# Stored data for newform 1050.3.h.a, downloaded from the LMFDB on 14 May 2024.
{"label": "1050.3.h.a", "space_label": "1050.3.h", "level": 1050, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 481086669850, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 559288550245870679, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[11, [18, 12, 1]]], "qexp_display": "q-\\zeta_{24}q^{2}-\\zeta_{24}^{2}q^{3}-2q^{4}-\\zeta_{24}^{7}q^{6}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 35, "char_orbit_label": "h", "char_is_real": true, "Nk2": 9450, "analytic_conductor": 28.610427757831175, "hecke_ring_index": 256, "level_radical": 210, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "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": "0.763", "prec": 17}, "analytic_rank_proved": true, "char_values": [1050, 2, [701, 127, 451], [2, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 4, "level_primes": [2, 3, 5, 7], "conrey_indexes": [349], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.841", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "524.346", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "58357.267", "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, -16, 0, 0, 0, 0, 24, 0, -48, 0, 0, 48, 0, 32, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, -48, 0, 0, -192, 0, 0, 0, 0, 96, 0, -144, 0, 0, 40, 0, -48, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, -240, 0, 0, -576, 0, 0, 0, 0, -256, 0, 72, 0, 0, -48, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, -192, 0, 0, 16, 0, 0, 0, 0, -384, 0, 480, 0, 0, -1104, 0, -536, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 672, 0, 0, 96, 0, 0, 0, 0, -1008, 0, 32, 0, 0, -192, 0, 384, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, -192, 0, 0, 816, 0, 0, 0, 0, 288, 0, -576, 0, 0, 72, 0, 48, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 512, 0, 0, -48, 0, 0, 0, 0, -96, 0, -672, 0, 0, 192, 0, -192, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, -336, 0, 0, -768, 0, 0, 0, 0, 384, 0, 128, 0, 0, 2048, 0, -720, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 0, -528, 0, 0, 480, 0, 0, 0, 0, 3592, 0, 1056, 0, 0, -96, 0, 1152, 0, 0, 0, 0, 928, 0, 0, 0, 0, 0, 0, 0, -672, 0, 0, 0, 0, 0, 0, 512, 0, 0, 1440, 0, 0, 0, 0, -144, 0, -576, 0, 0, 1056, 0, 2048, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 0, -576, 0, 0, -960, 0, 0, 0, 0, 816, 0, -280, 0, 0, 0, 0, -192, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, -576, 0, 0, 624, 0, 0, 0, 0, -384, 0, 288, 0, 0, 1248, 0, 1776, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 256, 0, 0, 384, 0, 0, 0, 0, 864, 0, 2544, 0, 0, -1728, 0, -32, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 1680, 0, 0, 0, 0, 0, 0, 768, 0, 0, -144, 0, 0, 0, 0, -960, 0, 1728, 0, 0, -1280, 0, 2016, 0, 0, 0, 0, 2208, 0, 0, 0, 0, 0, 0, 0, 1072, 0, 0, 0, 0, 0, 0, 1584, 0, 0, 3264, 0, 0, 0, 0, -1088, 0, -1632, 0, 0, -288, 0, 576, 0, 0, 0, 0, -2592, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, -1776, 0, 0, 2648, 0, 0, 0, 0, 1008, 0, -384, 0, 0, -1392, 0, -3008, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, 0, 0, 2112, 0, 0, 0, 0, 0, 0, 1872, 0, 0, -1344, 0, 0, 0, 0, -5520, 0, -2528, 0, 0, 1008, 0, -192, 0, 0, 0, 0, -2688, 0, 0, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 48, 0, 0, 0, 0, -64, 0, 1296, 0, 0, -720, 0, -4992, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, -1280, 0, 0, -6336, 0, 0, 0, 0, -720, 0, 528, 0, 0, -1056, 0, -288, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, -5232, 0, 0, 0, 0, 0, 0, -1728, 0, 0, 432, 0, 0, 0, 0, -1152, 0, -752, 0, 0, 2016, 0, -3168, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, -4368, 0, 0, 0, 0, 0, 0, -1872, 0, 0, 384, 0, 0, 0, 0, 112, 0, -768, 0, 0, 768, 0, -1632, 0, 0, 0, 0, 4320, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, -576, 0, 0, -8224, 0, 0, 0, 0, 1152, 0, -3456, 0, 0, 816, 0, 