, 0, -224, 0, 0, 0, 416, 0, -156, 0, 0, 0, -608, 0, -256, 0, 0, 0, 280, 0, 160, 0, 0, 0, 24, 0, 0, 0, 0, 0, 252, 0, -392, 0, 0, 0, 1408, 0, -768, 0, 0, 0, -856, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, -1088, 0, 0, 0, 536, 0, -136, 0, 0, 0, -800, 0, 192, 0, 0, 0, 584, 0, 224, 0, 0, 0, 704, 0, -104, 0, 0, 0, -184, 0, 756, 0, 0, 0, -168, 0, 0, 0, 0, 0, 400, 0, -192, 0, 0, 0, -136, 0, -964, 0, 0, 0, 32, 0, 1472, 0, 0, 0, 0, 0, -224, 0, 0, 0, 704, 0, 128, 0, 0, 0, 1072, 0, -320, 0, 0, 0, -864, 0, -352, 0, 0, 0, -1616, 0, -168, 0, 0, 0, 1128, 0, -960, 0, 0, 0, -60, 0, 360, 0, 0, 0, -288, 0, 0, 0, 0, 0, -704, 0, -1280, 0, 0, 0, -248, 0, -168, 0, 0, 0, 136, 0, 1408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2704, 0, 128, 0, 0, 0, 1016, 0, -840, 0, 0, 0, -344, 0, 960, 0, 0, 0, 0, 0, 432, 0, 0, 0, 2064, 0, -1104, 0, 0, 0, 1712, 0, 1408, 0, 0, 0, 748, 0, 0, 0, 0, 0, 296, 0, -896, 0, 0, 0, 1200, 0, -2880, 0, 0, 0, -360, 0, -112, 0, 0, 0, 0, 0, -840, 0, 0, 0, 1440, 0, -576, 0, 0, 0, 232, 0, -704, 0, 0, 0, 416, 0, 896, 0, 0, 0, -1208, 0, -2432, 0, 0, 0, -1120, 0, 376, 0, 0, 0, 856, 0, 448, 0, 0, 0, 352, 0, 0, 0, 0, 0, 520, 0, -416, 0, 0, 0, -192, 0, -1092, 0, 0, 0, -32, 0, 64, 0, 0, 0, 0, 0, 608, 0, 0, 0, 2280, 0, -640, 0, 0, 0, 2088, 0, -1216, 0, 0, 0, -2816, 0, -280, 0, 0, 0, 1304, 0, -320, 0, 0, 0, -736, 0, -2112, 0, 0, 0, -840, 0, -24, 0, 0, 0, -448, 0, 0, 0, 0, 0, -1032, 0, -1536, 0, 0, 0, 1984, 0, -252, 0, 0, 0, -3520, 0, 1288, 0, 0, 0, 0, 0, -1344, 0, 0, 0, -1640, 0, -1408, 0, 0, 0, 244, 0, 1536, 0, 0, 0, -3168, 0, 0, 0, 0, 0, -1888, 0, 856, 0, 0, 0, 2040, 0, -336, 0, 0, 0, 352, 0, -448, 0, 0, 0, -2144, 0, 0, 0, 0, 0, -2016, 0, 0, 0, 0, 0, -728, 0, -1184, 0, 0, 0, -936, 0, 104, 0, 0, 0, 0, 0, 2176, 0, 0, 0, 1744, 0, -1152, 0, 0, 0, 1408, 0, -536, 0, 0, 0, -2296, 0, -952, 0, 0, 0, 976, 0, 1408, 0, 0, 0, -1040, 0, 800, 0, 0, 0, 1704, 0, 480, 0, 0, 0, 3348, 0, 0, 0, 0, 0, -680, 0, -584, 0, 0, 0, -1872, 0, -448, 0, 0, 0, -1624, 0, 2368, 0, 0, 0, 0, 0, -704, 0, 0, 0, -2592, 0, -728, 0, 0, 0, -1832, 0, -128, 0, 0, 0, 864, 0, 184, 0, 0, 0, 1000, 0, -2484, 0, 0, 0, -1408, 0, 384, 0, 0, 0, 1024, 0, 168, 0, 0, 0, -792, 0, 0, 0, 0, 0, -1088, 0, 960, 0, 0, 0, 3088, 0, -400, 0, 0, 0, 1080, 