# Stored data for newform 2304.3.g.x, downloaded from the LMFDB on 20 April 2024. {"label": "2304.3.g.x", "space_label": "2304.3.g", "level": 2304, "weight": 3, "hecke_orbit": 24, "hecke_orbit_code": 103583203796715776, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 1808701634260804265, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-8, -8, 1]], [7, [8, 0, 1]], [11, [6400, 0, 352, 0, 1]], [13, [-80, 8, 1]]], "qexp_display": "q+(4+\\beta _{2})q^{5}+\\beta _{1}q^{7}+(-4\\beta _{1}-\\beta _{3})q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "g", "char_is_real": true, "Nk2": 20736, "analytic_conductor": 62.779452908612406, "hecke_ring_index": 64, "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": "0.505", "prec": 17}, "analytic_rank_proved": true, "char_values": [2304, 2, [1279, 2053, 1793], [1, 2, 2]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [1279], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.055", "prec": 17}, {"__RealLiteral__": 0, "data": "3.786", "prec": 17}, {"__RealLiteral__": 0, "data": "0.629", "prec": 17}, {"__RealLiteral__": 0, "data": "69.392", "prec": 20}, {"__RealLiteral__": 0, "data": "7.170", "prec": 17}, {"__RealLiteral__": 0, "data": "1742.787", "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, 16, 0], "traces": [0, 4, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 164, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 416, 0, 0, 0, -136, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, -328, 0, 0, 0, 0, 0, 0, 0, -220, 0, 0, 0, 608, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 976, 0, 0, 0, 0, 0, 0, 0, 304, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -228, 0, 0, 0, 848, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, -832, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 656, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 704, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 736, 0, 0, 0, 0, 0, 0, 0, -208, 0, 0, 0, 952, 0, 0, 0, 0, 0, 0, 0, 344, 0, 0, 0, 656, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, -1160, 0, 0, 0, 0, 0, 0, 0, 1248, 0, 0, 0, 400, 0, 0, 0, 0, 0, 0, 0, 816, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 396, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 640, 0, 0, 0, 1088, 0, 0, 0, 0, 0, 0, 0, -232, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 1296, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, -1040, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 740, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, -1280, 0, 0, 0, 0, 0, 0, 0, 896, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, 688, 0, 0, 0, 136, 0, 0, 0, 0, 0, 0, 0, -1160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1616, 0, 0, 0, 3192, 0, 0, 0, 0, 0, 0, 0, 248, 0, 0, 0, -1024, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, -1272, 0, 0, 0, 0, 0, 0, 0, 760, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, -512, 0, 0, 0, -2752, 0, 0, 0, 0, 0, 0, 0, -1472, 0, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, -1760, 0, 0, 0, 1088, 0, 0, 0, 0, 0, 0, 0, -1184, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 1032, 0, 0, 0, 0, 0, 0, 0, -1084, 0, 0, 0, -1056, 0, 0, 0, 0, 0, 0, 0, -848, 0, 0, 0, -1024, 0, 0, 0, 0, 0, 0, 0, -544, 0, 0, 0, -2224, 0, 0, 0, 0, 0, 0, 0, -3616, 0, 0, 0, -2744, 0, 0, 0, 0, 0, 0, 0, -1688, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, -328, 0, 0, 0, 0, 0, 0, 0, -920, 0, 0, 0, -3952, 0, 0, 0, 0, 0, 0, 0, 1200, 0, 0, 0, 2104, 0, 