# Stored data for newform 1152.3.e.d, downloaded from the LMFDB on 19 April 2024.
{"label": "1152.3.e.d", "space_label": "1152.3.e", "level": 1152, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511073810351232, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 452758585622257002, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [100, 0, 28, 0, 1]], [7, [-92, 4, 1]], [13, [-152, -16, 1]]], "qexp_display": "q+(-\\beta _{1}+\\beta _{2})q^{5}+(-2+2\\beta _{3})q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 10368, "analytic_conductor": 31.389726454306203, "hecke_ring_index": 16, "level_radical": 6, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [1152, 2, [127, 901, 641], [2, 2, 1]], "hecke_ring_generator_nbound": 41, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [1025], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.772", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "75.126", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2072.743", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, -8], "traces": [0, 4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 204, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, 488, 0, 0, 0, 0, 0, 296, 0, 0, 0, 0, 0, -640, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 260, 0, 0, 0, 0, 0, 536, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, -464, 0, 0, 0, 0, 0, 312, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 496, 0, 0, 0, 0, 0, 444, 0, 0, 0, 0, 0, 296, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, -592, 0, 0, 0, 0, 0, 232, 0, 0, 0, 0, 0, -248, 0, 0, 0, 0, 0, -648, 0, 0, 0, 0, 0, 592, 0, 0, 0, 0, 0, -624, 0, 0, 0, 0, 0, 408, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, -464, 0, 0, 0, 0, 0, -560, 0, 0, 0, 0, 0, -832, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 592, 0, 0, 0, 0, 0, -456, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, -580, 0, 0, 0, 0, 0, -1312, 0, 0, 0, 0, 0, -1248, 0, 0, 0, 0, 0, 816, 0, 0, 0, 0, 0, -680, 0, 0, 0, 0, 0, -624, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 496, 0, 0, 0, 0, 0, -656, 0, 0, 0, 0, 0, -1552, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, -804, 0, 0, 0, 0, 0, -616, 0, 0, 0, 0, 0, -1688, 0, 0, 0, 0, 0, 704, 0, 0, 0, 0, 0, -992, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -2040, 0, 0, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 1136, 0, 0, 0, 0, 0, -744, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 1208, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, -2200, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, -856, 0, 0, 0, 0, 0, -1992, 0, 0, 0, 0, 0, -1472, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, -1312, 0, 0, 0, 0, 0, 928, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 1316, 0, 0, 0, 0, 0, 2752, 0, 0, 0, 0, 0, 1696, 0, 0, 0, 0, 0, -592, 0, 0, 0, 0, 0, -2128, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, -872, 0, 0, 0, 0, 0, 1120, 0, 0, 0, 0, 0, 632, 0, 0, 0, 0, 0, 912, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, -1936, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, -1352, 0, 0, 0, 0, 0, 520, 0, 0, 0, 0, 0, -1216, 0, 0, 0, 0, 0, -532, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 3936, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 2624, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 904, 0, 0, 0, 0, 0, 4672, 0, 0, 0, 0, 