1952, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, -3312, 0, 0, -1440, 0, 0, 0, 0, -3360, 0, -1296, 0, 0, 160, 0, 576, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, -3456, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 1584, 0, 0, 0, 0, 2496, 0, -192, 0, 0, 0, 0, 7056, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 472, 0, 0, -1024, 0, 0, 0, 0, 4752, 0, -6144, 0, 0, 192, 0, 96, 0, 0, 0, 0, 1680, 0, 0, 0, 0, 0, 0, 0, 4992, 0, 0, 0, 0, 0, 0, 192, 0, 0, -1776, 0, 0, 0, 0, 1344, 0, 3312, 0, 0, -2048, 0, -432, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, -1200, 0, 0, -1152, 0, 0, 0, 0, -3872, 0, 1296, 0, 0, 864, 0, -3456, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, 0, 0, 3264, 0, 0, 0, 0, 0, 0, 4416, 0, 0, -1728, 0, 0, 0, 0, -576, 0, 2400, 0, 0, -5088, 0, -2680, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 1824, 0, 0, 0, 0, 0, 0, 48, 0, 0, 672, 0, 0, 0, 0, -2784, 0, 7328, 0, 0, -3264, 0, 1536, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 0, 5312, 0, 0, 0, 0, 0, 0, -768, 0, 0, 12048, 0, 0, 0, 0, -256, 0, -1152, 0, 0, 3672, 0, -3600, 0, 0, 0, 0, -4096, 0, 0, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 0, 5728, 0, 0, 7488, 0, 0, 0, 0, 4368, 0, -624, 0, 0, 384, 0, 4032, 0, 0, 0, 0, -3312, 0, 0, 0, 0, 0, 0, 0, 4224, 0, 0, 0, 0, 0, 0, -1824, 0, 0, -1608, 0, 0, 0, 0, 3456, 0, -3072, 0, 0, -1440, 0, -240, 0, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, 0, -9024, 0, 0, 1056, 0, 0, 0, 0, -64, 0, 5760, 0, 0, 432, 0, -960, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, -2784, 0, 0, 0, 0, 0, 0, -7184, 0, 0, -1728, 0, 0, 0, 0, -2112, 0, 3744, 0, 0, -4704, 0, -3328, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, 0, 8352, 0, 0, 3264, 0, 0, 0, 0, 1056, 0, 800, 0, 0, -1856, 0, 576, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 9648, 0, 0, 0, 0, -4608, 0, 1344, 0, 0, 4224, 0, 13920, 0, 0, 0, 0, 6192, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, -7488, 0, 0, -1024, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 2688, 0, -2880, 0, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, 12048, 0, 0, 0, 0, 0, 0, 288, 0, 0, -2304, 0, 0, 0, 0, 1152, 0, -6720, 0, 0, 8784, 0, -3744, 0, 0, 0, 0, -2112, 0, 0, 0, 0, 0, 0, 0, -4096, 0, 0, 0, 0, 0, 0, 7296, 0, 0, 4320, 0, 0, 0, 0, 10368, 0, -3024, 0, 0, -192, 0, -10176, 0, 0, 0, 0, 2176, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 2352, 0, 0, -12984, 0, 0, 0, 0, 288, 0, -1920, 0, 0, 3552, 0, 4112, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, -6720, 0, 0, 0, 0, 0, 0, -4032, 0, 0, 1152, 0, 0, 0, 0, 6480, 0, 12096, 0, 0, 5328, 0, 1920, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, -4064, 0, 0, 0, 0, 0, 0, -1632, 0, 0, -3504, 0, 0, 0, 0, 560, 0, 96, 0, 0, 1584, 0, 11568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 6560, 0, 0, 960, 0, 0, 0, 0, 1440, 0, -5232, 0, 0, 576, 0, 11568, 0, 0, 0, 0, 4752, 0, 0, 0, 0, 0, 0, 0, -9264, 0, 0, 0, 0, 0, 0, -1536, 0, 0, -3936, 0, 0, 0, 0, -3456, 0, -2048, 0, 0, 4608, 0, 1128, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 10368, 0, 0, 0, 0, 0, 0, 3840, 0, 0, 1152, 0, 0, 0, 0, 4768, 0, -4608, 0, 0, 192, 0, -1248, 0, 0, 0, 0, -3024, 0, 0, 0, 0, 0, 0, 0, 2400, 0, 0, 0, 0, 0, 0, 768, 0, 0, -4384, 0, 0, 0, 0, -576, 0, 1920, 0, 0, -5472, 0, -12160, 0, 0, 0, 0, -2496, 0, 0, 0, 0, 0, 0, 0, -3552, 0, 0, 0, 0, 0, 0, 2448, 0, 0, -2832, 0, 0, 0, 0, -7248, 0, -2432, 0, 0, 2880, 0, 2496, 0, 0, 0, 0, -1824, 0, 0, 0, 0, 0, 0, 0, 3168, 0, 0, 0, 0, 0, 0, 7488, 0, 0, -7392, 0, 0, 0, 0, 1776, 0, 864, 0, 0, -7680, 0, -2784, 0, 0, 0, 0, -10368, 0, 0, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, 0, 6392, 0, 0, -512, 0, 0, 0, 0, -8640, 0, 5472, 0, 0, -4368, 0, -768, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, -1728, 0, 0, 144, 0, 0, 0, 0, -5088, 0, 4848, 0, 0, -12096, 0, -5952, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, -26112, 0, 0, 2304, 0, 0, 0, 