# Stored data for newform 900.3.f.h, downloaded from the LMFDB on 19 April 2024.
{"label": "900.3.f.h", "space_label": "900.3.f", "level": 900, "weight": 3, "hecke_orbit": 8, "hecke_orbit_code": 31525541039309700, "dim": 16, "is_polredabs": true, "trace_hash": 645914785334583655, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [961, 0, -9532, 0, 6470, 0, -188, 0, 1]], [29, [93616, -29824, -1600, 16, 1]]], "qexp_display": "q+\\beta _{3}q^{2}+(1+\\beta _{5})q^{4}+(\\beta _{3}-\\beta _{4}-\\beta _{8}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 20, "char_orbit_label": "f", "char_is_real": true, "Nk2": 8100, "analytic_conductor": 24.52322379242672, "hecke_ring_index": 655360000, "level_radical": 30, "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": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [900, 2, [451, 101, 577], [1, 2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [199], "field_disc": 4239404325430861234176, "field_disc_factorization": [[2, 24], [3, 8], [443, 4]], "field_poly": [256, -512, 512, -448, 368, -208, 72, -20, 9, -10, 18, -26, 23, -14, 8, -4, 1], "hecke_ring_index_factorization": [[2, 20], [5, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.098", "prec": 20}, {"__RealLiteral__": 0, "data": "19.239", "prec": 20}, {"__RealLiteral__": 0, "data": "1886.857", "prec": 27}, {"__RealLiteral__": 0, "data": "8260.050", "prec": 27}, {"__RealLiteral__": 0, "data": "376064.830", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, -64, 0, 0, 0, 0, -248, 0, 0, 0, 0, 0, 0, 32, 0, 0, 80, 0, -152, 0, 0, -32, 0, 0, 0, 0, 0, 0, 344, 0, 0, 0, 0, 272, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -216, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -428, 0, 0, 256, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -224, 0, 0, 1016, 0, 240, 0, 0, 1040, 0, 0, 0, 0, 0, 0, 976, 0, 0, 0, 0, -880, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1124, 0, 304, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1112, 0, 0, 672, 0, 0, 0, 0, 232, 0, 0, 0, 0, 0, 0, 704, 0, 0, 1328, 0, -504, 0, 0, -704, 0, 0, 0, 0, 0, 0, 1792, 0, 0, 0, 0, -400, 0, 0, 528, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1524, 0, 1280, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1952, 0, 0, 512, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, -512, 0, 0, 960, 0, 176, 0, 0, 80, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, -2096, 0, 0, 1776, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2320, 0, 1472, 0, 0, 0, 0, 0, 0, 0, 0, 0, -596, 0, 0, -1536, 0, 0, 0, 0, -2056, 0, 0, 0, 0, 0, 0, -3136, 0, 0, -176, 0, -3464, 0, 0, -2032, 0, 0, 0, 0, 0, 0, 1712, 0, 0, 0, 0, 2288, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1308, 0, 1408, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3700, 0, 0, -3872, 0, 0, 0, 0, -2448, 0, 0, 0, 0, 0, 0, 4096, 0, 0, 1608, 0, -952, 0, 0, 32, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 1248, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2896, 0, -304, 0, 0, 0, 0, 0, 0, 0, 0, 0, -116, 0, 0, 5088, 0, 0, 0, 0, -1480, 0, 0, 0, 0, 0, 0, -2784, 0, 0, 5040, 0, 1240, 0, 0, 2288, 0, 0, 0, 0, 0, 0, 2464, 0, 0, 0, 0, -1120, 0, 0, -1760, 0, 0, 0, 0, 0, 0, 0, 0, 0, -260, 0, -464, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2060, 0, 0, -4608, 0, 0, 0, 0, 3136, 0, 0, 0, 0, 0, 0, 736, 0, 0, 3456, 0, -3040, 0, 0, 144, 0, 0, 0, 0, 0, 0, 3952, 0, 0, 0, 0, 1824, 0, 0, 4368, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1932, 0, -1520, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4304, 0, 0, 4832, 0, 0, 0, 0, 3600, 0, 0, 0, 0, 0, 0, -4928, 0, 0, 1872, 0, 1888, 0, 0, -528, 0, 0, 0, 0, 0, 0, -616, 0, 0, 0, 0, 816, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1364, 0, 544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1116, 0, 0, -5696, 0, 0, 0, 0, -5600, 0, 0, 0, 0, 0, 0, 10912, 0, 0, -3152, 0, -2776, 0, 0, 3632, 0, 0, 0, 0, 0, 0, -2240, 0, 0, 0, 0, 496, 0, 0, -4432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 884, 0, 3760, 0, 0, 0, 0, 0, 0, 0, 0, 0, -644, 0, 0, 7936, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, -1408, 0, 0, -688, 0, -1784, 0, 0, -1536, 0, 0, 0, 0, 0, 0, -800, 0, 0, 0, 0, 4512, 0, 0, 2768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3436, 0, -6592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7212, 0, 0, 4128, 0, 0, 0, 0, 2344, 0, 0, 0, 0, 0, 0, 5888, 0, 0, 64, 0, 2824, 0, 0, -3056, 0, 0, 0, 0, 0, 0, -1888, 0, 0, 0, 0, -6912, 0, 0, 3120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6068, 0, 7104, 0, 0, 0, 0, 0, 0, 0, 0, 0, -772, 0, 0, 224, 0, 0, 0, 0, -2264, 0, 0, 0, 0, 0, 0, -6592, 0, 0, -1616, 0, 1680, 0, 0, -4848, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 3456, 0, 0, -2208, 0, 0, 0, 0, 0, 0, 0, 0, 0, -764, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -12512, 0, 0, 0, 0, 4912, 0, 0, 0, 0, 0, 0, 5344, 0, 0, -8320, 0, -1464, 0, 0, 2656, 0, 0, 0, 0, 0, 0, -5808, 0, 0, 0, 0, 368, 0, 0, -1968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1204, 