# Stored data for newform 192.7.e.f, downloaded from the LMFDB on 15 January 2026.
{"Nk2": 9408, "analytic_conductor": 44.17038405501139, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 3, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": -1, "char_values": [192, 2, [127, 133, 65], [2, 2, 1]], "cm_discs": [], "conrey_index": 65, "dim": 2, "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[5, [28800, 0, 1]], [7, [2, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22518273132200128, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 12, "hecke_ring_index_factorization": [[2, 2], [3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "192.7.e.f", "level": 192, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "6.7.b.a", "nf_label": "2.0.8.1", "prim_orbit_index": 2, "qexp_display": "q+(21+\\beta )q^{3}+10\\beta q^{5}-2q^{7}+(153+\\cdots)q^{9}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "6.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "192.7.e", "trace_display": [0, 42, 0, -4], "trace_hash": 2020629220119325546, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.875", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.122", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "133.606", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 2, 0, 42, 0, 0, 0, -4, 0, 306, 0, 0, 0, 5900, 0, -5760, 0, 0, 0, 10516, 0, -84, 0, 0, 0, -26350, 0, -17766, 0, 0, 0, -45796, 0, 1152, 0, 0, 0, -68116, 0, 123900, 0, 0, 0, -12812, 0, -241920, 0, 0, 0, -235290, 0, -152064, 0, 0, 0, 11520, 0, 220836, 0, 0, 0, 125132, 0, -612, 0, 0, 0, 877396, 0, -347904, 0, 0, 0, -1461020, 0, -553350, 0, 0, 0, -681124, 0, -969246, 0, 0, 0, -1520640, 0, 74880, 0, 0, 0, -11800, 0, -961716, 0, 0, 0, -562172, 0, 48384, 0, 0, 0, 1731452, 0, 11520, 0, 0, 0, -1301620, 0, -1430436, 0, 0, 0, -3479040, 0, 902700, 0, 0, 0, 3540818, 0, 569088, 0, 0, 0, 4561052, 0, -269052, 0, 0, 0, -21032, 0, -5961600, 0, 0, 0, 9147892, 0, 6105600, 0, 0, 0, 748800, 0, -4941090, 0, 0, 0, 4416188, 0, -6386688, 0, 0, 0, 2577740, 0, -6535296, 0, 0, 0, 1759828, 0, 241920, 0, 0, 0, 7751382, 0, 1608948, 0, 0, 0, 52700, 0, 11092608, 0, 0, 0, 12952364, 0, 2627772, 0, 0, 0, 304128, 0, 35532, 0, 0, 0, 7001860, 0, -16992000, 0, 0, 0, 19019516, 0, 18425316, 0, 0, 0, 5690880, 0, -14611968, 0, 0, 0, 14128276, 0, -2315520, 0, 0, 0, 91592, 0, -30681420, 0, 0, 0, -9337828, 0, -4031550, 0, 0, 0, 8963564, 0, -2304, 0, 0, 0, 61056000, 0, -14303604, 0, 0, 0, -13991612, 0, -27756918, 0, 0, 0, 31022200, 0, -16843392, 0, 0, 0, 695808, 0, -31933440, 0, 0, 0, 136232, 0, 3144960, 0, 0, 0, -65352960, 0, 13125888, 0, 0, 