# Stored data for newform 1152.3.g.d, downloaded from the LMFDB on 25 April 2024. {"label": "1152.3.g.d", "space_label": "1152.3.g", "level": 1152, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511211249304704, "dim": 8, "is_polredabs": true, "nf_label": "8.0.157351936.1", "trace_hash": 914580219418942079, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [400, 0, -72, 0, 1]], [13, [-188, 12, 1]]], "qexp_display": "q-\\beta _{3}q^{5}-\\beta _{5}q^{7}+\\beta _{1}q^{11}+(-6+\\beta _{7})q^{13}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "g", "char_is_real": true, "Nk2": 10368, "analytic_conductor": 31.389726454306203, "hecke_ring_index": 4194304, "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": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [1152, 2, [127, 901, 641], [1, 2, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [127], "field_disc": 157351936, "field_disc_factorization": [[2, 16], [7, 4]], "field_poly": [16, 0, 0, 0, 1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 22]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "6.843", "prec": 17}, {"__RealLiteral__": 0, "data": "5.259", "prec": 17}, {"__RealLiteral__": 0, "data": "447.999", "prec": 24}, {"__RealLiteral__": 0, "data": "566.242", "prec": 24}, {"__RealLiteral__": 0, "data": "39445.896", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4976, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1488, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7952, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1984, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4016, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24848, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3472, 0, 0, 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, 3, 2, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0], [1, 1, 12, 2, 1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 2, "minimal_twist": "1152.3.g.d", "char_is_minimal": true, "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], [0, 0, 0, 0, 0, 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, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 0, 0, 0, 0], [-6, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [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, -1, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [11, 0, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [14, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 19, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -6, 0, 0, 12, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-38, 0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -10, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -8, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [40, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, -10, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 13, 0, 0, 10, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 0, 0, 0, 0, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [14, 0, 0, 0, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}