0, -5600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6396, 0, 0, 7680, 0, 0, 0, 0, 456, 0, 0, 0, 0, 0, 0, 1728, 0, 0, -6768, 0, 5792, 0, 0, -9088, 0, 0, 0, 0, 0, 0, -3872, 0, 0, 0, 0, 5504, 0, 0, -6880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2936, 0, 3184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1616, 0, 0, -5504, 0, 0, 0, 0, -3640, 0, 0, 0, 0, 0, 0, -4384, 0, 0, -96, 0, 8728, 0, 0, 11680, 0, 0, 0, 0, 0, 0, 2544, 0, 0, 0, 0, -7264, 0, 0, -6320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6148, 0, -10192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9232, 0, 0, 1984, 0, 0, 0, 0, 2272, 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": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 1, 20, 4, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 4, "minimal_twist": "300.3.c.e", "char_is_minimal": false, "conrey_index": 199, "id": null, "nf_label": 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, 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, 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], [1, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, -1, -1, 0, 2, -1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -3, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, -1, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 2, 2, 1, 0, -4, 1, -1, 0, 0, 0, 0], [0, -2, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, -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, 1, -1, 0, -1, 2, -1, 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, 3, -1, 1, 6, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0], [0, -3, -1, -2, 2, 0, 0, 0, -2, 0, 0, 0, 1, 1, 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], [9, 0, 0, 0, 0, -4, -4, -1, 0, 3, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 3, -5, 0, 0, 0, -2, 0, 0, 0, 1, 4, 2, 0], [-6, 0, 0, 0, 0, 5, 0, 0, 0, -6, 0, -2, 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, -4, -3, 4, 0, -3, -1, 4, 0, 0, 0, -1], [0, -2, 2, 6, 4, 0, 0, 0, -2, 0, 0, 0, 2, 2, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-16, 0, 0, 0, 0, 8, 0, -1, 0, -2, 3, -3, 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, 0, 0, 0, 0, 0], [0, 2, 8, 4, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 8, 0], [0, -1, -4, -4, -4, 0, 0, 0, 2, 0, 0, 0, 1, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, -2, -4, 0, -6, -4, 2, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, -2, 9, 0, 0, 0, -4, 0, 0, 0, -3, 3, 1, 0], [6, 0, 0, 0, 0, 2, -4, 2, 0, -4, 6, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 0, 0, 0, -4, 0, -1, 0, -2, -3, -5, 0, 0, 0, -4], [0, 6, 2, 2, 18, 0, 0, 0, 6, 0, 0, 0, -2, -4, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 2, -4, 4, 0, 12, 4, 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, 0, 0, 0, 0, 0], [0, 5, -5, 4, -9, 0, 0, 0, -1, 0, 0, 0, 2, 0, -5, 0], [0, 0, -1, -5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 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, 0, 0, 0, 0, 0, 0], [24, 0, 0, 0, 0, -2, 1, 1, 0, 8, 2, 0, 0, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, 1, 22, 0, 0, 0, -3, 0, 0, 0, 7, 8, -3, 0], [0, 0, 0, 0, 0, 2, 4, -4, 0, 2, 2, -4, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [23, 0, 0, 0, 0, 0, -8, -1, 0, 18, -1, 7, 0, 0, 0, -4], [0, 1, 8, -2, -20, 0, 0, 0, -2, 0, 0, 0, 7, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 0, -2, 0, 0, -6, -2, 0, 0, 0, -8], [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, -11, -3, -18, 3, 0, 0, 0, -4, 0, 0, 0, 1, -1, 5, 0], [0, -2, -10, -12, 14, 0, 0, 0, -6, 0, 0, 0, 0, 8, -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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, -3, 5, 0, -4, -1, 5, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -10, -8, 16, 0, 0, 0, 0, 6, 0, 0, 0, -10, -4, 4, 0], [-10, 0, 0, 0, 0, -8, -8, 0, 0, 14, -10, 10, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [15, 0, 0, 0, 0, 1, 4, -9, 0, 4, 1, -5, 0, 0, 0, 0], [0, 2, -5, -5, 0, 0, 0, 0, -6, 0, 0, 0, 2, -4, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, 0, 2, 0, -8, 6, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -3, 7, 38, 0, 0, 0, 9, 0, 0, 0, 7, 0, -15, 0], [0, -4, 0, -4, -22, 0, 0, 0, -16, 0, 0, 0, -4, 12, 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, 0, 0, 0, 0, 0, 0], [-27, 0, 0, 0, 0, -4, 0, 7, 0, -9, 9, -1, 0, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, -12, -4, -32, 0, 0, 0, -4, 0, 0, 0, 8, 6, -10, 0], [16, 0, 0, 0, 0, 8, -4, 0, 0, 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, -15, 3, 0, -1, -2, 3, 0, 0, 0, 15], [0, 12, 8, -6, 26, 0, 0, 0, -4, 0, 0, 0, 6, 4, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 8, 0, 0, 0, -18, 4, 12, 0, 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], [0, -8, 4, 28, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 1, 0], [0, 6, 2, 0, -36, 0, 0, 0, -6, 0, 0, 0, -2, 16, -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, 0, 0, 0, 0, 0, 0]]}