0, -1344, 0, 0, 0, 0, 0, 128, 0, 0, 0, 2816, 0, 136, 0, 0, 0, 2520, 0, 1316, 0, 0, 0, 4128, 0, 1248, 0, 0, 0, 1192, 0, -32, 0, 0, 0, 1696, 0, -2944, 0, 0, 0, -1800, 0, 2368, 0, 0, 0, 2488, 0, 0, 0, 0, 0, 5280, 0, -1568, 0, 0, 0, 24, 0, 192, 0, 0, 0, 2168, 0, -704, 0, 0, 0, 0, 0, 320, 0, 0, 0, 1336, 0, 2752, 0, 0, 0, -224, 0, -1072, 0, 0, 0, 544, 0, 640, 0, 0, 0, 0, 0, -608, 0, 0, 0, 2936, 0, 864, 0, 0, 0, 272, 0, -2464, 0, 0, 0, -3608, 0, 0, 0, 0, 0, -728, 0, 1616, 0, 0, 0, -576, 0, 552, 0, 0, 0, 2532, 0, -1024, 0, 0, 0, 0, 0, -1128, 0, 0, 0, -2560, 0, 1920, 0, 0, 0, -1128, 0, -1408, 0, 0, 0, 2400, 0, 60, 0, 0, 0, -4448, 0, 2520, 0, 0, 0, -1152, 0, 1408, 0, 0, 0, 872, 0, 288, 0, 0, 0, -3168, 0, 0, 0, 0, 0, 5280, 0, -960, 0, 0, 0, -3104, 0, 704, 0, 0, 0, 1576, 0, 2560, 0, 0, 0, 0, 0, -320, 0, 0, 0, -1520, 0, 248, 0, 0, 0, -424, 0, -1176, 0, 0, 0, 2184, 0, -4384, 0, 0, 0, -648, 0, -136, 0, 0, 0, 288, 0, 3520, 0, 0, 0, -4768, 0, 928, 0, 0, 0, 304, 0, 0, 0, 0, 0, -2292, 0, 0, 0, 0, 0, 1456, 0, 4608, 0, 0, 0, 2816, 0, -2704, 0, 0, 0, 0, 0, 896, 0, 0, 0, 1152, 0, 704, 0, 0, 0, -2280, 0, -1016, 0, 0, 0, -2192, 0, 2760, 0, 0, 0, 5184, 0, 6720, 0, 0, 0, -1400, 0, 344, 0, 0, 0, -2816, 0, -1920, 0, 0, 0, 3048, 0, 0, 0, 0, 0, -1952, 0, 0, 0, 0, 0, 56, 0, 3024, 0, 0, 0, -88, 0, -576, 0, 0, 0, 0, 0, -2064, 0, 0, 0, -4632, 0, -816, 0, 0, 0, -5280, 0, 3840, 0, 0, 0, 3376, 0, -1712, 0, 0, 0, -1744, 0, -2816, 0, 0, 0, -6056, 0, 3392, 0, 0, 0, -144, 0, -748, 0, 0, 0, -2952, 0, 0, 0, 0, 0, 3064, 0, 7872, 0, 0, 0, 3520, 0, -296, 0, 0, 0, -1280, 0, -2240, 0, 0, 0, 0, 0, 4928, 0, 0, 0, -5184, 0, -1200, 0, 0, 0, 680, 0, 5760, 0, 0, 0, -4520, 0, 2176, 0, 0, 0, 9120, 0, 360, 0, 0, 0, 2816, 0, -784, 0, 0, 0, 2128, 0, -4512, 0, 0, 0, 3288, 0, 0, 0, 0, 0, 1376, 0, 2760, 0, 0, 0, -2016, 0, 1888, 0, 0, 0, 2616, 0, -1440, 0, 0, 0, 0, 0, 1152, 0, 0, 0, -8448, 0, 832, 0, 0, 0, 1600, 0, -232, 0, 0, 0, 9728, 0, -4928, 0, 0, 0, -2136, 0, -3264, 0, 0, 0, -4768, 0, -416, 0, 0, 0, -3640, 0, -352, 0, 0, 0, 4176, 0, 0, 0, 0, 0, -4212, 0, 1208, 0, 0, 0, -4816, 0, 4864, 0, 0, 0, -6200, 0, -4224, 0, 0, 0, 0, 0, 1120, 0, 0, 0, -2616, 0, 2632, 0, 0, 0, -5888, 0, 1728, 0, 0, 0, 2912, 0, -856, 0, 0, 0, 0, 0, 1120, 0, 0, 0, -3728, 0, 2176, 0, 0, 0, 