# Stored data for newform 162.7.d.b, downloaded from the LMFDB on 24 April 2024.
{"label": "162.7.d.b", "space_label": "162.7.d", "level": 162, "weight": 7, "hecke_orbit": 2, "hecke_orbit_code": 4503805903241378, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 1922538473050658272, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [829440000, 0, -28800, 0, 1]]], "qexp_display": "q+(\\beta _{1}-\\beta _{3})q^{2}+(2^{5}-2^{5}\\beta _{2})q^{4}+30\\beta _{1}q^{5}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "d", "char_is_real": false, "Nk2": 7938, "analytic_conductor": 37.26876154641586, "hecke_ring_index": 16, "level_radical": 6, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [162, 6, [83], [5]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [53, 107], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.038", "prec": 17}, {"__RealLiteral__": 0, "data": "3.852", "prec": 17}, {"__RealLiteral__": 0, "data": "0.458", "prec": 17}, {"__RealLiteral__": 0, "data": "90.805", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3297.846", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "6.2.3.c6", "trace_display": [0, 0, 0, -4], "traces": [0, 4, 0, 0, 64, 0, 0, -4, 0, 0, 3840, 0, 0, 5900, 0, 0, -2048, 0, 0, 21032, 0, 0, -384, 0, 0, 26350, 0, 0, -256, 0, 0, -45796, 0, 0, 50688, 0, 0, 136232, 0, 0, 61440, 0, 0, 12812, 0, 0, 231936, 0, 0, 235290, 0, 0, -188800, 0, 0, -23040, 0, 0, 24960, 0, 0, 125132, 0, 0, -131072, 0, 0, -877396, 0, 0, -3840, 0, 0, -2922040, 0, 0, 336512, 0, 0, -681124, 0, 0, 379392, 0, 0, -1520640, 0, 0, 12288, 0, 0, -23600, 0, 0, 2035200, 0, 0, 562172, 0, 0, 1686400, 0, 0, 1731452, 0, 0, -2178432, 0, 0, 2603240, 0, 0, -4096, 0, 0, 3479040, 0, 0, 7395072, 0, 0, -3540818, 0, 0, 1465472, 0, 0, -9122104, 0, 0, 5664000, 0, 0, -21032, 0, 0, 3244032, 0, 0, -9147892, 0, 0, -771840, 0, 0, 1497600, 0, 0, 2179712, 0, 0, 4416188, 0, 0, 1536, 0, 0, 2577740, 0, 0, -1966080, 0, 0, 3519656, 0, 0, 5614464, 0, 0, -7751382, 0, 0, 819968, 0, 0, 52700, 0, 0, -4375296, 0, 0, -25904728, 0, 0, 3710976, 0, 0, -304128, 0, 0, 20190720, 0, 0, -7001860, 0, 0, -7529280, 0, 0, -38039032, 0, 0, -10695552, 0, 0, 5690880, 0, 0, -12083200, 0, 0, -14128276, 0, 0, 16677504, 0, 0, 183184, 0, 0, -368640, 0, 0, -9337828, 0, 0, -39465984, 0, 0, 8963564, 0, 0, -798720, 0, 0, 122112000, 0, 0, 101376, 0, 0, 13991612, 0, 0, 8008448, 0, 0, 31022200, 0, 0, -4704000, 0, 0, -1391616, 0, 0, -2097152, 0, 0, -136232, 0, 0, 24255744, 0, 0, 65352960, 0, 0, 28076672, 0, 0, 55778120, 0, 0, -31490304, 0, 0, -56258644, 0, 0, -245760, 0, 0, -20283700, 0, 0, 1132800, 0, 0, 16260484, 0, 0, -46752640, 0, 0, 110926080, 0, 0, -100920576, 0, 0, 25624, 0, 0, -10768384, 0, 0, -145301464, 0, 0, -43964160, 0, 0, -80219812, 0, 0, -43591936, 0, 0, -149760, 0, 0, -231936, 0, 0, 155465000, 0, 0, 6070272, 0, 0, -55672564, 0, 0, -135031296, 0, 0, 47579324, 