0, -568, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 3048, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 3872, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 1840, 0, 0, 0, 0, 0, 1896, 0, 0, 0, 0, 0, 1632, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 1272, 0, 0, 0, 0, 0, -2120, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 3032, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, -4448, 0, 0, 0, 0, 0, -704, 0, 0, 0, 0, 0, 2384, 0, 0, 0, 0, 0, 2080, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 3928, 0, 0, 0, 0, 0, 5440, 0, 0, 0, 0, 0, -2720, 0, 0, 0, 0, 0, 940, 0, 0, 0, 0, 0, 1016, 0, 0, 0, 0, 0, -1192, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 1512, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, -2776, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 2384, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 1656, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 312, 0, 0, 0, 0, 0, 1736, 0, 0, 0, 0, 0, -3168, 0, 0, 0, 0, 0, 664, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, 3328, 0, 0, 0, 0, 0, -2272, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0, 2696, 0, 0, 0, 0, 0, -3296, 0, 0, 0, 0, 0, -2416, 0, 0, 0, 0, 0, -1336, 0, 0, 0, 0, 0, 1400, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 7072, 0, 0, 0, 0, 0, -1024, 0, 0, 0, 0, 0, -1392, 0, 0, 0, 0, 0, 2808, 0, 0, 0, 0, 0, 5632, 0, 0, 0, 0, 0, -736, 0, 0, 0, 0, 0, -952, 0, 0, 0, 0, 0, -1664, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, -1648, 0, 0, 0, 0, 0, -680, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, -3120, 0, 0, 0, 0, 0, -800, 0, 0, 0, 0, 0, 392, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, -5808, 0, 0, 0, 0, 0, 4384, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 3424, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 1968, 0, 0, 0, 0, 0, -6368, 0, 0, 0, 0, 0, 1872, 0, 0, 0, 0, 0, -4256, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -2328, 0, 0, 0, 0, 0, 7712, 0, 0, 0, 0, 0, -5504, 0, 0, 0, 0, 0, -10104, 0, 0, 0, 0, 0, 2856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3208, 0, 0, 0, 0, 0, -3024, 0, 0, 0, 0, 0, -2528, 0, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 708, 0, 0, 0, 0, 0, 1144, 0, 0, 0, 0, 0, -1760, 0, 0, 0, 0, 0, 1744, 0, 0, 0, 0, 0, -1328, 0, 0, 0, 0, 0, -816, 0, 0, 0, 0, 0, -6208, 0, 0, 0, 0, 0, 7232, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 2792, 0, 0, 0, 0, 0, 3528, 0, 0, 0, 0, 0, 4016, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, -8008, 0, 0, 0, 0, 0, 3872, 0, 0, 0, 0, 0, 2976, 0, 0, 0, 0, 0, -4904, 0, 0, 0, 0, 0, -4344, 0, 0, 0, 0, 0, -2784, 0, 0, 0, 0, 0, -2560, 0, 0, 0, 0, 0, -2008, 0, 0, 0, 0, 0, -9680, 0, 0, 0, 0, 0, -1600, 0, 0, 0, 0, 0, 2448, 0, 0, 0, 0, 0, -2004, 0, 0, 0, 0, 0, 3264, 0, 0, 0, 0, 0, -4384, 0, 0, 0, 0, 0, -2944, 0, 0, 0, 0, 0, -7568, 0, 0, 0, 0, 0, 5016, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 3408, 0, 0, 0, 0, 0, 672, 0, 0, 0, 0, 0, -1848, 0, 0, 0, 0, 0, -1672, 0, 0, 0, 0, 0, 7248, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, -5896, 0, 0, 0, 0, 0, -4384, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, 1208, 0, 0, 0, 0, 0, -632, 0, 0, 0, 0, 0, -5408, 0, 0, 0, 0, 0, -1520, 0, 0, 0, 0, 0, 6368, 0, 0, 0, 0, 0, -3520, 0, 0, 0, 0, 0, -5056, 0, 0, 0, 0, 0, 1136, 0, 0, 0, 0, 0, -7928, 0, 0, 0, 0, 0, 7656, 0, 0, 0, 0, 0, 3736, 0, 0, 0, 0, 0, -3152, 