# Stored data for newform 1089.3.b.h, downloaded from the LMFDB on 19 April 2024.
{"label": "1089.3.b.h", "space_label": "1089.3.b", "level": 1089, "weight": 3, "hecke_orbit": 8, "hecke_orbit_code": 31525266161402945, "dim": 8, "is_polredabs": true, "nf_label": "8.0.3317760000.7", "trace_hash": 1483146929643481899, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 0, 8, 0, 1]], [7, [4, 0, -16, 0, 1]]], "qexp_display": "q-\\beta _{7}q^{2}+\\beta _{3}q^{4}-\\beta _{1}q^{5}+(\\beta _{2}+\\beta _{4}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 9801, "analytic_conductor": 29.673100788836333, "hecke_ring_index": 16, "level_radical": 33, "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": "0.761", "prec": 17}, "analytic_rank_proved": true, "char_values": [1089, 2, [848, 244], [1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [3, 11], "conrey_indexes": [485], "field_disc": 3317760000, "field_disc_factorization": [[2, 16], [3, 4], [5, 4]], "field_poly": [1, 0, 12, 0, 23, 0, 12, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.159", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "483.556", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "43493.606", "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, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 96, 0, 0, 176, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -328, 0, 0, 0, 0, 0, 0, 0, 0, 416, 0, 0, 0, 0, 0, 448, 0, 0, 216, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 352, 0, 0, -120, 0, 0, 1256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -664, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 480, 0, 0, -224, 0, 0, 344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1080, 0, 0, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 488, 0, 0, -928, 0, 0, 688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1016, 0, 0, 0, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 240, 0, 0, -216, 0, 0, 872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1288, 0, 0, 0, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, -520, 0, 0, 104, 0, 0, -688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 1800, 0, 0, 0, 0, 0, -2072, 0, 0, -576, 0, 0, -2520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, -792, 0, 0, 1808, 0, 0, -544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1064, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, -728, 0, 0, 800, 0, 0, -3080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2856, 0, 0, 0, 0, 0, 0, 0, 0, 1672, 0, 0, 0, 0, 0, -1864, 0, 0, -120, 0, 0, -1880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2392, 0, 0, 0, 0, 0, 0, 0, 0, -840, 0, 0, 0, 0, 0, -1688, 0, 0, -208, 0, 0, -616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 0, 0, 0, -2008, 0, 0, 0, 0, 0, 544, 0, 0, 1192, 0, 0, -4248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 856, 0, 0, 0, 0, 0, 0, 0, 0, 4744, 0, 0, 0, 0, 0, 120, 0, 0, 1896, 0, 0, 424, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1744, 0, 0, 0, 0, 0, 0, 0, 0, -4088, 0, 0, 0, 0, 0, -2288, 0, 0, 1824, 0, 0, 3944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1984, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -2576, 0, 0, -5192, 0, 0, -960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 2256, 0, 0, 0, 0, 0, 5640, 0, 0, -2728, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 440, 0, 0, 0, 0, 0, 0, 0, 0, -4936, 0, 0, 0, 0, 0, 4304, 0, 0, -1544, 0, 0, 10440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1328, 0, 0, 0, 0, 0, 0, 0, 0, -920, 0, 0, 0, 0, 0, 832, 0, 0, 4560, 0, 0, -920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4800, 0, 0, 0, 0, 0, 0, 0, 0, 6360, 0, 0, 0, 0, 0, 176, 0, 0, -4256, 0, 0, 368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7200, 0, 0, 0, 0, 0, 0, 0, 0, -776, 0, 0, 0, 0, 0, 2808, 0, 0, -2096, 0, 0, 6656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2112, 0, 0, 0, 0, 0, 0, 0, 0, -2712, 0, 0, 0, 0, 0, 3600, 0, 0, 632, 0, 0, 2272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 792, 0, 0, 0, 0, 0, 0, 0, 0, 4600, 0, 0, 0, 0, 0, -120, 0, 0, -592, 0, 0, 1176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 0, 1288, 0, 0, 0, 0, 0, 912, 0, 0, 3600, 0, 0, 8760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1928, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 6824, 0, 0, 864, 0, 0, -5096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1320, 0, 0, 0, 0, 0, 0, 0, 0, 3352, 0, 0, 0, 0, 0, -1928, 0, 0, -1720, 0, 0, -3064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3328, 0, 0, 0, 0, 0, 0, 0, 0, -3440, 0, 0, 0, 0, 0, -96, 0, 0, 1200, 0, 0, 2912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4728, 0, 0, 0, 0, 0, 0, 0, 0, -2400, 0, 0, 0, 0, 0, -3000, 0, 0, -808, 0, 0, -6240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1920, 0, 0, 0, 0, 0, 0, 0, 0, 12960, 0, 0, 0, 0, 0, -432, 0, 0, 6632, 0, 0, -4616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, 3120, 0, 0, 7952, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1848, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, -3584, 0, 0, -1408, 0, 0, -1920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9232, 0, 0, 0, 0, 0, 0, 0, 0, -488, 0, 0, 0, 0, 0, 672, 0, 0, -3696, 0, 0, -6120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10296, 0, 0, 0, 0, 0, 0, 0, 0, -5968, 0, 0, 0, 0, 0, -7440, 0, 0, -2688, 0, 0, -464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, -1128, 0, 0, 0, 0, 0, 1080, 0, 0, 10240, 0, 0, -2392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6152, 0, 0, 0, 0, 0, 0, 0, 0, 4512, 0, 0, 0, 0, 0, -8672, 0, 0, -10920, 0, 0, -3584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1680, 0, 0, 0, 0, 0, 0, 0, 0, -6840, 0, 0, 0, 0, 0, -5632, 0, 0, -2704, 0, 0, 2552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 0, -3104, 0, 0, 0, 0, 0, 3384, 0, 0, 2640, 0, 