0, -11744, 0, -4032, 0, 0, -240, 0, -3168, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, -2640, 0, 0, 0, 0, 0, 0, -10368, 0, 0, 10336, 0, 0, 0, 0, 4032, 0, -3360, 0, 0, -1296, 0, 5024, 0, 0, 0, 0, -4512, 0, 0, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 0, -4848, 0, 0, -1536, 0, 0, 0, 0, -3456, 0, -19520, 0, 0, 2880, 0, 288, 0, 0, 0, 0, 1392, 0, 0, 0, 0, 0, 0, 0, -7800, 0, 0, 0, 0, 0, 0, 1920, 0, 0, 2352, 0, 0, 0, 0, -3456, 0, 3648, 0, 0, -432, 0, 336, 0, 0, 0, 0, 2560, 0, 0, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 0, -1152, 0, 0, -1872, 0, 0, 0, 0, 1536, 0, 20880, 0, 0, -4416, 0, 4608, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 8352, 0, 0, 0, 0, 0, 0, -144, 0, 0, 720, 0, 0, 0, 0, -4416, 0, -2144, 0, 0, -8000, 0, 0, 0, 0, 0, 0, 10752, 0, 0, 0, 0, 0, 0, 0, -17856, 0, 0, 0, 0, 0, 0, 1728, 0, 0, -3168, 0, 0, 0, 0, -7920, 0, -288, 0, 0, 3648, 0, -6528, 0, 0, 0, 0, 2448, 0, 0, 0, 0, 0, 0, 0, -2016, 0, 0, 0, 0, 0, 0, 2176, 0, 0, 20288, 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, 5, 2, 1, 2, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 35, 3, -1, 2, 0]], "char_orbit_index": 8, "prim_orbit_index": 3, "minimal_twist": "42.3.c.a", "char_is_minimal": false, "conrey_index": 349, "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, -1, 0, 0, 0, 0, 0, 0], [0, 0, -1, 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, -1], [0, 3, -1, -2, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 0, 0, -3, 0], [0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 8, -2, 0, 0, 0, 0], [6, 0, 0, 0, -2, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 11, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, -1, 0, 6, 3], [0, 6, 0, 0, 0, -3, 0, 0], [0, -9, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 8], [0, 0, -3, 0, 0, 0, 0, 0], [0, -6, 2, 4, 0, -2, 0, 0], [-30, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -6, 0, 0, -12], [0, -4, 0, 0, 0, 0, 0, 0], [0, 0, 6, 3, 0, 0, 0, 0], [0, 0, 0, 0, 11, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 0, 0, 0, 0], [0, -36, 0, 0, 0, -10, 0, 0], [0, 0, 16, -2, 0, 0, 0, 0], [-24, 0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, -7], [0, -3, -6, 2, 0, 6, 0, 0], [0, -30, 0, 0, 0, 16, 0, 0], [12, 0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-18, 0, 0, 0, 0, 0, 6, 0], [0, 0, -28, -4, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, 0, 0], [5, 0, 0, 0, 10, 0, 24, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 0, 0, -33, 0], [0, 0, -16, 4, 0, 0, 0, 0], [0, -12, 0, 0, 0, 27, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 0, 0, 4, 0, 4, 2], [0, -24, 0, 0, 0, -3, 0, 0], [0, 30, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 14, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, -4], [0, 0, 24, 12, 0, 0, 0, 0], [0, 9, -3, -6, 0, 3, 0, 0], [-8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 6], [0, 12, 0, 0, 0, 22, 0, 0], [0, 0, -4, -22, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0], [-30, 0, 0, 0, 0, 0, 57, 0], [0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 4, 26, 0, 0, 0, 0], [-72, 0, 0, 0, 0, 0, 20, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 16], [0, -12, 18, 15, 0, 3, 0, 0], [0, 24, 0, 0, 0, 6, 0, 0], [-32, 0, 0, 0, 0, 0, -72, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 14, -14, 0, 0, 0, 0], [0, 0, 32, 20, 0, 0, 0, 0], [-6, 0, 0, 0, 2, 0, -12, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-60, 0, 0, 0, 0, 0, -32, 0], [0, 0, 30, 0, 0, 0, 0, 0], [0, -12, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 27, 0, 0, 21], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 14, 0, -42, -28], [0, 18, 0, 0, 0, 6, 0, 0], [0, -36, 0, 0, 0, 18, 0, 0], [0, 0, 0, 0, -4, 0, 0, -28], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4], [0, 0, -44, -10, 0, 0, 0, 0], [0, -5, 4, -20, 0, 24, 0, 0], [-18, 0, 0, 0, 0, 0, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}