# Stored data for newform 336.7.bh.c, downloaded from the LMFDB on 25 April 2024.
{"label": "336.7.bh.c", "space_label": "336.7.bh", "level": 336, "weight": 7, "hecke_orbit": 3, "hecke_orbit_code": 9009467114914128, "dim": 8, "is_polredabs": true, "trace_hash": 434402370797300282, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [2121293306250000, 14300853750000, -917799187500, -6404062500, 357598125, 4331250, -5925, -210, 1]]], "qexp_display": "q+(-18+9\\beta _{2})q^{3}+(15-5\\beta _{1}+20\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "bh", "char_is_real": false, "Nk2": 16464, "analytic_conductor": 77.29817209626994, "hecke_ring_index": 254016, "level_radical": 42, "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": "0.167", "prec": 17}, "analytic_rank_proved": true, "char_values": [336, 6, [127, 85, 113, 241], [6, 6, 6, 5]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [145, 241], "field_disc": 4001792200704, "field_disc_factorization": [[2, 12], [3, 4], [23, 2], [151, 2]], "field_poly": [38416, 5488, 6468, -28, 701, 2, 33, -2, 1], "hecke_ring_index_factorization": [[2, 6], [3, 4], [7, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "7.570", "prec": 17}, {"__RealLiteral__": 0, "data": "1.523", "prec": 17}, {"__RealLiteral__": 0, "data": "237.605", "prec": 24}, {"__RealLiteral__": 0, "data": "172.485", "prec": 24}, {"__RealLiteral__": 0, "data": "12530.089", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "6.2.3.c6", "trace_display": [0, -108, 210, 608], "traces": [0, 8, 0, -108, 0, 210, 0, 608, 0, 972, 0, -2058, 0, 0, 0, -3780, 0, -11244, 0, -21834, 0, -4482, 0, -15504, 0, -6550, 0, 0, 0, 35316, 0, 51060, 0, 55566, 0, -71460, 0, 20282, 0, 101682, 0, 0, 0, -387812, 0, 51030, 0, 55212, 0, -277780, 0, 101196, 0, -336174, 0, 0, 0, 393012, 0, 560454, 0, 850728, 0, -26730, 0, 826380, 0, 947882, 0, 0, 0, -147192, 0, -533034, 0, 176850, 0, -1848102, 0, 6260, 0, -236196, 0, 0, 0, 560040, 0, -476766, 0, 413460, 0, -256074, 0, -459540, 0, 170880, 0, 0, 0, -1000188, 0, -2195604, 0, 4801062, 0, 1842210, 0, 270, 0, 2820302, 0, 0, 0, 2052096, 0, -10414440, 0, -2745414, 0, 8631372, 0, -395222, 0, -629640, 0, 0, 0, 942176, 0, 5235462, 0, -2086074, 0, -690126, 0, -459270, 0, 8763096, 0, 0, 0, -993816, 0, -1866060, 0, -12442770, 0, 95958, 0, 12487812, 0, -6446390, 0, 0, 0, 19664700, 0, 12211200, 0, 9076698, 0, -2881608, 0, -403204, 0, 1374570, 0, 0, 0, -9796, 0, -5305662, 0, 10720944, 0, 5076800, 0, -5044086, 0, -10751568, 0, 0, 0, -15313104, 0, -53384160, 0, 51942996, 0, 1810836, 0, -22643748, 0, 16975544, 0, 0, 0, 24279480, 0, 7995408, 0, -25592814, 0, 16702110, 0, 9643260, 0, 3767472, 0, 0, 0, -52646792, 0, 1987092, 0, 19209120, 0, -16722546, 0, 4797306, 0, -7471008, 0, 0, 0, -3183300, 0, -8778006, 0, 8888754, 0, 8338140, 0, 72269520, 0, 11756640, 0, 0, 0, -66078984, 0, -25434570, 0, 6377292, 0, -49237590, 0, -12878682, 0, 13276494, 0, 0, 0, -43485840, 0, -7560540, 0, -7048584, 0, 9741818, 0, 