# Stored data for newform 731.2.k.b, downloaded from the LMFDB on 20 April 2024. {"label": "731.2.k.b", "space_label": "731.2.k", "level": 731, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504286855693019, "dim": 180, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [234897341502321, 9909769777383906, 207334981656246843, 3011312552582751219, 35603842950244814409, 350233411613421777348, 2897409023805544940506, 20893712711598650128238, 134543828092850549873014, 790486578598087707050091, 4600043128795107852506833, 24672650299101369956913645, 113256791322759450134130922, 500061162153224379474203008, 2290086388501510389444308614, 8545089392689653358819355222, 32815119310617928968942801135, 106925245074237526450410307273, 358529173377047921086468237154, 1016925818640909703269468218139, 3028470673583581559448823296320, 7514418458340273113280254622536, 20391946255507674542593146485271, 42355399832376302771372615034162, 110113314944209329664944108978057, 179299691566729805665529571643637, 490701192952318905468979014026855, 609712870349527579711335491922867, 1765932500656369636682877059425666, 1664031093404652261780838287286616, 5593260093897927044854278555629188, 4698576231695625386698950962811542, 18957886797182050600958253648159820, 12539234082072758717215678194570704, 56427473461049250595172814996469538, 22669829223964082205947103442275634, 148478421192457106252076015865327615, 19063003351227848493772777074030640, 361090508689814823152142796149509336, -34740748488425844654253618625175978, 831450077329704033193897883002698430, -238159444407065017481516917665000665, 1814365716466658125716608327564632640, -825746640385634925201685459530534390, 3749527632777952655823113577046590950, -2253159058171033997238667746001550623, 7299112738643456085938114605538313836, -5190577700506942637911281286777638563, 13234470316340226567285487113722922777, -10257451046845964995379436569006686129, 22035515106903050795650375396455385767, -17552601534436661334180274841816678882, 33319127861431433538686747188979228103, -26285520648970108624771031158072848159, 45540139084759593543612489340785603123, -34803772935693670099457685186262967861, 56412916852848192622342225725436292688, -41210734729479620493615357342486715996, 63841116960305714876721848817269036468, -44188193508454931303501098418336300242, 66644422511572892577914716837912031955, -43413165137171672906398099295078455253, 64662461878082480092034923847301881453, -39439770086392630134430878085981524949, 58495235717674155402353514913184508956, -33304928768149260886379345623619426943, 49292727265911325340045451432969383125, -26151750739704499568587115584572803832, 38617380881732110207770338874041535451, -19044291386642897000385641612997044271, 28123440339687130161571987525416627138, -12835354976876253129989786588286440218, 19090963011196852685391735831946587967, -8012169574291372755127283342399373174, 12137342299778675112133701659865278937, -4649014575621049245192664934135802700, 7265181659454132353828488057658937832, -2521559064974671022831908853747539082, 4113378053891983838228100982343453512, -1285811430711095762888596908451542815, 2210805749305287207992447307220266953, -619076632913111080363696656031943419, 1131316820097177474923100291950813155, -282176918797157713623394549821050738, 552625524704307552617897483521791476, -122013265578856131957752332103013418, 258266088125105272342182638547870886, -50173869851044025607090131114639243, 115677873237221559944303429831352180, -19691208449611389470362318855356655, 49717443319624258688703835725242324, -7406123766364331122913008384107390, 20523758940946114392943203889554967, -2679563247729506242718208109554058, 