0, -27889060, 0, -247800, 0, 0, 0, -56258644, 0, -7006788, 0, 0, 0, 20283700, 0, -30286080, 0, 0, 0, 8130242, 0, -11805612, 0, 0, 0, 110926080, 0, 1192320, 0, 0, 0, 25624, 0, -32086656, 0, 0, 0, -72650732, 0, 36360492, 0, 0, 0, 80219812, 0, 483840, 0, 0, 0, -149760, 0, -50032512, 0, 0, 0, -77732500, 0, -27334020, 0, 0, 0, 55672564, 0, -10421748, 0, 0, 0, -47579324, 0, -59198976, 0, 0, 0, 941176, 0, -73059840, 0, 0, 0, -94335412, 0, -52409700, 0, 0, 0, -23155200, 0, 304128, 0, 0, 0, -38798634, 0, 74357178, 0, 0, 0, 68092124, 0, 23901696, 0, 0, 0, 103156268, 0, -14112000, 0, 0, 0, 85765684, 0, 95782092, 0, 0, 0, -23040, 0, -1960236, 0, 0, 0, -91846656, 0, 36383616, 0, 0, 0, 171163148, 0, -441672, 0, 0, 0, -135098200, 0, -74027520, 0, 0, 0, 122111140, 0, 94470912, 0, 0, 0, -168433920, 0, 192105732, 0, 0, 0, 39231212, 0, 256435200, 0, 0, 0, -250264, 0, 3398400, 0, 0, 0, -1691708, 0, 15724800, 0, 0, 0, 149640764, 0, -35999370, 0, 0, 0, 131258880, 0, 151380864, 0, 0, 0, -1138176, 0, 92739948, 0, 0, 0, 314716900, 0, -157386240, 0, 0, 0, -355955620, 0, 131892480, 0, 0, 0, -1754792, 0, 54132540, 0, 0, 0, -138548300, 0, -274482432, 0, 0, 0, -200942200, 0, 695808, 0, 0, 0, 8288636, 0, 36956388, 0, 0, 0, 19768320, 0, 1762560, 0, 0, 0, 234871060, 0, 202546944, 0, 0, 0, -320866560, 0, 162779022, 0, 0, 0, 2922040, 0, -93413628, 0, 0, 0, -12211200, 0, 14216832, 0, 0, 0, -299612300, 0, 1106700, 0, 0, 0, 85937762, 0, 465889536, 0, 0, 0, -500325120, 0, -10253952, 0, 0, 0, 314034764, 0, 271999644, 0, 0, 0, -558937004, 0, 19145196, 0, 0, 0, 1362248, 0, 196174080, 0, 0, 0, -37795400, 0, 6386688, 0, 0, 0, -591989760, 0, 1938492, 0, 0, 0, 56807860, 0, -170440704, 0, 0, 0, 130495108, 0, 147039060, 0, 0, 0, 13070592, 0, -713664000, 0, 0, 0, -240795368, 0, 164757888, 0, 0, 0, 3041280, 0, 399409836, 0, 0, 0, 216955300, 0, 134241588, 0, 0, 0, 686642972, 0, -149760, 0, 0, 0, -592650004, 0, 119508480, 0, 0, 0, -829546124, 0, -360080640, 0, 0, 0, -552838750, 0, 6057216, 0, 0, 0, -607716292, 0, 296693796, 0, 0, 0, -694105500, 0, -97251840, 0, 0, 0, 347621332, 0, 36898560, 0, 0, 0, -22185216, 0, 1923432, 0, 0, 0, 363836160, 0, -223536060, 0, 0, 0, 198692780, 0, -448588800, 0, 0, 0, 45227520, 0, -196094388, 0, 0, 0, -558823676, 0, 234067050, 0, 0, 0, 1124344, 0, -667027584, 0, 0, 0, 944709120, 0, 188234844, 0, 0, 0, 230328724, 0, -96768, 0, 0, 0, 150239232, 0, -77822208, 0, 0, 0, -358153928, 0, 1282176000, 0, 0, 0, 257303660, 0, -104211972, 0, 0, 0, 33984000, 0, -89796096, 0, 0, 0, -3462904, 0, -293823852, 0, 0, 0, -1046415172, 0, -459210222, 0, 0, 0, 1314744908, 0, 677635200, 0, 0, 0, 700990420, 