4290894, 0, -8261916, 0, 0, 0, -7442280, 0, 18544782, 0, 34167882, 0, 1973916, 0, 14035800, 0, 11283634, 0, 0, 0, 79594896, 0, -34666590, 0, -4613760, 0, 57489096, 0, 62180228, 0, 89802, 0, 0, 0, -143739300, 0, 13502538, 0, 183620664, 0, -96303842, 0, 19760436, 0, 67812000, 0, 0, 0, -86419116, 0, -105468576, 0, -86765796, 0, -32374890, 0, -3664086, 0, -40029534, 0, 0, 0, 8822544, 0, 111501150, 0, -76148154, 0, 12375108, 0, 28623358, 0, -4928526, 0, 0, 0, -245891536, 0, -27703296, 0, -64499778, 0, 53312048, 0, 93729960, 0, -59266260, 0, 0, 0, 49417452, 0, 35797596, 0, -74607480, 0, -194947128, 0, 172532400, 0, -3162646, 0, 0, 0, -33135000, 0, -94305312, 0, 17000280, 0, -30531966, 0, 98868646, 0, -77280750, 0, 0, 0, 101375740, 0, -12719376, 0, 257015604, 0, -27599490, 0, -47119158, 0, -137102736, 0, 0, 0, 37549332, 0, 11045130, 0, 296910330, 0, 17776746, 0, -58177824, 0, -163405182, 0, 0, 0, -217496688, 0, -276533268, 0, -236603592, 0, 387939306, 0, 70609650, 0, 795690, 0, 0, 0, 67325788, 0, 13416516, 0, -122425800, 0, 3984984, 0, 16794540, 0, 265739688, 0, 0, 0, 223969860, 0, -32028984, 0, -10367694, 0, 64909674, 0, 144659178, 0, -253561140, 0, 0, 0, 311402904, 0, 258609852, 0, 174052530, 0, -463714020, 0, 207719420, 0, -24590628, 0, 0, 0, -218787100, 0, -265473450, 0, 193667148, 0, 448535132, 0, -109900800, 0, -18999768, 0, 0, 0, -163380564, 0, 476769732, 0, 686709714, 0, 109130976, 0, -190439790, 0, -36584924, 0, 0, 0, -576051540, 0, -467019180, 0, -37113390, 0, 239724228, 0, 108128674, 0, -60868692, 0, 0, 0, -780147360, 0, 132246, 0, 65164110, 0, 264191208, 0, 47750958, 0, 293133420, 0, 0, 0, -192976992, 0, 269247396, 0, -528476574, 0, 146406150, 0, 277234332, 0, -233447180, 0, 0, 0, -251640216, 0, -339779430, 0, 290292336, 0, 336229464, 0, -500559866, 0, 41901786, 0, 0, 0, 535647968, 0, 206726904, 0, -243892692, 0, 253222058, 0, 480457440, 0, 172260906, 0, 0, 0, -934973928, 0, 824081058, 0, -188791380, 0, -42397182, 0, 6905664, 0, 116206082, 0, 0, 0, -1188654000, 0, 1478187156, 0, -458339688, 0, 768907482, 0, 51232014, 0, -200810340, 0, 0, 0, -1321767180, 0, -327772980, 0, -137637804, 0, 418572060, 0, -71958672, 0, 347989152, 0, 0, 0, 460670652, 0, 664663260, 0, -298808496, 0, -145786554, 0, 127050012, 0, 4074388, 0, 0, 0, -252846840, 0, 116483718, 0, -101721744, 0, 351404280, 0, -362357500, 0, -249636168, 0, 0, 0, 76406156, 0, 710731692, 0, -670682670, 0, 1270884174, 0, -17883828, 0, -170837784, 0, 0, 0, -345764160, 0, 774962748, 0, 425223126, 0, 72376470, 0, 791352594, 0, -785701710, 0, 0, 0, -732307512, 0, 660096774, 0, 201717216, 0, 569796180, 0, 942312456, 0, 43785522, 0, 0, 0, -655273432, 0, 42974550, 0, -637309386, 0, 692822046, 0, 79002054, 0, -410837214, 0, 0, 0, -159997572, 0, -1183905648, 0, -1364327250, 0, 223959006, 0, 464266440, 0, -873002040, 0, 0, 0, -629020788, 0, -582322554, 0, -317429280, 0, 1661880312, 0, 71429720, 0, -1521180, 0, 0, 0, -1451484000, 0, 892066284, 0, -2227125480, 0, 