8145171483673903782743117760509555, -935931050379315600082805877593359, 3110416394234918509793356608858682, -317071446612796322928993700517450, 1143673105333934748354663485433009, -104823064654466715557549724898560, 405086093343948970051778999766464, -34050903961628780617256045421909, 138263506547071343819625935935456, -10929313435674982953937764403700, 45495986783313493869347868529934, -3474801227783161307341777605916, 14440755228367646987068566752416, -1093868628284672359193720068395, 4423864242695419274754472994908, -340195078971330127103763117806, 1308582413916766263751378262877, -104150232212491478312804287635, 373877798707713321154694795200, -31248870382634134699830845647, 103205922207848779827510974233, -9144472809685877753429259485, 27532583714874528743752352966, -2598376758253407057215441087, 7100042913508397962769747651, -714473707853748961931386913, 1770085302824222628039727559, -189649280279226802251223697, 426604562831505353095458979, -48503627441321484185146895, 99376820485511318004550776, -11933897086383648601206759, 22370670685299216706852864, -2821132216411347453443927, 4865157675436174577628698, -640158129358453253833966, 1021848548535327413319361, -139345889850588682109343, 207174372635095526861351, -29079767581432508531598, 40521983933076570466169, -5814240663545485129006, 7641685870126036530518, -1113116973440503225480, 1388642782662726515858, -203974900233525075546, 243039775833490434189, -35774949332709351712, 40947247670704099090, -6005996547340558075, 6637007826760501168, -964957045250734826, 1034218534022328929, -148267048236483138, 154803139225079602, -21764687475872815, 22234963091764851, -3049039329094421, 3060942732974356, -407209553340849, 403258069583959, -51771194696693, 50747422071711, -6248933789412, 6086180990952, -713120439090, 693555052205, -76555733421, 74803926942, -7689301603, 7598549987, -717994004, 722348320, -61675826, 63729368, -4769772, 5155277, -319362, 374892, -17353, 23692, -677, 1230, -14, 47, 0, 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": [0, 2, 2, -54], "traces": [180, 0, 2, -34, 2, 6, -54, 14, -18, -8, 4, -4, -5, 24, 11, -58, 30, -84, 0, -4, -28, -49, -23, -6, -14, 14, 20, -14, -60, -5, 36, 39, -39, 0, -14, 224, -184, 32, 58, 22, -48, -58, 2, 134, -54, -5, -35, 44, 174, -70, -2, -22, 8, 70, 51, -61, 72, 29, 35, 96, -40, 20, -35, -18, -17, -218, 16, 27, 50, 72, -20, -143, -4, -35, -45, -148, 40, -220, -12, -222, 12, 50, 16, -170, -2, 108, 78, -14, 55, 105, -53, -28, -142, 108, -49, -148, 73, 6, -73, 139, 18, 29, 48, -42, 66, -56, -36, -153, 7, 18, 40, 198, 38, -40, -52, 88, 34, 32, -23, 142, -46, 172, -320, 18, 58, 88, -28, -104, 42, 78, 37, -4, -32, 13, -158, 42, 71, -178, -78, 270, 58, -117, 16, 137, 94, 153, -75, 165, -97, 80, 122, -236, 18, -191, 58, 355, 0, -18, 124, -58, -86, -377, 103, -2, 340, 24, 42, -98, 19, -20, -98, 229, 164, 110, -94, 30, -102, -44, -82, 99, -101, 27, 154, 93, -48, -40, -4, 213, 115, -341, 160, 99, -156, -74, -93, -34, 119, 105, 76, -141, -124, 22, 61, 4, -78, 281, 79, 272, -408, 151, 41, 129, -152, -54, 53, 246, -42, -3, -196, -212, 12, -156, 119, -332, -168, 147, 98, -74, -157, 322, 336, -89, -176, 4, 28, -85, -3, 46, -42, -287, 99, 220, 106, -154, 154, -154, 26, -618, 184, -74, 198, -674, 224, 0, -4, -114, -246, 510, 48, 189, -215, 167, -13, 68, 20, 130, -347, -82, 71, 236, -154, 16, 334, 51, 12, -659, 26, -120, -70, -176, -76, 233, -26, -227, 30, -361, -122, 676, -30, 315, -348, 408, -104, 266, -734, -166, 106, -25, -103, 208, 72, 144, 55, 157, -150, -49, -6, -128, 32, -724, -182, 516, 200, -51, 39, 358, 110, -397, -11, 276, -162, 