# Stored data for newform 1200.3.bg.h, downloaded from the LMFDB on 20 April 2024. {"label": "1200.3.bg.h", "space_label": "1200.3.bg", "level": 1200, "weight": 3, "hecke_orbit": 8, "hecke_orbit_code": 31527396465181872, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.2", "trace_hash": 797913355826081800, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [144, 0, 0, 0, 1]]], "qexp_display": "q+\\beta _{3}q^{3}+2\\beta _{1}q^{7}-3\\beta _{2}q^{9}-6q^{11}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "bg", "char_is_real": false, "Nk2": 10800, "analytic_conductor": 32.69763172323563, "hecke_ring_index": 1, "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": "0.755", "prec": 17}, "analytic_rank_proved": true, "char_values": [1200, 4, [751, 901, 401, 577], [4, 4, 4, 3]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [193, 1057], "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.792", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "116.912", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4596.068", "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, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 312, 0, 0, 0, 0, 0, 0, 0, 0, 0, -340, 0, 0, 0, 0, 0, 0, 0, 0, 0, -408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760, 0, 0, 0, 0, 0, 0, 0, 0, 0, -816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, -816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1008, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1044, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -912, 0, 0, 0, 0, 0, 0, 0, 0, 0, -444, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 0, 0, 0, 0, 0, 0, 0, 0, -936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 392, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1920, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3112, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1416, 0, 0, 0, 0, 0, 0, 0, 0, 0, -624, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4808, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3112, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4488, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1800, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4224, 0, 0, 0, 0, 0, 0, 0, 0, 0, -792, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7488, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1632, 0, 0, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3456, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1048, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3408, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1632, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2640, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5760, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3024, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1256, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9792, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1464, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5528, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1704, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, -952, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10080, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7104, 0, 0, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2520, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2952, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2960, 0, 0, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1572, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14976, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7488, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2664, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1832, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5088, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3888, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3124, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14976, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3544, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4320, 0, 0, 0, 0, 0, 0, 0, 0, 0, -552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2312, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10008, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1032, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4464, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6632, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5232, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14016, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9096, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5472, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4560, 0, 0, 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, 2, 5, 3, -1, 4, 0], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 33, "prim_orbit_index": 3, "minimal_twist": "300.3.k.b", "char_is_minimal": false, "conrey_index": 193, "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, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, -3, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -10], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 0], [0, 0, 0, 0], [0, 0, 10, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 24], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, 48, 0], [0, 0, 0, 0], [26, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -26, 0, 0], [0, 0, 0, 0], [0, 0, 30, 0], [0, 0, 0, 0], [30, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 24], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 0], [0, 0, 0, 0], [0, 0, -37, 0], [0, 0, 0, 0], [36, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -10, 0, 0], [0, 0, 0, 0], [0, 0, -78, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -52, 0, 0], [0, 0, 0, 0], [0, 0, -72, 0], [0, 0, 0, 0], [-120, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 68], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 0], [0, 0, 0, 0], [0, 0, 74, 0], [0, 0, 0, 0], [-9, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -36], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -48, 0, 0], [0, 0, 0, 0], [0, 0, 150, 0], [0, 0, 0, 0], [60, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 26], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 18, 0], [0, 0, 0, 0]]}