# Stored data for newform 1792.3.g.f, downloaded from the LMFDB on 25 April 2024. {"label": "1792.3.g.f", "space_label": "1792.3.g", "level": 1792, "weight": 3, "hecke_orbit": 6, "hecke_orbit_code": 22518410504046336, "dim": 8, "is_polredabs": true, "nf_label": "8.0.1997017344.2", "trace_hash": 2026896838035354968, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [32, 48, -20, -4, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{3}+(\\beta _{5}-\\beta _{6})q^{5}-\\beta _{5}q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "g", "char_is_real": true, "Nk2": 16128, "analytic_conductor": 48.8284633733652, "hecke_ring_index": 4096, "level_radical": 14, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [1792, 2, [1023, 1541, 1025], [1, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [127], "field_disc": 1997017344, "field_disc_factorization": [[2, 8], [3, 2], [7, 4], [19, 2]], "field_poly": [4, 0, 56, 0, 53, 0, 14, 0, 1], "hecke_ring_index_factorization": [[2, 12]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "6.956", "prec": 17}, {"__RealLiteral__": 0, "data": "1.793", "prec": 17}, {"__RealLiteral__": 0, "data": "280.228", "prec": 24}, {"__RealLiteral__": 0, "data": "253.695", "prec": 24}, {"__RealLiteral__": 0, "data": "17025.190", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 8, 0, 0], "traces": [0, 8, 0, 8, 0, 0, 0, 0, 0, 40, 0, 32, 0, 0, 0, 0, 0, -16, 0, 88, 0, 0, 0, 0, 0, -104, 0, 176, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -144, 0, -224, 0, 0, 0, 0, 0, -56, 0, 16, 0, 0, 0, 0, 0, 400, 0, 232, 0, 0, 0, 0, 0, -304, 0, -368, 0, 0, 0, 0, 0, -272, 0, -664, 0, 0, 0, 0, 0, 504, 0, -424, 0, 0, 0, 0, 0, 80, 0, 56, 0, 0, 0, 0, 0, 528, 0, 544, 0, 0, 0, 0, 0, 336, 0, -176, 0, 0, 0, 0, 0, -160, 0, -288, 0, 0, 0, 0, 0, 376, 0, 1072, 0, 0, 0, 0, 0, -320, 0, 1016, 0, 0, 0, 0, 0, -464, 0, 312, 0, 0, 0, 0, 0, -608, 0, -56, 0, 0, 0, 0, 0, -1360, 0, -1120, 0, 0, 0, 0, 0, -112, 0, -224, 0, 0, 0, 0, 0, 920, 0, 1064, 0, 0, 0, 0, 0, -144, 0, -848, 0, 0, 0, 0, 0, -352, 0, -1728, 0, 0, 0, 0, 0, 256, 0, -928, 0, 0, 0, 0, 0, 224, 0, 112, 0, 0, 0, 0, 0, 256, 0, 1296, 0, 0, 0, 0, 0, 224, 0, -208, 0, 0, 0, 0, 0, 152, 0, -1000, 0, 0, 0, 0, 0, 752, 0, 2080, 0, 0, 0, 0, 0, 144, 0, 2712, 0, 0, 0, 0, 0, -48, 0, -232, 0, 0, 0, 0, 0, 400, 0, -336, 0, 0, 0, 0, 0, -960, 0, -1104, 0, 0, 0, 0, 0, 336, 0, -1312, 0, 0, 0, 0, 0, -528, 0, 392, 0, 0, 0, 0, 0, 728, 0, -880, 0, 0, 0, 0, 0, -128, 0, -352, 0, 0, 0, 0, 0, -1808, 0, 888, 0, 0, 0, 0, 0, 1840, 0, 840, 0, 0, 0, 0, 0, -2144, 0, -80, 0, 0, 0, 0, 0, 0, 0, 1696, 0, 0, 0, 0, 0, 640, 0, 464, 0, 0, 0, 0, 0, 1024, 0, -672, 0, 0, 0, 0, 0, 496, 0, 2752, 0, 0, 0, 0, 0, -984, 0, -2120, 0, 0, 0, 0, 0, 3056, 0, -224, 0, 0, 0, 0, 0, -288, 0, 448, 0, 0, 0, 0, 0, 1120, 0, -3552, 0, 0, 0, 0, 0, 272, 0, 256, 0, 0, 0, 0, 0, 1952, 0, -928, 0, 0, 0, 0, 0, -1072, 0, -272, 0, 0, 0, 0, 0, -3120, 0, 3240, 0, 0, 0, 0, 0, -688, 0, 1064, 0, 0, 