88, -35, -276, 266, 183, -68, -34, 48, -51, 309, -235, -2, 68, 125, -89, 256, -476, 16, 4, 114, -378, -426, 289, 174, 84, 65, -9, -41, -136, 292, 281, -79, 396, 101, 430, -14, -298, 8, 634, -106, -547, 138, 380, 51, -682, -38, -13, 170, -35, 68, -255, 74, -21, 145, 214, -102, 641, 64, 532, -536, 159, 113, 221, -243, -142, 125, -284, -242, -155, 23, -171, 94, -24, 273, -613, -40, 265, 112, -1006, -66, 307, 261, 284, -348, 365, 199, -36, 33, -212, -179, -192, -149, 509, -16, -78, 164, -89, -88, -1138, 298, 80, 402, -700, 21, -123, 235, -487, -110, 82, 152, -27, -291, 298, -217, -310, 162, 87, -164, 129, -42, 0, -118, -192, 177, 465, -57, -405, 152, 214, -130, -699, 343, -86, -54, -289, -4, 58, -20, -12, -21, 310, -92, 492, -189, 88, -718, -43, 124, 330, -333, -430, 258, -352, 403, -21, -349, -263, 76, 656, 269, -624, -178, 309, 379, -782, -159, 378, 66, -439, -144, 73, -24, 333, -279, -110, -102, 327, -62, 449, 73, 172, 44, -39, 97, -429, 84, 171, 634, 12, 111, 76, -18, -496, -112, 224, 224, 332, -58, 343, -271, 316, -98, 201, -338, 261, 6, 265, -275, -30, 420, 696, 34, -471, 176, 284, -143, -254, 10, 343, -104, -227, 416, -39, 11, 319, -64, 31, 27, 977, 22, 1052, -468, -438, -24, 5, -60, 388, 107, 338, 4, -199, 57, -326, 46, 290, 541, -316, 91, 497, 214, -250, 77, 15, -55, -761, -371, 0, -92, -201, -34, -30, 40, -30, -113, 10, -74, -84, -248, -190, 85, 23, -194, -448, -14, -198, -116, 179, -72, -983, -148, -200, 512, 800, -228, 238, -64, 408, 134, 446, -524, 56, -92, 83, 176, 193, 275, 612, 34, -688, 449, 326, -84, -807, 372, -424, 183, 257, -19, -868, 78, 255, 69, 245, -556, 531, 88, 188, -488, 445, 366, 505, -183, -8, 287, -60, -65, -373, -298, -254, 268, 364, 360, -551, 46, 397, 395, -1003, -79, 976, 44, -501, 47, 66, -191, -179, 164, -198, 251, -255, -211, 650, -77, -259, 653, 295, 279, -987, 350, -36, 40, -82, -58, 495, -141, -770, -282, 88, 416, 410, 18, 38, -661, -204, -286, 236, -22, 215, 718, -302, -141, -277, 166, 3, -30, -694, 30, 252, -53, -833, 89, -208, 125, -61, -190, -52, -688, 104, -88, -126, -139, 541, -163, 242, -790, 176, 296, -108, -264, 136, -9, 278, -24, -597, 69, -259, 236, 352, 365, -520, -378, 415, -50, -149, -290, 707, 119, 76, -343, -163, 176, -229, -127, 284, -319, -24, 69, 280, -309, -428, 238, 244, 34, -461, 33, 202, 584, -1400, 304, 549, 373, -408, -274, -596, 80, 149, -28, 262, -441, 930, 40, 12, -289, 134, 212, 421, -276, 116, 502, 148, -34, -1578, 47, -164, -156, -261, 271, -302, 28, -47, -329, -592, -592, 234, 167, 264, -225, 332, 183, -180, 126, -162, 383, 541, -966, 12, 332, 380, 258, -635, 207, -766, -76, 300, 289, -488, -165, 763, -182, -694, 178, 648, 64, -38, 39, 202, -496, 76, -615, 26, -122, 249, 206, 9, -100, -31, 134, 39, 342, -56, 57, 95, 668, -416, -407, 586, -56, -578, -1052, -75, 784, 699, 337, 553, 59, 120, -12, 571, -299, -280, -59, -7, 40, 14, 294, 917, 40, -372, 94, 257, 184, -421, -138, 22, 204, 108, 117, -221, -652, -103, 575, 511, -585, 1335, 232, 656, -1084, 325, 158, 299, -36, 260, 488, 604, 50, -1098, 186, -734, 972, 512, 396, -1210, 488, 872, 53, -1518, -287, -70, -134, 1005, -573, 545, -40, -599, -423, -196, -487, 222, -377, 915, -6, -403, 249, 42, -16, -1173, 196, -516, 490, 648, 192, -340, 171, -622, 322, -406, 118, 71, -157, -215, -640, -86, -318, 894, -400, 106, 340, 95, -237, -989, 574, 853, -65, 253, -151, 816, 8, -451, 40, 710, 294, -124, 69, -600, -1109, -490, 57, -4, -303, 763, -266, 48, -514, 636, 381, -1, -336, -1208, 347, -612, 318, -105, 43, -448, 82, 988, 673, -490, 55, 164], "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.b", "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}