3560, 0, -352, 0, 0, 0, -9696, 0, 0, 0, 0, 0, -1432, 0, -3008, 0, 0, 0, -4616, 0, -520, 0, 0, 0, -1384, 0, -2912, 0, 0, 0, 0, 0, -5568, 0, 0, 0, -3104, 0, 192, 0, 0, 0, -808, 0, 3588, 0, 0, 0, 2320, 0, -1728, 0, 0, 0, -688, 0, 32, 0, 0, 0, 800, 0, -128, 0, 0, 0, 3952, 0, -4992, 0, 0, 0, 4224, 0, 0, 0, 0, 0, -5472, 0, 4256, 0, 0, 0, -800, 0, 11264, 0, 0, 0, -468, 0, -2280, 0, 0, 0, 0, 0, 3584, 0, 0, 0, 4912, 0, 3840, 0, 0, 0, -5584, 0, -2088, 0, 0, 0, 2112, 0, 2432, 0, 0, 0, 6032, 0, 1408, 0, 0, 0, 1376, 0, 2816, 0, 0, 0, -6592, 0, -1960, 0, 0, 0, 6816, 0, 0, 0, 0, 0, 5512, 0, -1304, 0, 0, 0, -8160, 0, -800, 0, 0, 0, 11264, 0, -5440, 0, 0, 0, 0, 0, 736, 0, 0, 0, -1984, 0, 4224, 0, 0, 0, -4504, 0, -64, 0, 0, 0, -2184, 0, 840, 0, 0, 0, -9152, 0, -168, 0, 0, 0, -3984, 0, 4608, 0, 0, 0, 2816, 0, 448, 0, 0, 0, -5512, 0, 0, 0, 0, 0, -5272, 0, 7744, 0, 0, 0, 5184, 0, 1032, 0, 0, 0, 3392, 0, 3072, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 1984, 0, -1984, 0, 0, 0, 936, 0, -1764, 0, 0, 0, 112, 0, 3616, 0, 0, 0, -5240, 0, 3520, 0, 0, 0, -2144, 0, 952, 0, 0, 0, -5992, 0, -4288, 0, 0, 0, -1512, 0, 0, 0, 0, 0, 4208, 0, 2688, 0, 0, 0, 4224, 0, -960, 0, 0, 0, 6552, 0, 1640, 0, 0, 0, 0, 0, -9856, 0, 0, 0, 4360, 0, 3584, 0, 0, 0, -12368, 0, -244, 0, 0, 0, 2192, 0, 3840, 0, 0, 0, -80, 0, -6784, 0, 0, 0, -3520, 0, 3168, 0, 0, 0, -1000, 0, 0, 0, 0, 0, 5952, 0, 0, 0, 0, 0, -1752, 0, 1888, 0, 0, 0, -6488, 0, 5992, 0, 0, 0, 6480, 0, -11584, 0, 0, 0, 0, 0, -2040, 0, 0, 0, -5632, 0, 1104, 0, 0, 0, -4512, 0, 1920, 0, 0, 0, 2856, 0, -352, 0, 0, 0, -192, 0, 896, 0, 0, 0, 1232, 0, -3968, 0, 0, 0, -14936, 0, 2144, 0, 0, 0, -252, 0, 0, 0, 0, 0, -1408, 0, 5376, 0, 0, 0, -3200, 0, 2016, 0, 0, 0, -1016, 0, 0, 0, 0, 0, 0, 0, -5888, 0, 0, 0, 576, 0, 728, 0, 0, 0, 3712, 0, 2368, 0, 0, 0, 7416, 0, -5856, 0, 0, 0, -3520, 0, 936, 0, 0, 0, 12192, 0, 728, 0, 0, 0, 5512, 0, 1408, 0, 0, 0, -280, 0, 0, 0, 0, 0, -2984, 0, 5440, 0, 0, 0, 6256, 0, 512, 0, 0, 0, -5952, 0, -1744, 0, 0, 0, 0, 0, 2304, 0, 0, 0, -40, 0, -128, 0, 0, 0, -2120, 0, -1408, 0, 0, 0, -3824, 0, -3752, 0, 0, 0, -5152, 0, 2976, 0, 0, 0, -5720, 0, 2296, 0, 0, 0, 7328, 0, 3128, 0, 0, 0, 4680, 0, 0, 0, 0, 0, 6336, 0, -976, 0, 0, 0, -16888, 0, -2816, 0, 0, 0, 3160, 0, 3392, 