0, 0, 0, -4496, 0, -1568, 0, 0, 0, 0, 0, -280, 0, 1616, 0, 0, 0, 0, 0, 2320, 0, 704, 0, 0, 0, 0, 0, -320, 0, -2208, 0, 0, 0, 0, 0, -1920, 0, -1480, 0, 0, 0, 0, 0, 960, 0, -2824, 0, 0, 0, 0, 0, -1056, 0, -896, 0, 0, 0, 0, 0, -384, 0, 592, 0, 0, 0, 0, 0, 224, 0, -3024, 0, 0, 0, 0, 0, -560, 0, 232, 0, 0, 0, 0, 0, 4000, 0, 1504, 0, 0, 0, 0, 0, 2768, 0, -1592, 0, 0, 0, 0, 0, -376, 0, 1304, 0, 0, 0, 0, 0, -1504, 0, -224, 0, 0, 0, 0, 0, -4448, 0, 1088, 0, 0, 0, 0, 0, -448, 0, -2272, 0, 0, 0, 0, 0, 2944, 0, 104, 0, 0, 0, 0, 0, 1568, 0, 2624, 0, 0, 0, 0, 0, 560, 0, -2992, 0, 0, 0, 0, 0, -1872, 0, -1128, 0, 0, 0, 0, 0, 1168, 0, -1008, 0, 0, 0, 0, 0, -1264, 0, 3376, 0, 0, 0, 0, 0, 672, 0, 1760, 0, 0, 0, 0, 0, -448, 0, 200, 0, 0, 0, 0, 0, 4280, 0, 2496, 0, 0, 0, 0, 0, 1504, 0, 4448, 0, 0, 0, 0, 0, -2016, 0, 552, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, -5712, 0, -576, 0, 0, 0, 0, 0, 1456, 0, -416, 0, 0, 0, 0, 0, 656, 0, 3312, 0, 0, 0, 0, 0, 1296, 0, -1360, 0, 0, 0, 0, 0, -768, 0, 1464, 0, 0, 0, 0, 0, -2336, 0, 880, 0, 0, 0, 0, 0, 5504, 0, 2296, 0, 0, 0, 0, 0, -4608, 0, -576, 0, 0, 0, 0, 0, 1568, 0, 3856, 0, 0, 0, 0, 0, 6808, 0, 832, 0, 0, 0, 0, 0, 1344, 0, 800, 0, 0, 0, 0, 0, -3520, 0, 4904, 0, 0, 0, 0, 0, -2736, 0, -1568, 0, 0, 0, 0, 0, -976, 0, 560, 0, 0, 0, 0, 0, -5488, 0, -4976, 0, 0, 0, 0, 0, 2912, 0, 2064, 0, 0, 0, 0, 0, 3664, 0, -1736, 0, 0, 0, 0, 0, -1040, 0, -3552, 0, 0, 0, 0, 0, -4656, 0, -5312, 0, 0, 0, 0, 0, -1344, 0, 1064, 0, 0, 0, 0, 0, -2752, 0, 1736, 0, 0, 0, 0, 0, -8064, 0, -4656, 0, 0, 0, 0, 0, 112, 0, 864, 0, 0, 0, 0, 0, 4712, 0, -6032, 0, 0, 0, 0, 0, -1552, 0, 5280, 0, 0, 0, 0, 0, -4784, 0, -3048, 0, 0, 0, 0, 0, 3984, 0, -6120, 0, 0, 0, 0, 0, 1168, 0, -2800, 0, 0, 0, 0, 0, 48, 0, -2800, 0, 0, 0, 0, 0, 112, 0, -4768, 0, 0, 0, 0, 0, 3328, 0, -2720, 0, 0, 0, 0, 0, 9840, 0, 2352, 0, 0, 0, 0, 0, -640, 0, -7584, 0, 0, 0, 0, 0, -5488, 0, 2240, 0, 0, 0, 0, 0, 2032, 0, -616, 0, 0, 0, 0, 0, -2960, 0, 5424, 0, 0, 0, 0, 0, 1120, 0, 4224, 0, 0, 0, 0, 0, 2608, 0, -5184, 0, 0, 0, 0, 0, -440, 0, 112, 0, 0, 0, 0, 0, -4384, 0, 5288, 0, 0, 0, 0, 0, 16, 0, -2624, 0, 0, 0, 0, 0, 10112, 0, -3584, 0, 0, 0, 0, 0, 2880, 0, 544, 0, 0, 0, 0, 0, 1568, 0, -3888, 0, 0, 0, 0, 0, -1984, 0, 7248, 0, 0, 0, 0, 0, 6720, 0, -6256, 0, 0, 0, 0, 0, -3952, 0, 2176, 0, 0, 0, 0, 0, -4304, 0, 11040, 0, 0, 0, 0, 0, 2496, 0, 2912, 0, 0, 0, 0, 0, -7664, 0, 976, 0, 0, 0, 0, 0, 560, 0, 10768, 0, 0, 0, 0, 0, 4736, 0, 8128, 0, 0, 0, 0, 0, 1056, 0, -6944, 0, 0, 0, 0, 0, -512, 0, 5880, 0, 0, 0, 0, 0, -6696, 0, -3928, 0, 0, 0, 0, 0, -2256, 0, 56, 0, 0, 0, 0, 0, -928, 0, 6944, 0, 0, 0, 0, 0, 3584, 0, -3200, 0, 0, 0, 0, 0, 1424, 0, -552, 0, 0, 0, 0, 0, -1872, 0, -1376, 0, 0, 0, 0, 0, 3328, 0, -6112, 0, 0, 0, 0, 0, -1232, 0, 7328, 0, 0, 0, 0, 0, -3216, 0, 2240, 0, 0, 0, 0, 0, -18176, 0, -16, 0, 0, 0, 0, 0, 448, 0, 1680, 0, 0, 0, 0, 0, 5312, 0, 904, 0, 0, 0, 0, 0, 768, 0, 5776, 0, 0, 0, 0, 0, -3376, 