# Stored data for newform 900.3.l.h, downloaded from the LMFDB on 24 April 2024.
{"label": "900.3.l.h", "space_label": "900.3.l", "level": 900, "weight": 3, "hecke_orbit": 8, "hecke_orbit_code": 31525953356170116, "dim": 4, "is_polredabs": true, "nf_label": "4.0.6400.3", "trace_hash": 494471142593254854, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [2, -2, 1]], [11, [-250, 0, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{7}-\\beta _{3}q^{11}+(6+6\\beta _{1})q^{13}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "l", "char_is_real": false, "Nk2": 8100, "analytic_conductor": 24.52322379242672, "hecke_ring_index": 50, "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": "0.628", "prec": 17}, "analytic_rank_proved": true, "char_values": [900, 4, [451, 101, 577], [4, 4, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [757, 793], "field_disc": 6400, "field_disc_factorization": [[2, 8], [5, 2]], "field_poly": [25, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 1], [5, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.871", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "93.481", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3175.015", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c4", "trace_display": [0, 0, 0, 4], "traces": [0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 276, 0, 0, 0, 0, 0, 380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 516, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -536, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, -1000, 0, 0, 0, 0, 0, -876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -424, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, -1000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1032, 0, 0, 0, 0, 0, -456, 0, 0, 0, 0, 0, -1256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, -1464, 0, 0, 0, 0, 0, -804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2552, 0, 0, 0, 0, 0, 1164, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 660, 0, 0, 0, 0, 0, -1196, 0, 0, 0, 0, 0, -1264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2000, 0, 0, 0, 0, 0, 464, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -568, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, -780, 0, 0, 0, 0, 0, 1180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 516, 0, 0, 0, 0, 0, 1000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 520, 0, 0, 0, 0, 0, 3000, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2536, 0, 0, 0, 0, 0, -1320, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1976, 0, 0, 0, 0, 0, 1196, 0, 0, 0, 0, 0, 4000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2296, 0, 0, 0, 0, 0, 3060, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -944, 0, 0, 0, 0, 0, -1128, 0, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3512, 0, 0, 0, 0, 0, -1000, 0, 0, 0, 0, 0, 1700, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1272, 0, 0, 0, 0, 0, 2000, 0, 0, 0, 0, 0, 1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760, 0, 0, 0, 0, 0, 1716, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4000, 0, 0, 0, 0, 0, 1784, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1544, 0, 0, 0, 0, 0, -3024, 0, 0, 0, 0, 0, -1124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2364, 0, 0, 0, 0, 0, 516, 0, 0, 0, 0, 0, -1216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1632, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, -4384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8000, 0, 0, 0, 0, 0, -1120, 0, 0, 0, 0, 0, -3000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2632, 0, 0, 0, 0, 0, -1156, 0, 0, 0, 0, 0, 2000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2820, 0, 0, 0, 0, 0, 1460, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6856, 0, 0, 0, 0, 0, -5080, 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, 3, -1, 4, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 15, 5, 1, 4, 0]], "char_orbit_index": 12, "prim_orbit_index": 3, "minimal_twist": "180.3.l.c", "char_is_minimal": true, "conrey_index": 757, "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], [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, -1], [0, 0, 0, 0], [6, 6, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 1], [0, 0, 0, 0], [0, 14, 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, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [16, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [30, -30, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [54, 54, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 3, -3], [0, 0, 0, 0], [0, 47, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 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, -5, 0], [0, 0, 0, 0], [54, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [34, -34, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 0, 0], [65, 65, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, -1], [0, 0, 0, 0], [0, 108, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 3, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 8, 0], [0, 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], [69, -69, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}