0, 0, 0, 0, 0, 1040, 0, 0, 0, -7856, 0, 5600, 0, 0, 0, -2388, 0, 5696, 0, 0, 0, -1408, 0, -1704, 0, 0, 0, -4400, 0, -2688, 0, 0, 0, 6680, 0, -1408, 0, 0, 0, -4616, 0, -3348, 0, 0, 0, -2600, 0, 0, 0, 0, 0, -7808, 0, 6656, 0, 0, 0, 992, 0, 680, 0, 0, 0, -8096, 0, -4088, 0, 0, 0, 0, 0, 7232, 0, 0, 0, 5472, 0, 1872, 0, 0, 0, 11376, 0, -1120, 0, 0, 0, -1728, 0, 2496, 0, 0, 0, 3488, 0, 1624, 0, 0, 0, -352, 0, -4736, 0, 0, 0, -1056, 0, -3424, 0, 0, 0, 10960, 0, 0, 0, 0, 0, -6984, 0, -4928, 0, 0, 0, 7984, 0, 4512, 0, 0, 0, 2016, 0, 2592, 0, 0, 0, 0, 0, 2392, 0, 0, 0, -3776, 0, -11008, 0, 0, 0, -7040, 0, 1832, 0, 0, 0, 4696, 0, 256, 0, 0, 0, 8600, 0, -4224, 0, 0, 0, -7936, 0], "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, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-1, -1, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-7, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-12, 0, 1, 0], [0, 0, 0, 0], [8, -1, -2, 1], [0, 0, 0, 0], [0, 4, 0, 2], [0, 0, 0, 0], [14, 0, 2, 0], [0, 0, 0, 0], [0, 0, -1, -4], [0, 0, 0, 0], [0, -3, 0, -3], [0, 0, 0, 0], [-27, 0, 4, 0], [0, 0, 0, 0], [23, 5, 0, 0], [0, 0, 0, 0], [0, -2, 0, 2], [0, 0, 0, 0], [6, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -22, 0, 4], [0, 0, 0, 0], [30, 0, 2, 0], [0, 0, 0, 0], [12, 12, -1, -4], [0, 0, 0, 0], [0, 14, 0, -2], [0, 0, 0, 0], [30, 0, -2, 0], [0, 0, 0, 0], [-16, -7, 4, 7], [0, 0, 0, 0], [0, -7, 0, 1], [0, 0, 0, 0], [39, 0, 0, 0], [0, 0, 0, 0], [32, -4, 4, -2], [0, 0, 0, 0], [0, 5, 0, 7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-14, -14, -2, -8], [0, 0, 0, 0], [0, -24, 0, -6], [0, 0, 0, 0], [12, 0, 1, 0], [0, 0, 0, 0], [0, 0, -7, 8], [0, 0, 0, 0], [0, -34, 0, 16], [0, 0, 0, 0], [34, 0, -8, 0], [0, 0, 0, 0], [-24, 3, -6, 3], [0, 0, 0, 0], [0, 7, 0, 11], [0, 0, 0, 0], [26, 0, -10, 0], [0, 0, 0, 0], [27, 27, -4, -16], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [48, 0, 1, 0], [0, 0, 0, 0], [17, -28, 0, 0], [0, 0, 0, 0], [0, 46, 0, 2], [0, 0, 0, 0], [56, 0, 4, 0], [0, 0, 0, 0], [-16, 2, 4, -2], [0, 0, 0, 0], [0, -10, 0, -2], [0, 0, 0, 0], [88, 0, -12, 0], [0, 0, 0, 0], [-6, -6, -2, -8], [0, 0, 0, 0], [0, -30, 0, -6], [0, 0, 0, 0], [-90, 0, -4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}