0, -6432, 0, 0, 0, 0, 0, 320, 0, -3120, 0, 0, 0, 0, 0, 512, 0, -2856, 0, 0, 0, 0, 0, -5328, 0, 5152, 0, 0, 0, 0, 0, 728, 0, -5968, 0, 0, 0, 0, 0, 752, 0, -5216, 0, 0, 0, 0, 0, 9248, 0, 2304, 0, 0, 0, 0, 0, 6000, 0, -5304, 0, 0, 0, 0, 0, 5424, 0, -2552, 0, 0, 0, 0, 0, 1408, 0, -280, 0, 0, 0, 0, 0, -2272, 0, 5840, 0, 0, 0, 0, 0, 1904, 0, 1280, 0, 0, 0, 0, 0, 1632, 0, -7432, 0, 0, 0, 0, 0, 7328, 0, -2672, 0, 0, 0, 0, 0, 864, 0, 7112, 0, 0, 0, 0, 0, -1072, 0, -2240, 0, 0, 0, 0, 0, 12656, 0, -1232, 0, 0, 0, 0, 0, -5280, 0, -3392, 0, 0, 0, 0, 0, 3808, 0, 2208, 0, 0, 0, 0, 0, 2192, 0, 2704, 0, 0, 0, 0, 0, 7040, 0, -7232, 0, 0, 0, 0, 0, -7024, 0, 4960, 0, 0, 0, 0, 0, -11672, 0, 4144, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, -3584, 0, -2800, 0, 0, 0, 0, 0, 1120, 0, 8032, 0, 0, 0, 0, 0, -5680, 0, 1312, 0, 0, 0, 0, 0, 5968, 0, -6480, 0, 0, 0, 0, 0, -5280, 0, 3712, 0, 0, 0, 0, 0, -7664, 0, 1240, 0, 0, 0, 0, 0, -4656, 0, 3248, 0, 0, 0, 0, 0, -2944, 0, -8096, 0, 0, 0, 0, 0, -1680, 0, -160, 0, 0, 0, 0, 0, 4288, 0, -2456, 0, 0, 0, 0, 0, -1648, 0, 800, 0, 0, 0, 0, 0, -6688, 0, -3128, 0, 0, 0, 0, 0, 816, 0, -4952, 0, 0, 0, 0, 0, 176, 0, -3136, 0, 0, 0, 0, 0, -4640, 0, -1904, 0, 0, 0, 0, 0, 1120, 0, -6464, 0, 0, 0, 0, 0, 5472, 0, -10336, 0, 0, 0, 0, 0, 3224, 0, 11552, 0, 0, 0, 0, 0, 2304, 0, -6264, 0, 0, 0, 0, 0, -2400, 0, 16920, 0, 0, 0, 0, 0, -1280, 0, -2352, 0, 0, 0, 0, 0, -6160, 0, -1728, 0, 0, 0, 0, 0, -3360, 0, 10160, 0, 0, 0, 0, 0, 3504, 0, -4360, 0, 0, 0, 0, 0, -3536, 0, 3456, 0, 0, 0, 0, 0, -768, 0, -1144, 0, 0, 0, 0, 0, 1376, 0, -8064, 0, 0, 0, 0, 0, 4656, 0, -4088, 0, 0, 0, 0, 0, 912, 0, 2064, 0, 0, 0, 0, 0, 0, 0, -12816, 0, 0, 0, 0, 0, 1504, 0, 5528, 0, 0, 0, 0, 0, 4992, 0, -4640, 0, 0, 0, 0, 0, 9280, 0, 3744, 0, 0, 0, 0, 0, -8416, 0, 5152, 0, 0, 0, 0, 0, 1168, 0, 2240, 0, 0, 0, 0, 0, -20384, 0, 9216, 0, 0, 0, 0, 0, 1680, 0, 7696, 0, 0, 0, 0, 0, 6360, 0, 1600, 0, 0, 0, 0, 0, 3952, 0, -2672, 0, 0, 0, 0, 0, 9552, 0, 9608, 0, 0, 0, 0, 0, -10368, 0, -1232, 0, 0, 0, 0, 0, 15616, 0, -392, 0, 0, 0, 0, 0, 2448, 0, 400, 0, 0, 0, 0, 0, 1456, 0, -368, 0, 0, 0, 0, 0, 1056, 0, 11424, 0, 0, 0, 0, 0, -240, 0, 1632, 0, 0, 0, 0, 0, 976, 0, -8128, 0, 0, 0, 0, 0, 1680, 0, 2496, 0, 0, 0, 0, 0, -5536, 0, 4928, 0, 0, 0, 0, 0, -13872, 0, -10864, 0, 0, 0, 0, 0, -2016, 0, 4288, 0, 0, 0, 0, 0, 5184, 0, 3360, 0, 0, 0, 0, 0, 2912, 0, -336, 0, 0, 0, 0, 0, 5952, 0, 2776, 0, 0, 0, 0, 0, 7168, 0, -10592, 0, 0, 0, 0, 0, -1840, 0, -560, 0, 0, 0, 0, 0, 8192, 0, -2432, 0, 0, 0, 0, 0, 2016, 0, 1584, 0, 0, 0, 0, 0, 6008, 0, -19792, 0, 0, 0, 0, 0, 11504, 0, 5856, 0, 0, 0, 0, 0, 7744, 0, -9368, 0, 0, 0, 0, 0, -432, 0, 1256, 0, 0, 0, 0, 0, 3968, 0, -1064, 0, 0, 0, 0, 0, -5264, 0, -8096, 0, 0, 0, 0, 0, -1120, 0, 16304, 0, 0, 0, 0, 0, 10624, 0, -11816, 0, 0, 0, 0, 0, -12544, 0, 12960, 0, 0, 0, 0, 0, -8896, 0, 1744, 0, 0, 0, 0, 0, -2064, 0, -4120, 0, 0, 0, 0, 0, -4480, 0, -3584, 0, 0, 0, 0, 0, -224, 0, -4800, 