87216126, 0, 228911130, 0, -924918300, 0, 0, 0, -114791256, 0, 601530456, 0, -2361398826, 0, 463872690, 0, 917842188, 0, 196276046, 0, 0, 0, -2342013096, 0, -468289260, 0, -358465338, 0, 1969283412, 0, -936285080, 0, 471463470, 0, 0, 0, -126637336, 0, 587058840, 0, -2288333280, 0, 1571745452, 0, 68044860, 0, 285241824, 0, 0, 0, 126874512, 0, -2330822820, 0, 527647650, 0, 412614486, 0, 153327684, 0, 678179160, 0, 0, 0, 547088400, 0, 2112355896, 0, 223071732, 0, 683134296, 0, 1347084360, 0, 235895490, 0, 0, 0, -1538668032, 0, 100470780, 0, 1561229676, 0, 2292699240, 0, -166903038, 0, -1525474164, 0, 0, 0, -615021876, 0, 1478356800, 0, -104296014, 0, 8930250, 0, 617064630, 0, -452881120, 0, 0, 0, -3846379620, 0, 1569580326, 0, -304658118, 0, 1457316720, 0, -295881720, 0, 111668220, 0, 0, 0, -1906592804, 0, -1074531096, 0, -4042663170, 0, 3254615854, 0, 311999310, 0, -3907991112, 0, 0, 0, 83047680, 0, -1840784880, 0, -1923032868, 0, -863328564, 0, 378659856, 0, -486613800, 0, 0, 0, 123960540, 0, 2633728650, 0, -2424654, 0, 3277917750, 0, 2375704516, 0, -674445474, 0, 0, 0, -89098580, 0, 1940480550, 0, 3646119444, 0, 2307494492, 0, -121522842, 0, 864901884, 0, 0, 0, -3305171952, 0, -2333913102, 0, -203865084, 0, 1335894228, 0, 274538040, 0, -2875050914, 0, 0, 0, -4912031040, 0, 4593853530, 0, -1830924000, 0, 1495809900, 0, 1291852162, 0, 617291982, 0, 0, 0, -7394608300, 0, 1166658066, 0, -1353486552, 0, 3941414340, 0, 949217184, 0, -464818860, 0, 0, 0, 1561784328, 0, 5845198494, 0, 3066087168, 0, 426465000, 0, 425070576, 0, 274905294, 0, 0, 0, -1077293640, 0, -3127219560, 0, 1080797418, 0, 592368816, 0, 1489698296, 0, -65610, 0, 0, 0, -7488437224, 0, -119104344, 0, 4710818730, 0, -4969715730, 0, -1003510350, 0, -788593800, 0, 0, 0, 1370666772, 0, -3328474980, 0, 2081911860, 0, 534518244, 0, -712788024, 0, -989385188, 0, 0, 0, -4048345200, 0, 175670022, 0, 133070202, 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, 7, 4, -1, 6, 0]], "char_orbit_index": 34, "prim_orbit_index": 4, "minimal_twist": "42.7.g.b", "char_is_minimal": false, "conrey_index": 145, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0], [-18, 0, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [15, -5, 20, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [113, 8, -73, -3, 3, -5, 5, -5], [0, 0, 0, 0, 0, 0, 0, 0], [243, 0, -243, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -516, -17, -3, -38, 0, -17], [0, 0, 0, 0, 0, 0, 0, 0], [972, 0, -1883, 0, -61, 9, -4, 13], [0, 0, 0, 0, 0, 0, 0, 0], [-450, 90, -45, 0, 45, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1874, -76, 975, -147, -76, 95, -190, 147], [0, 0, 0, 0, 0, 0, 0, 0], [-1802, 35, -1837, 2, 0, -424, 213, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1377, -117, 1674, 99, -99, 18, -18, 18], [0, 0, 0, 0, 0, 0, 0, 0], [-4033, 314, 3719, 95, 628, -95, 99, -190], [0, 0, 0, 0, 0, 0, 0, 0], [-325, -325, -1475, 75, 325, -350, 0, 75], [0, 0, 0, 0, 0, 0, 0, 0], [-2187, 