0, 0, 48660480, 0, 0, -1882352, 0, 0, 4738944, 0, 0, -94335412, 0, 0, 786432, 0, 0, 23155200, 0, 0, 3417984, 0, 0, -77597268, 0, 0, -377600, 0, 0, 68092124, 0, 0, 130782720, 0, 0, 103156268, 0, 0, -65126400, 0, 0, 171531368, 0, 0, -56813568, 0, 0, 23040, 0, 0, 35979008, 0, 0, -91846656, 0, 0, 54919296, 0, 0, -342326296, 0, 0, 26982400, 0, 0, 135098200, 0, 0, -99840, 0, 0, -122111140, 0, 0, -55406464, 0, 0, 336867840, 0, 0, -2019072, 0, 0, 39231212, 0, 0, -139419648, 0, 0, 250264, 0, 0, 12299520, 0, 0, -3383416, 0, 0, 41651840, 0, 0, 149640764, 0, 0, 299059200, 0, 0, 131258880, 0, 0, 131072, 0, 0, -2276352, 0, 0, 222342528, 0, 0, -314716900, 0, 0, 222658560, 0, 0, -355955620, 0, 0, 25940736, 0, 0, 3509584, 0, 0, 118321152, 0, 0, 138548300, 0, 0, 59864064, 0, 0, 200942200, 0, 0, 113306176, 0, 0, -16577272, 0, 0, 225878400, 0, 0, 19768320, 0, 0, 93790208, 0, 0, -234871060, 0, 0, -322429824, 0, 0, -641733120, 0, 0, -145953664, 0, 0, 2922040, 0, 0, 4227072, 0, 0, -12211200, 0, 0, -181248000, 0, 0, -599224600, 0, 0, -97472256, 0, 0, -85937762, 0, 0, -1346048, 0, 0, -500325120, 0, 0, -85433472, 0, 0, -628069528, 0, 0, 51904512, 0, 0, 558937004, 0, 0, -10118400, 0, 0, -1362248, 0, 0, 292732544, 0, 0, 75590800, 0, 0, 252781824, 0, 0, -591989760, 0, 0, -49397760, 0, 0, -56807860, 0, 0, -379392, 0, 0, 260990216, 0, 0, 23961600, 0, 0, 13070592, 0, 0, 630101760, 0, 0, -240795368, 0, 0, -69750784, 0, 0, 6082560, 0, 0, 342105600, 0, 0, -216955300, 0, 0, 282636032, 0, 0, 686642972, 0, 0, 120126720, 0, 0, 1185300008, 0, 0, 24576, 0, 0, 829546124, 0, 0, -814407168, 0, 0, 552838750, 0, 0, -82487680, 0, 0, 1215432584, 0, 0, -446186112, 0, 0, -694105500, 0, 0, -125829120, 0, 0, -347621332, 0, 0, 266517504, 0, 0, -44370432, 0, 0, 56314496, 0, 0, 363836160, 0, 0, -8140800, 0, 0, 198692780, 0, 0, -179662848, 0, 0, 90455040, 0, 0, -842300160, 0, 0, 558823676, 0, 0, -496088448, 0, 0, 1124344, 0, 0, -8792832, 0, 0, -1889418240, 0, 0, 13119488, 0, 0, -230328724, 0, 0, 1208479488, 0, 0, -150239232, 0, 0, -1686400, 0, 0, 716307856, 0, 0, -198491136, 0, 0, 257303660, 0, 0, -280018944, 0, 0, -33984000, 0, 0, 699469056, 0, 0, -6925808, 0, 0, -414475648, 0, 0, -1046415172, 0, 0, -2805158400, 0, 0, 1314744908, 0, 0, -118751232, 0, 0, 1401980840, 0, 0, -4356864, 0, 0, -1513808640, 0, 0, -19464192, 0, 0, 67398620, 0, 0, -73632000, 0, 0, 1194206120, 0, 0, 323051520, 0, 0, -2603240, 0, 0, -342368256, 0, 0, 1034744828, 0, 0, 224059520, 0, 0, -1206724600, 0, 0, -696153984, 0, 0, 4631040, 0, 0, -481873920, 0, 0, -629435668, 0, 0, -653879040, 0, 0, 738278800, 0, 0, -608624512, 0, 0, 1611878400, 0, 0, -927132672, 0, 0, 6958080, 0, 0, 342257664, 0, 0, -471718936, 0, 0, -13078272, 0, 0, 67365496, 0, 0, 364216320, 0, 0, -32124100, 0, 0, -7395072, 0, 0, -1452613528, 0, 0, -193331200, 0, 0, -2025469440, 0, 0, 766752000, 0, 0, -1179912242, 0, 0, 452104832, 