0, 0, 0, 0, 0, 1032, 0, 0, 0, 0, 0, -856, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 2912, 0, 0, 0, 0, 0, -6576, 0, 0, 0, 0, 0, 7432, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, -2128, 0, 0, 0, 0, 0, -2520, 0, 0, 0, 0, 0, -6240, 0, 0, 0, 0, 0, -2688, 0, 0, 0, 0, 0, 6592, 0, 0, 0, 0, 0, 9472, 0, 0, 0, 0, 0, -3712, 0, 0, 0, 0, 0, 1088, 0, 0, 0, 0, 0, -5568, 0, 0, 0, 0, 0, -4320, 0, 0, 0, 0, 0, -2544, 0, 0, 0, 0, 0, 4384, 0, 0, 0, 0, 0, -896, 0, 0, 0, 0, 0, 4152, 0, 0, 0, 0, 0, -2360, 0, 0, 0, 0, 0, 2144, 0, 0, 0, 0, 0, -1616, 0, 0, 0, 0, 0, -1604, 0, 0, 0, 0, 0, 4576, 0, 0, 0, 0, 0, 3608, 0, 0, 0, 0, 0, 2064, 0, 0, 0, 0, 0, 4128, 0, 0, 0, 0, 0, 7584, 0, 0, 0, 0, 0, -3480, 0, 0, 0, 0, 0, 8480, 0, 0, 0, 0, 0, 9344, 0, 0, 0, 0, 0, 3120, 0, 0, 0, 0, 0, 968, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, -2816, 0, 0, 0, 0, 0, -1928, 0, 0, 0, 0, 0, -1320, 0, 0, 0, 0, 0, -4160, 0, 0, 0, 0, 0, -1056, 0, 0, 0, 0, 0, -6824, 0, 0, 0, 0, 0, 3336, 0, 0, 0, 0, 0, -8848, 0, 0, 0, 0, 0, -1416, 0, 0, 0, 0, 0, 2624, 0, 0, 0, 0, 0, 1416, 0, 0, 0, 0, 0, -16192, 0, 0, 0, 0, 0, 2224, 0, 0, 0, 0, 0, 5560, 0, 0, 0, 0, 0, 5440, 0, 0, 0, 0, 0, 3712, 0, 0, 0, 0, 0, 3932, 0, 0, 0, 0, 0, 7056, 0, 0, 0, 0, 0, 8392, 0, 0, 0, 0, 0, -544, 0, 0, 0, 0, 0, 3664, 0, 0, 0, 0, 0, 6104, 0, 0, 0, 0, 0, 3648, 0, 0, 0, 0, 0, 4464, 0, 0, 0, 0, 0, -4592, 0, 0, 0, 0, 0, -3024, 0, 0, 0, 0, 0, 6240, 0, 0, 0, 0, 0, -5760, 0, 0, 0, 0, 0, 3752, 0, 0, 0, 0, 0, -5520, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, -9792, 0, 0, 0, 0, 0, 6488, 0, 0, 0, 0, 0, 5048, 0, 0, 0, 0, 0, 1600, 0, 0, 0, 0, 0, 1792, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 4216, 0, 0, 0, 0, 0, -6336, 0, 0, 0, 0, 0, -1504, 0, 0, 0, 0, 0, 872, 0, 0, 0, 0, 0, 11016, 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, 3, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "1152.3.e.b", "char_is_minimal": true, "conrey_index": 1025, "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 1, 0], [0, 0, 0, 0], [-2, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, -2, 0], [0, 0, 0, 0], [8, 0, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, -6, 0], [0, 0, 0, 0], [-8, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -10, 0, 0], [0, 0, 0, 0], [11, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, -7, 0], [0, 0, 0, 0], [30, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 26, -6, 0], [0, 0, 0, 0], [22, 0, 0, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -21, 10, 0], [0, 0, 0, 0], [-36, 0, 0, -8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -10, 8, 0], [0, 0, 0, 0], [51, 0, 0, -8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -27, 5, 0], [0, 0, 0, 0], [28, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -20, 24, 0], [0, 0, 0, 0], [50, 0, 0, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -44, 14, 0], [0, 0, 0, 0], [-28, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -54, -12, 0], [0, 0, 0, 0], [68, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -52, 12, 0], [0, 0, 0, 0], [122, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 78, 14, 0], [0, 0, 0, 0], [74, 0, 0, -7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -17, -28, 0], [0, 0, 0, 0], [-160, 0, 0, 22], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 32, -12, 0], [0, 0, 0, 0], [40, 0, 0, 26], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}