0, 651466200, 0, 0, 0, 1513808640, 0, -707422464, 0, 0, 0, 67398620, 0, 967289472, 0, 0, 0, -597103060, 0, 14611968, 0, 0, 0, 2603240, 0, -232657920, 0, 0, 0, -1034744828, 0, 6340608, 0, 0, 0, 603362300, 0, 2860872, 0, 0, 0, 4631040, 0, 77500800, 0, 0, 0, 629435668, 0, -292416768, 0, 0, 0, 369139400, 0, -1372412160, 0, 0, 0, 1611878400, 0, 551287296, 0, 0, 0, 6958080, 0, -256300416, 0, 0, 0, -235859468, 0, -585670260, 0, 0, 0, -67365496, 0, -1805400, 0, 0, 0, -32124100, 0, -15177600, 0, 0, 0, 726306764, 0, -1181431524, 0, 0, 0, 2025469440, 0, 406805868, 0, 0, 0, 1179912242, 0, -758345472, 0, 0, 0, -7081636, 0, 425957700, 0, 0, 0, 769448876, 0, -1272015360, 0, 0, 0, -774885452, 0, -1138176, 0, 0, 0, 142168320, 0, 170735082, 0, 0, 0, 2588318200, 0, -86012316, 0, 0, 0, 998562956, 0, -945152640, 0, 0, 0, 15704212, 0, 2329447680, 0, 0, 0, -9122104, 0, 14805504, 0, 0, 0, -102539520, 0, -1026316800, 0, 0, 0, -1725318144, 0, 538104, 0, 0, 0, 2323855732, 0, -1347639552, 0, 0, 0, 33686784, 0, -360380160, 0, 0, 0, -2408616004, 0, -1525665372, 0, 0, 0, 897428300, 0, 264912156, 0, 0, 0, -1237154820, 0, 1221610752, 0, 0, 0, -494275100, 0, 1684616052, 0, 0, 0, 343729152, 0, 11923200, 0, 0, 0, -4310009000, 0, -1338558336, 0, 0, 0, -1704407040, 0, -3144960, 0, 0, 0, -726370554, 0, -2101365504, 0, 0, 0, 2326440956, 0, -799552512, 0, 0, 0, -18295784, 0, -1632382500, 0, 0, 0, -26251776, 0, -199147860, 0, 0, 0, 1647578880, 0, -12211200, 0, 0, 0, 3678299420, 0, 1169123844, 0, 0, 0, -1139854612, 0, 605074428, 0], "weight": 7, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [21, 1], [0, 0], [0, 10], [0, 0], [-2, 0], [0, 0], [153, 42], [0, 0], [0, -2], [0, 0], [2950, 0], [0, 0], [-2880, 210], [0, 0], [0, 264], [0, 0], [5258, 0], [0, 0], [-42, -2], [0, 0], [0, 604], [0, 0], [-13175, 0], [0, 0], [-8883, 1035], [0, 0], [0, -130], [0, 0], [-22898, 0], [0, 0], [576, -42], [0, 0], [0, -20], [0, 0], [-34058, 0], [0, 0], [61950, 2950], [0, 0], [0, -988], [0, 0], [-6406, 0], [0, 0], [-120960, 1530], [0, 0], [0, -10600], [0, 0], [-117645, 0], [0, 0], [-76032, 5544], [0, 0], [0, 11346], [0, 0], [5760, 0], [0, 0], [110418, 5258], [0, 0], [0, -19258], [0, 0], [62566, 0], [0, 0], [-306, -84], [0, 0], [0, 29500], [0, 0], [438698, 0], [0, 0], [-173952, 12684], [0, 0], [0, 4020], [0, 0], [-730510, 0], [0, 0], [-276675, -13175], [0, 0], [0, 4], [0, 0], [-340562, 0], [0, 0], [-484623, 12852], [0, 0], [0, 29242], [0, 0], [-760320, 0], [0, 0], [37440, -2730], [0, 0], [0, -22788], [0, 0], [-5900, 0], [0, 0], [-480858, -22898], [0, 0], [0, 52580], [0, 0], [-281086, 0], [0, 0], [24192, -306], [0, 0]]}