0, 0, 14163272, 0, 0, -667814400, 0, 0, 769448876, 0, 0, 1067360256, 0, 0, 774885452, 0, 0, 454344192, 0, 0, 284336640, 0, 0, 2930944, 0, 0, 2588318200, 0, 0, 1219519488, 0, 0, 998562956, 0, 0, 11796480, 0, 0, 31408424, 0, 0, 1416991872, 0, 0, 9122104, 0, 0, -597620992, 0, 0, -102539520, 0, 0, -1276323840, 0, 0, 3450636288, 0, 0, -631455744, 0, 0, -2323855732, 0, 0, -22656000, 0, 0, -33686784, 0, 0, -286834048, 0, 0, 4817232008, 0, 0, 2071620480, 0, 0, 897428300, 0, 0, -51118080, 0, 0, 1237154820, 0, 0, 1058732928, 0, 0, -988550200, 0, 0, 1953792000, 0, 0, 343729152, 0, 0, -4919808, 0, 0, -4310009000, 0, 0, -3244032, 0, 0, -3408814080, 0, 0, -1218057216, 0, 0, 726370554, 0, 0, 895463168, 0, 0, 2326440956, 0, 0, 539685120, 0, 0, 36591568, 0, 0, 128135168, 0, 0, 26251776, 0, 0, 2700503808, 0, 0, -1647578880, 0, 0, -992710400, 0, 0, -7356598840, 0, 0, -1543680, 0, 0, -1139854612, 0, 0, -301056000], "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, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "6.7.b.a", "char_is_minimal": false, "conrey_index": 53, "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, 1, 0, -1], [0, 0, 0, 0], [32, 0, -32, 0], [0, 30, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, -32], [0, 0, 0, 0], [960, 0, 0, 0], [0, -6, 0, 6], [0, 0, 0, 0], [2950, 0, -2950, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, -1024, 0], [0, 0, 0, 792], [0, 0, 0, 0], [5258, 0, 0, 0], [0, 960, 0, -960], [0, 0, 0, 0], [-192, 0, 192, 0], [0, 1812, 0, 0], [0, 0, 0, 0], [0, 0, 13175, 0], [0, 0, 0, -2950], [0, 0, 0, 0], [-64, 0, 0, 0], [0, 390, 0, -390], [0, 0, 0, 0], [-22898, 0, 22898, 0], [0, -1024, 0, 0], [0, 0, 0, 0], [0, 0, 25344, 0], [0, 0, 0, -60], [0, 0, 0, 0], [34058, 0, 0, 0], [0, 5258, 0, -5258], [0, 0, 0, 0], [30720, 0, -30720, 0], [0, 2964, 0, 0], [0, 0, 0, 0], [0, 0, 6406, 0], [0, 0, 0, 192], [0, 0, 0, 0], [57984, 0, 0, 0], [0, 31800, 0, -31800], [0, 0, 0, 0], [117645, 0, -117645, 0], [0, 13175, 0, 0], [0, 0, 0, 0], [0, 0, -94400, 0], [0, 0, 0, -34038], [0, 0, 0, 0], [-5760, 0, 0, 0], [0, -64, 0, 64], [0, 0, 0, 0], [12480, 0, -12480, 0], [0, 57774, 0, 0], [0, 0, 0, 0], [0, 0, 62566, 0], [0, 0, 0, 22898], [0, 0, 0, 0], [-32768, 0, 0, 0], [0, 88500, 0, -88500], [0, 0, 0, 0], [-438698, 0, 438698, 0], [0, 25344, 0, 0], [0, 0, 0, 0], [0, 0, -1920, 0], [0, 0, 0, -12060], [0, 0, 0, 0], [-730510, 0, 0, 0], [0, 34058, 0, -34058], [0, 0, 0, 0], [168256, 0, -168256, 0], [0, 12, 0, 0], [0, 0, 0, 0], [0, 0, -340562, 0], [0, 0, 0, -30720], [0, 0, 0, 0], [94848, 0, 0, 0], [0, 87726, 0, -87726], [0, 0, 0, 0], [-760320, 0, 760320, 0], [0, 6406, 0, 0], [0, 0, 0, 0], [0, 0, 6144, 0], [0, 0, 0, -68364], [0, 0, 0, 0], [-5900, 0, 0, 0], [0, 57984, 0, -57984], [0, 0, 0, 0], [1017600, 0, -1017600, 0], [0, 157740, 0, 0], [0, 0, 0, 0], [0, 0, 281086, 0], [0, 0, 0, -117645], [0, 0, 0, 0], [421600, 0, 0, 0]]}