0, 0, 0, 0, 0, 0, 3044, 0, 0, 0, -3104, 0, 0, 0, 0, 0, 0, 0, -656, 0, 0, 0, -568, 0, 0, 0, 0, 0, 0, 0, 960, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -896, 0, 0, 0, 0, 0, 0, 0, -1544, 0, 0, 0, -3120, 0, 0, 0, 0, 0, 0, 0, 2720, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, -1392, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, -2320, 0, 0, 0, 2496, 0, 0, 0, 0, 0, 0, 0, 1056, 0, 0, 0, -2640, 0, 0, 0, 0, 0, 0, 0, -2832, 0, 0, 0, 704, 0, 0, 0, 0, 0, 0, 0, 3616, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, -3448, 0, 0, 0, 0, 0, 0, 0, -488, 0, 0, 0, -560, 0, 0, 0, 0, 0, 0, 0, -3584, 0, 0, 0, 448, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, -3056, 0, 0, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 4168, 0, 0, 0, 0, 0, 0, 0, 2752, 0, 0, 0, 656, 0, 0, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 328, 0, 0, 0, 0, 0, 0, 0, 636, 0, 0, 0, -2448, 0, 0, 0, 0, 0, 0, 0, -3792, 0, 0, 0, -2360, 0, 0, 0, 0, 0, 0, 0, 2336, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -464, 0, 0, 0, 2808, 0, 0, 0, 0, 0, 0, 0, -1760, 0, 0, 0, -2304, 0, 0, 0, 0, 0, 0, 0, 2976, 0, 0, 0, 4608, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, -512, 0, 0, 0, 0, 0, 0, 0, -6384, 0, 0, 0, -2680, 0, 0, 0, 0, 0, 0, 0, 2440, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, -5240, 0, 0, 0, 0, 0, 0, 0, -1820, 0, 0, 0, -3488, 0, 0, 0, 0, 0, 0, 0, 1536, 0, 0, 0, -1272, 0, 0, 0, 0, 0, 0, 0, 2912, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 0, 0, -4880, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, -3208, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 5104, 0, 0, 0, -1992, 0, 0, 0, 0, 0, 0, 0, -2680, 0, 0, 0, 1888, 0, 0, 0, 0, 0, 0, 0, 5888, 0, 0, 0, 2616, 0, 0, 0, 0, 0, 0, 0, -672, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, -4112, 0, 0, 0, 3520, 0, 0, 0, 0, 0, 0, 0, -6528, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, -1360, 0, 0, 0, -456, 0, 0, 0, 0, 0, 0, 0, 1792, 0, 0, 0, 1616, 0, 0, 0, 0, 0, 0, 0, 6704, 0, 0, 0, -960, 0, 0, 0, 0, 0, 0, 0, 2392, 0, 0, 0, -5760, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, -6016, 0, 0, 0, 0, 0, 0, 0, 1288, 0, 0, 0, 2080, 0, 0, 0, 0, 0, 0, 0, 1504, 0, 0, 0, -1664, 0, 0, 0, 0, 0, 0, 0, -4416, 0, 0, 0, -560, 0, 0, 0, 0, 0, 0, 0, 3360, 0, 0, 0, 3640, 0, 0, 0, 0, 0, 0, 0, -1048, 0, 0, 0, 608, 0, 0, 0, 0, 0, 0, 0, -4944, 0, 0, 0, -3400, 0, 0, 0, 0, 0, 0, 0, 2460, 0, 0, 0, 464, 0, 0, 0, 0, 0, 0, 0, 2864, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, -1240, 0, 0, 0, -1536, 0, 0, 0, 0, 0, 0, 0, 2592, 0, 0, 0, 11008, 0, 0, 0, 0, 0, 0, 0, -704, 0, 0, 0, 8016, 0, 0, 0, 0, 0, 0, 0, -4640, 0, 0, 0, -1992, 0, 0, 0, 0, 0, 0, 0, -4200, 0, 0, 0, 4688, 0, 0, 0, 0, 0, 0, 0, 1792, 0, 0, 0, -4864, 0, 0, 0, 0, 0, 0, 0, 3576, 0, 0, 0, 7536, 0, 0, 0, 0, 0, 0, 0, 4992, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -2336, 0, 0, 0, 3584, 0, 0, 0, 0, 0, 0, 0, -3840, 0, 0, 0, -8504, 0, 0, 0, 0, 0, 0, 0, 732, 0, 0, 0, 3152, 0, 0, 0, 0, 0, 0, 0, 944, 0, 0, 0, 3072, 0, 0, 0, 0, 0, 0, 0, 1056, 0, 0, 0, 7808, 0, 0, 0, 0, 0, 0, 0, 3808, 0, 0, 0, 1480, 0, 0, 0, 0, 0, 0, 0, -4160, 0, 0, 0, 3280, 0, 0, 0, 0, 0, 0, 0, -3664, 0, 0, 0, 1656, 0, 0, 0, 0, 0, 0, 0, 5696, 0, 0, 0, 3120, 0, 0, 0, 0, 0, 0, 0, 1840, 0, 0, 0, 4416, 0, 0, 0, 0, 0, 0, 0, 2272, 0, 0, 0, -3296, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 1720, 0, 0, 0, 0, 0, 0, 0, 6008, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 2944, 0, 0, 0, 0, 0, 0, 0, 2800, 