# Stored data for newform 731.2.k.a, downloaded from the LMFDB on 23 April 2024. {"label": "731.2.k.a", "space_label": "731.2.k", "level": 731, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 687228322523, "dim": 180, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [8960497441281, -256471565306022, 16689291542058591, -160865227453883409, -440269585431761691, -56069653527013085772, 1665337118620762492642, 5963055387330785411970, 16556745135335272715546, 642720253010761750773103, 6924774115805673979804033, 24671751961821254036782005, 226461783883438288635165898, 574909663231729471749341088, 2739295332874143385614607918, 579339013718484379462236950, 16516377179914416002630904651, 35608643685673751264872534793, 451407096211210976258138971330, 1411296703497680860622606277023, 5532516343722812171226624252436, 11983029968304836694461978338764, 32113716733288016089969477038671, 60613107996342499880588728728750, 167877194547186470102388747073845, 393323808680389738962875234759677, 1164301722255407866494862374828059, 2863500688529433461356334379180643, 7266209623429103369128597113403834, 15764132043289985402102418412510288, 33668301053609256124662343935522200, 64126493110260826204201476568118806, 120414616051084204423380033578294256, 207664455551576460747341481657772048, 356186943763543784797020504377939710, 571917426298378563984648330987306090, 920594235601030696981483681735704923, 1403402789270799038705766928179584276, 2154090558594201704398308322604600568, 3153616216702220838997764821433413178, 4645245236752716268506498525463737758, 6539912024139129157199493775610975043, 9225356418007175093233977642050388596, 12442081591347972352014430525956324398, 16752789056449312707605812598262232258, 21571649034653490637464577454441491665, 27695834314193186853973665970658541928, 34018019490686165977891691672504850561, 41727088790389336180828919637966848641, 49026902470917687741712996734088247511, 57663985203310517945685295823445166103, 65133823949458103345611453846145436886, 73864726541516887032178651570500489711, 80432670268885833973420531259065003085, 88220186258885670656712464670148552079, 92688783158740471816637065610452803459, 98310149894864713884983375256189009260, 99531660111850157322094773189514412544, 101850443763776312095604670689605524040, 99023555824824590789288093327345407570, 97665895792332783762507408675420521271, 91036835054627170135759830135898802335, 86756996412965868020039633993904973285, 77669723856436321892436920425542483043, 71861216639384701093994469998348467264, 61961584046139513294709090716236978417, 55919971513093818331240930629304459589, 46497169615419172866592327781398308848, 41089049259585258621226838348122614595, 32927233867276815385586335837094839097, 28588892384214990985264414612302916158, 22040375915820826364939972059456560330, 18872157544738591032129360291455402807, 13967760930439444296624965471637378378, 11846163255895085687783411871441914681, 8398869580452800210938947662243708212, 7090853011981838213683026265429269044, 4801640696709795391256488056990743130, 4058001276270544536897336197989229096, 2613135737398484936675337425432090169, 2223884930216987722350577187357566505, 1354669172363575980016033371693453653, 1167970505737907176880084938300520071, 669532058902745391928668552335401122, 588123993011506933439676028050805856, 315910135854167707395188595736130218, 284079421816453603127079221959971546, 142535976283347066478822187930345125, 131708744662067102848457141703827440, 61595495414726400452455554334816569, 58643373486791011497345491091871308, 25532323159807382949939574559192166, 25079434833106823110114707060163879, 10170004445285443468863476896017426, 10299271442904707279007496652114615, 3901920511252395425447270480505949, 4059673666718186949646525088222658, 1446132898678521533330412201894274, 1535374478430012088040735414794105, 519137656331010702384715204316520, 