0, 0, 0, 0, 0, -672, 0, -11840, 0, 0, 0, 0, 0, -18400, 0, -864, 0, 0, 0, 0, 0, 1600, 0, -15072, 0, 0, 0, 0, 0, -6976, 0, -5992, 0, 0, 0, 0, 0, 272, 0, -1656, 0, 0, 0, 0, 0, 2064, 0, 6720, 0, 0, 0, 0, 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, 8, 4, -1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "224.3.d.b", "char_is_minimal": false, "conrey_index": 127, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, -2, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, 6, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 3, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [11, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, -1, -2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-13, 6, -4, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [22, -6, -6, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 3, 4, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, -3, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, -11, -6, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, -3, 6, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-18, -12, -3, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-28, 0, 5, 0, 0, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, -16, 15, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, -5, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 14, -2, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 3, -4, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 24, 20, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [50, -14, -6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [29, 3, -2, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 12, 19, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 14, -5, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-38, 6, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-46, -6, -9, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 36, -16, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -8, 4, 12, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-34, 0, 10, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-83, 3, -2, 0, 0, 0, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 7, -4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 30, -8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [63, -34, -10, 0, 0, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-53, -3, -14, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -6, -10, -18, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 3, 12, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, 12, 6, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [7, -3, -2, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 38, 0, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, -3, 26, -14, 0], [0, 0, 0, 0, 0, 0, 0, 0], [66, 12, -3, 0, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [68, 8, -3, 0, 0, 0, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0]]}