0, 4374, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4633, 874, -437, 206, 437, -20, 123, -103], [0, 0, 0, 0, 0, 0, 0, 0], [8510, -1290, -3610, -159, -1290, 1076, -2152, 159], [0, 0, 0, 0, 0, 0, 0, 0], [4590, -81, 4671, 459, 0, 531, -36, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-485, -340, -16080, -35, -985, 1030, 620, -140], [0, 0, 0, 0, 0, 0, 0, 0], [4171, 1799, -5970, 353, 3598, -353, 612, -706], [0, 0, 0, 0, 0, 0, 0, 0], [-549, -549, 25695, -117, 549, -126, 0, -117], [0, 0, 0, 0, 0, 0, 0, 0], [-5240, 0, 11660, 0, -1180, 280, -446, 726], [0, 0, 0, 0, 0, 0, 0, 0], [-49091, -2458, 1229, 288, -1229, 2201, -2057, -144], [0, 0, 0, 0, 0, 0, 0, 0], [8505, -1215, -3645, 0, -1215, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4395, -412, 4807, 729, 0, -2485, 1607, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-68717, 2348, 66494, -906, 2669, -5217, 3972, -187], [0, 0, 0, 0, 0, 0, 0, 0], [24957, 684, -25641, 1323, 1368, -1323, 2565, -2646], [0, 0, 0, 0, 0, 0, 0, 0], [-41, -41, -84023, 456, 41, 2992, 0, 456], [0, 0, 0, 0, 0, 0, 0, 0], [14235, 0, -25455, 0, -3015, 3200, 2705, 495], [0, 0, 0, 0, 0, 0, 0, 0], [48969, -630, 315, -36, -315, 5733, -5751, 18], [0, 0, 0, 0, 0, 0, 0, 0], [93409, 7421, -50415, -2016, 7421, 1241, -2482, 2016], [0, 0, 0, 0, 0, 0, 0, 0], [68304, -5180, 73484, 1024, 0, 1296, -136, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9720, 1215, -27459, -1944, 1944, 729, -729, 729], [0, 0, 0, 0, 0, 0, 0, 0], [210245, -7300, -202945, 925, -14600, -925, 4035, -1850], [0, 0, 0, 0, 0, 0, 0, 0], [637, 637, 236652, 2204, -637, -9919, 0, 2204], [0, 0, 0, 0, 0, 0, 0, 0], [39123, 0, -69768, 0, -8478, 1674, -891, 2565], [0, 0, 0, 0, 0, 0, 0, 0], [-15463, 11744, -5872, 602, 5872, -26088, 26389, -301], [0, 0, 0, 0, 0, 0, 0, 0], [-88839, 569, 44135, -3643, 569, 830, -1660, 3643], [0, 0, 0, 0, 0, 0, 0, 0], [19125, 8775, 10350, -2025, 0, 6975, -4500, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-384774, -939, 308085, -6581, -1032, -9127, 5827, 5218], [0, 0, 0, 0, 0, 0, 0, 0], [3052, -2974, -78, -1669, -5948, 1669, -19842, 3338], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -59049, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [122402, 0, -245861, 0, 1057, 23213, 11171, 12042], [0, 0, 0, 0, 0, 0, 0, 0], [73760, 15020, -7510, -480, 7510, 17750, -17990, 240], [0, 0, 0, 0, 0, 0, 0, 0], [-79461, -11799, 45630, -2781, -11799, 1107, -2214, 2781], [0, 0, 0, 0, 0, 0, 0, 0], [47232, 25554, 21678, -20082, 0, -17174, -1454, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-47952, 12987, 20971, -10552, 17408, 22596, -34681, 10866], [0, 0, 0, 0, 0, 0, 0, 0], [-120690, 11610, 109080, 1431, 23220, -1431, 29052, -2862], [0, 0, 0, 0, 0, 0, 0, 0], [-2030, -2030, 43735, 5845, 2030, 5315, 0, 5845], [0, 0, 0, 0, 0, 0, 0, 0], [1513, 0, -1663, 0, -1363, -45351, -47776, 2425], [0, 0, 0, 0, 0, 0, 0, 0], [-124659, 1458, -729, -8262, 729, -5103, 972, 4131], [0, 0, 0, 0, 0, 0, 0, 0]]}