557143712999513796914917724674556, 180830579596523077558025190179211, 194052516689420655367763769677044, 61151032504861319467214103904748, 64919545025265992918485074159546, 20067486996448486860583802963400, 20879109536548282588961718421296, 6385210779186902228860404281421, 6461198322624486445929874139940, 1968227760751885908728120381230, 1925471250262393771732105846505, 587276917087662213366307904129, 552973040472463814469562142008, 169481805097246844130384922321, 153139696176741034012610703865, 47267754559116203206635277551, 40918019844790131610699601458, 12731561792766758948575681937, 10552924119929564626157377851, 3310461665729781073611411811, 2627964808188306945693490979, 830795961804135407541268815, 632093765443297601992978399, 201209382741560187723991857, 146873573471376584830062528, 47020392310100463878683389, 32971619786732759489741252, 10600544962419538156034577, 7150969934042707242270906, 2305203428495678980528514, 1498269041451838163428813, 483491776288988676599897, 303227378355149144592875, 97797671229518656785982, 59268304467267617616233, 19073961825359006674818, 11184458798535396847710, 3585604595179692175188, 2036785509979488809122, 649354059549559178438, 357746617698722702725, 113234684403342472600, 60568154316649557114, 19002573015663037541, 9877343914510074860, 3066602158135169438, 1550107903246492489, 475396395775189254, 233820882676892274, 70698418995850693, 33851072248825263, 10070549034451655, 4696077035766332, 1371744079529251, 623143793221131, 178321246817211, 78913094680859, 22063474941116, 9508885823648, 2588867125870, 1086110096521, 286798469975, 117070327334, 29852542645, 11849642759, 2903607324, 1119398176, 261833266, 97785336, 21601100, 7779841, 1593150, 549556, 101083, 33112, 5195, 1598, 194, 55, 4, 1]]], "char_order": 7, "char_parity": 1, "char_degree": 6, "char_conductor": 43, "char_orbit_label": "k", "char_is_real": false, "Nk2": 2924, "analytic_conductor": 5.837064387755596, "level_radical": 731, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [731, 7, [173, 562], [7, 3]], "inner_twist_count": 2, "level_primes": [17, 43], "conrey_indexes": [35, 188, 256, 477, 494, 613], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 30, "sato_tate_group": "1.2.3.c7", "trace_display": [-4, -6, -6, 66], "traces": [180, -4, -6, -34, -6, -14, 66, 2, -26, -8, -12, -24, -5, -8, -1, -58, -30, 36, -24, -36, -28, 5, 27, -46, -38, 6, -36, -54, 28, -21, 36, 11, 5, -4, 6, 192, 164, 32, -34, 2, 42, -2, -22, 14, 58, -53, 21, -20, 166, 18, -6, 54, 8, -154, -5, -35, 8, 9, -13, -88, -34, -36, -31, -18, 9, 222, -48, -27, 2, -64, -42, 77, -44, -35, -21, 44, -32, 124, -96, 490, -12, -130, -8, 170, 22, -12, -90, -122, -81, 49, -27, -116, 18, -124, 117, 52, -79, -54, -39, -181, -50, 21, 8, 126, -206, -144, 120, 111, 57, -46, -20, -58, -90, 220, 40, -68, 22, -52, 3, -290, -50, -40, 184, -178, -112, -40, 32, 88, -122, -134, -15, -148, 76, 89, -126, 30, -69, 150, 90, -282, -38, 295, -58, -111, -98, 89, 81, -47, 79, 220, 62, -16, -26, 265, -38, -165, 44, 102, -72, -118, 50, 347, -105, 204, -24, 320, -50, -26, -45, 20, 46, -15, -132, -66, -118, -58, -50, 212, 30, -133, 109, 27, -78, -51, 48, -76, -12, -67, 79, 101, -64, 23, -72, -90, 159, -62, -9, -199, 0, 23, 124, -186, -15, -24, 66, -167, -15, -304, 700, -191, -81, 41, 60, 166, -183, -534, 10, 57, -96, 180, -12, -356, -181, 312, -24, -257, -74, 190, -73, -142, -76, -19, 126, -292, 0, 155, -91, 34, 22, -211, -123, -120, -18, -110, -94, -94, -86, 488, -80, -60, -26, 846, 172, -68, -8, 142, -46, 6, -280, 65, 115, 171, -113, -180, 104, 88, 233, -6, -201, -148, 202, -16, -70, -217, 72, 865, -190, -280, 278, 220, 20, -19, 46, -55, -130, 245, 46, -96, -30, 203, 556, -336, -120, -714, 674, -66, 30, -289, 163, 284, -264, -264, -241, 465, 330, -27, 186, -248, -426, 548, 138, -224, 20, 313, -33, -170, -142, -195, 