0, 0, 0, 2784, 0, 0, 0, 0, 0, 0, 0, 5712, 0, 0, 0, -5568, 0, 0, 0, 0, 0, 0, 0, -480, 0, 0, 0, 4352, 0, 0, 0, 0, 0, 0, 0, 6384, 0, 0, 0, -1608, 0, 0, 0, 0, 0, 0, 0, 2720, 0, 0, 0, 5216, 0, 0, 0, 0, 0, 0, 0, -5264, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 1760, 0, 0, 0, 1408, 0, 0, 0, 0, 0, 0, 0, -1168, 0, 0, 0, 3896, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, 0, 2960, 0, 0, 0, 0, 0, 0, 0, 6896, 0, 0, 0, 1792, 0, 0, 0, 0, 0, 0, 0, -896, 0, 0, 0, 4304, 0, 0, 0, 0, 0, 0, 0, -3840, 0, 0, 0, 2544, 0, 0, 0, 0, 0, 0, 0, -648, 0, 0, 0, 7296, 0, 0, 0, 0, 0, 0, 0, 8176, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, -3892, 0, 0, 0, 2208, 0, 0, 0, 0, 0, 0, 0, 8816, 0, 0, 0, 3784, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, -2032, 0, 0, 0, 0, 0, 0, 0, -7648, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 0, -5680, 0, 0, 0, 0, 0, 0, 0, 4336, 0, 0, 0, -9920, 0, 0, 0, 0, 0, 0, 0, 5640, 0, 0, 0, 1664, 0, 0, 0, 0, 0, 0, 0, 7648, 0, 0, 0, 1600, 0, 0, 0, 0, 0, 0, 0, 8072, 0, 0, 0, 3040, 0, 0, 0, 0, 0, 0, 0, -3152, 0, 0, 0, -4416, 0, 0, 0, 0, 0, 0, 0, -1688, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, -656, 0, 0, 0, 8128, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 3840, 0, 0, 0, 0, 0, 0, 0, 7424, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5596, 0, 0, 0, -6560, 0, 0, 0, 0, 0, 0, 0, -4816, 0, 0, 0, -4800, 0, 0, 0, 0, 0, 0, 0, -8360, 0, 0, 0, 2064, 0, 0, 0, 0, 0, 0, 0, 640, 0, 0, 0, 7096, 0, 0, 0, 0, 0, 0, 0, 928, 0, 0, 0, 8976, 0, 0, 0, 0, 0, 0, 0, 7680, 0, 0, 0, -3848, 0, 0, 0, 0, 0, 0, 0, -9872, 0, 0, 0, 4992, 0, 0, 0, 0, 0, 0, 0, -9040, 0, 0, 0, -4480, 0, 0, 0, 0, 0, 0, 0, 1824, 0, 0, 0, 1808, 0, 0, 0, 0, 0, 0, 0, 5760, 0, 0, 0, -5952, 0, 0, 0, 0, 0, 0, 0, 3648, 0, 0, 0, -5936, 0, 0, 0, 0, 0, 0, 0, -1536, 0, 0, 0, -704, 0, 0, 0, 0, 0, 0, 0, -6632, 0, 0, 0, 4432, 0, 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, 4, 2, -1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 2, "minimal_twist": "384.3.b.c", "char_is_minimal": false, "conrey_index": 1279, "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], [4, 0, 1, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, -1], [0, 0, 0, 0], [-4, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 4, 0], [0, 0, 0, 0], [0, 4, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, 4], [0, 0, 0, 0], [15, 0, 8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [20, 0, -5, 0], [0, 0, 0, 0], [0, 9, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 2], [0, 0, 0, 0], [-4, 0, -8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [18, 0, -4, 0], [0, 0, 0, 0], [0, -20, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, 0, 8], [0, 0, 0, 0], [41, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [36, 0, 7, 0], [0, 0, 0, 0], [0, -28, 0, -12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 5], [0, 0, 0, 0], [44, 0, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [32, 0, 4, 0], [0, 0, 0, 0], [0, 16, 0, -7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -34, 0, 4], [0, 0, 0, 0], [10, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [32, 0, 4, 0], [0, 0, 0, 0], [0, 17, 0, -12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 12, 0, -11], [0, 0, 0, 0], [104, 0, 18, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-34, 0, 8, 0], [0, 0, 0, 0], [0, -4, 0, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 28, 0, 12], [0, 0, 0, 0], [-66, 0, 8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}