0, -5816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6488, 0, 0, 0, 0, 0, 0, 0, 0, -392, 0, 0, 0, 0, 0, 2160, 0, 0, 4344, 0, 0, -2888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3408, 0, 0, 0, 0, 0, 0, 0, 0, -784, 0, 0, 0, 0, 0, -2704, 0, 0, 992, 0, 0, 9664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -752, 0, 0, 0, 0, 0, 0, 0, 0, -9360, 0, 0, 0, 0, 0, -10432, 0, 0, -13016, 0, 0, -10320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1640, 0, 0, 0, 0, 0, 0, 0, 0, 6584, 0, 0, 0, 0, 0, 136, 0, 0, -14960, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 0, -15840, 0, 0, 0, 0, 0, -936, 0, 0, 3584, 0, 0, 1272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6848, 0, 0, 0, 0, 0, 0, 0, 0, -896, 0, 0, 0, 0, 0, -12600, 0, 0, 3240, 0, 0, 1448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3848, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 8632, 0, 0, 11752, 0, 0, -360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8520, 0, 0, 0, 0, 0, 0, 0, 0, -1952, 0, 0, 0, 0, 0, 7464, 0, 0, -11784, 0, 0, 976, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8736, 0, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 2280, 0, 0, -2976, 0, 0, -248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15480, 0, 0, 0, 0, 0, 0, 0, 0, -4656, 0, 0, 0, 0, 0, -7696, 0, 0, -3712, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4768, 0, 0, 0, 0, 0, 0, 0, 0, 1168, 0, 0, 0, 0, 0, 120, 0, 0, 2568, 0, 0, -600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7736, 0, 0, 0, 0, 0, 0, 0, 0, 3136, 0, 0, 0, 0, 0, 6544, 0, 0, 12744, 0, 0, -1816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17152, 0, 0, 0, 0, 0, 0, 0, 0, -2984, 0, 0, 0, 0, 0, -2696, 0, 0, 12720, 0, 0, -1720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7936, 0, 0, 0, 0, 0, 0, 0, 0, 6192, 0, 0, 0, 0, 0, -8184, 0, 0, -2400, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 872, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 16200, 0, 0, -21896, 0, 0, -872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5760, 0, 0, 0, 0, 0, 0, 0, 0, 9360, 0, 0, 0, 0, 0, 10768, 0, 0, 216, 0, 0, 9312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1552, 0, 0, 0, 0, 0, 0, 0, 0, 10728, 0, 0, 0, 0, 0, 3600, 0, 0, 16664, 0, 0, -1696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1248, 0, 0, 0, 0, 0, 0, 0, 0, 1080, 0, 0, 0, 0, 0, 1504, 0, 0, 2536, 0, 0, 15416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16312, 0, 0, 0, 0, 0, 0, 0, 0, 1144, 0, 0, 0, 0, 0, -12120, 0, 0, 1592, 0, 0, 2760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2864, 0, 0, 0, 0, 0, 0, 0, 0, 16608, 0, 0, 0, 0, 0, 2072, 0, 0, 4792, 0, 0, -6240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7536, 0, 0, 0, 0, 0, 0, 0, 0, -7736, 0, 0, 0, 0, 0, 2176, 0, 0, 7800, 0, 0, -1088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3088, 0, 0, 0, 0, 0, 0, 0, 0, -3192, 0, 0, 0, 0, 0, 12184, 0, 0, 3000, 0, 0, -3096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18480, 0, 0, 0, 0, 0, 0, 0, 0, 4680, 0, 0, 0, 0, 0, 26992, 0, 0, -624, 0, 0, 4896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3480, 0, 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, 11, 2, -1, 2, 0], [1, 1, 33, 4, 1, 2, 0], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "1089.3.b.h", "char_is_minimal": true, "conrey_index": 485, "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, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, -6, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -10, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -6, 0, -2, 0, 0, 0], [0, -1, 0, 0, 0, -7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -12, 0, 0, 0, 13, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [17, 0, 0, -1, 0, 0, 0, 0], [0, 11, 0, 0, 0, -28, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 13], [0, 0, 0, 0, 0, 0, 0, 0], [12, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 17], [0, 0, 0, 0, 0, 0, 0, 0], [22, 0, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -5, -1], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 9, 0, 0, 0, 0], [0, -4, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 26, 13], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 0, -19, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 37, 0, -25, 0, 0, 0], [0, -10, 0, 0, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-41, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, -21], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -30, 0, 15, 0, 0, 0], [0, -3, 0, 0, 0, -48, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [52, 0, 0, -13, 0, 0, 0, 0], [0, -6, 0, 0, 0, -51, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 26, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [56, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 17], [0, 0, 0, 0, 0, 0, 0, 0], [27, 0, 0, -21, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -43, -22], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0], [0, 26, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, -52, 0, 0, 0], [0, 0, 0, 0, 0, 0, 9, 34], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -10, 0, -18, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 44, 0, 30, 0, 0, 0], [0, -3, 0, 0, 0, -28, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [26, 0, 0, -13, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -20, -34], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -36, 0, -17, 0, 0, 0], [0, 28, 0, 0, 0, -75, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 11, 0, 0, 0, 19, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, 0, 0, -1, 0, 0, 0, 0], [0, 14, 0, 0, 0, -97, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 14, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 18, -2], [0, 0, 0, 0, 0, 0, 0, 0], [44, 0, 0, -7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 49], [0, 0, 0, 0, 0, 0, 0, 0], [-15, 0, 0, 17, 0, 0, 0, 0]]}