161, -76, -74, 32, 11, -92, 98, 149, 136, -58, 46, 229, -27, -23, -70, 324, -387, 479, -184, -188, 32, -36, 26, 450, 270, -359, -626, -356, 57, -185, 331, -292, 600, -441, -19, 120, -79, 14, 14, -114, -184, -58, -170, 573, -202, 132, 219, 422, -116, -105, -2, -199, -204, -31, -46, -51, 225, -226, 236, -735, 38, -480, 720, -229, 105, -275, 277, -342, -279, -364, 102, 357, 27, 61, -234, 92, -247, 769, -152, -335, -344, 778, -64, -365, -47, 336, 476, 53, 47, -4, 141, -104, 273, 424, -21, 69, 56, 146, -176, -267, 188, 836, -62, 124, -262, 996, -45, -99, -17, 573, -190, -114, -240, -183, 89, 114, 277, 98, -182, 367, 308, 81, -146, -8, 6, -156, -215, -167, -41, 987, -68, -182, 158, 259, 231, -554, -358, 301, 108, 254, -36, 20, -129, -158, -64, -544, -177, -720, 538, -303, -314, 18, 443, -166, -102, -424, -77, -19, -169, 69, -148, -392, -357, 478, 246, -251, 19, 578, 79, -538, -230, -211, 488, 9, -28, 149, 333, -110, 30, 107, -120, -331, 133, 316, -276, 127, -527, 959, -436, 195, -46, 84, -45, -132, 126, 472, -16, -174, -88, -356, -166, 187, -149, -432, 198, -407, 214, -163, -6, -351, 313, 4, -496, -104, 274, 421, 72, 4, -203, 336, -174, 79, -70, 309, -168, 11, 531, -53, -240, -265, 397, -267, 202, -268, 692, -194, -244, -623, 120, 224, -85, -326, -44, 53, -271, 632, 158, -330, -447, 586, 51, -895, -146, 260, 255, -641, -91, -493, 149, -4, 388, -125, 154, 354, 248, -258, 135, -118, 62, 248, -352, 166, -83, -67, -266, -468, -50, -550, -92, 7, -184, 747, -168, -326, -128, -152, -182, -206, 488, 0, -758, -282, 720, -88, 24, -361, 310, 581, -325, -656, -34, 884, -151, -66, -28, 1315, -68, -340, -425, -19, -11, -128, -210, -379, -119, -507, 602, -585, -124, -4, 1040, -69, 34, 289, 105, -88, -253, 60, 31, 59, -158, 910, -128, 836, -72, 937, -114, -859, 43, 1069, -171, -320, -188, 547, 57, -218, 253, -331, 164, 466, 75, 219, 217, -814, 201, 85, -31, -97, -121, 973, -338, 16, -304, 46, 132, -65, -357, 968, 758, 344, -352, -302, 136, 10, -149, 552, -406, -776, -14, 31, -114, -702, 167, 195, -194, -689, 134, 18, -286, -620, -33, 879, -39, -448, -331, -51, -126, -96, 580, 128, -80, -602, 131, -639, -155, -786, 850, 558, -320, -140, 280, 664, -15, 214, -56, -75, -231, 453, -132, -312, -351, 1056, -294, -553, -502, 471, 514, 123, -449, 28, 217, -59, -332, -653, -157, -50, 333, -276, -135, -780, -17, -60, 34, 514, -54, 139, 37, 334, -240, 720, 16, 617, 117, 384, -290, -296, -64, -835, 0, -290, 325, -518, -288, 24, 843, -310, -324, -699, 296, 900, -74, -828, -274, 558, -321, -720, 532, 231, 55, -334, 0, 817, -57, 264, 280, -294, -347, -32, 159, -532, -349, -724, 458, -70, 35, -595, 346, 120, -20, 764, -402, 841, -97, 112, -376, -1188, -1143, 552, -149, -825, -54, 108, 78, -64, -72, -282, 67, -358, -168, -328, 203, 76, -94, 77, 712, -113, 310, 49, -268, 263, 30, 116, -243, -117, -100, 48, -463, -608, 372, 850, 1484, -225, -196, -293, -67, 81, 227, -584, 36, -393, 205, -138, 217, -659, 400, -44, -390, -483, 418, 1304, 466, -271, 108, 1447, -514, 54, -600, 136, -419, 999, 368, -171, 443, -273, 87, -137, -40, 792, 980, 209, -338, -1045, 36, -108, 4, 584, 198, -42, -270, 386, 348, -360, -536, 926, -80, -528, 61, 1418, 373, -154, -166, 485, 813, -71, -284, -1375, -127, -488, 97, -4, 161, -99, -90, 309, -107, 274, -40, 1187, 312, 128, -470, 996, 64, -62, -221, 174, 1054, 266, -814, -1009, 373, -487, 356, -14, -334, -198, 324, -114, -646, -241, -195, 147, -166, -615, -97, 21, -199, -48, -228, 229, 50, -82, -234, 462, 445, 648, 207, -154, 189, -628, 19, -525, -364, -376, 490, 1396, -531, -19, 600, 824, -25, -292, -178, -101, -161, 912, -774, 1096, -391, 582, -217, -658], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 43, 5, 1, 7, 0]], "char_orbit_index": 11, "prim_orbit_index": 5, "minimal_twist": "731.2.k.a", "char_is_minimal": true, "conrey_index": 35, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}