Magma V2.7-1 Mon Jan 29 2001 02:56:08 on modular [Seed = 2033686729] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2501 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.821 s) III. 3-term relations. Computing quotient by 868 relations. Form quot and then images (0.54 s) (total time to create space = 1.411 s) Computing cuspidal part of Full Modular symbols space of level 2501, weight 2, and dimension 218 Computing new part of Modular symbols space of level 2501, weight 2, and dimension 215. Computing 41-new part of Modular symbols space of level 2501, weight 2, and dimension 215. Computing space of modular symbols of level 61 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.02 s) III. 3-term relations. Computing quotient by 22 relations. Form quot and then images (0.009 s) (total time to create space = 0.029 s) Computing index-1 degeneracy map from level 2501 to 61. (0.051 s) Computing index-41 degeneracy map from level 2501 to 61. (1.41 s) Computing index-1 degeneracy map from level 61 to 2501. (0.67 s) Computing index-41 degeneracy map from level 61 to 2501. (0.87 s) Computing DualVectorSpace of Modular symbols space of level 2501, weight 2, and dimension 215. Computing complement of Modular symbols space of level 2501, weight 2, and dimension 215 Computing representation of Modular symbols space of level 2501, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 218. (0.221 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2501, weight 2, and dimension 3 Computing 61-new part of Modular symbols space of level 2501, weight 2, and dimension 215. Computing space of modular symbols of level 41 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.01 s) III. 3-term relations. Computing quotient by 14 relations. Form quot and then images (0.011 s) (total time to create space = 0.021 s) Computing index-1 degeneracy map from level 2501 to 41. (0.049 s) Computing index-61 degeneracy map from level 2501 to 41. (2.36 s) Computing index-1 degeneracy map from level 41 to 2501. (0.869 s) Computing index-61 degeneracy map from level 41 to 2501. (1.001 s) Finding newform decomposition of Modular symbols space of level 2501, weight 2, and dimension 215. Computing cuspidal part of Modular symbols space of level 2501, weight 2, and dimension 215 Decomposing space of level 2501 and dimension 201 using T_2. (will stop at 434) Computing T_2 on dual space of dimension 201. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing characteristic polynomial of T_2. x^201 + x^200 - 302*x^199 - 302*x^198 + 44849*x^197 + 44845*x^196 - 4366104*x^195 - 4364924*x^194 + 313400424*x^193 + 313229332*x^192 - 17689372328*x^191 - 17673118468*x^190 + 817662333998*x^189 + 816524371790*x^188 - 31829476670150*x^187 - 31766860947946*x^186 + 1064982850781218*x^185 + 1062162773562006*x^184 - 31107106103345936*x^183 - 31000200081676384*x^182 + 802934856748999884*x^181 + 799453354096801752*x^180 - 18495760695917386894*x^179 - 18396837766207583334*x^178 + 383300932867926658639*x^177 + 380818436751503351363*x^176 - 7194622646130347475524*x^175 - 7139057207772076729956*x^174 + 123012693659381093293852*x^173 + 121894426341912384068960*x^172 - 1925220651350918445916606*x^171 - 1904848762250836949227382*x^170 + 27696520369758077800225761*x^169 + 27358665426684276869299677*x^168 - 367597162803310008910373692*x^167 - 362471470725709314521661928*x^166 + 4515567474068564038449111167*x^165 + 4444131278517222531944170983*x^164 - 51483861181413769291553914230*x^163 - 50565929203363850341667585634*x^162 + 546176659455671121162757408805*x^161 + 535266915647814841394623394221*x^160 - 5403342151291624149947027180962*x^159 - 5283074145218379775208224634446*x^158 + 49948087193334407369093824929780*x^157 + 48715277829082672053586510155980*x^156 - 432186453476710981154198266367554*x^155 - 420410124706965181047082590215374*x^154 + 3505971079289000077425711866883463*x^153 + 3400933304672865050104794836215787*x^152 - 26702307201589852251485391588278206*x^151 - 25825982688844743882158812921825870*x^150 + 191182472121577598794865626083796689*x^149 + 184333104866577353270205176822495145*x^148 - 1288265715417166060880181280806673742*x^147 - 1238041480206293936214740543198861346*x^146 + 8178421249547320471390244778365095062*x^145 + 7832480402454005295946795476612892286*x^144 - 48960153892882418864388275076329451292*x^143 - 46719330156638622932172354600250364752*x^142 + 276621613767273109011658463888464663716*x^141 + 262957809858383114483315065964150548920*x^140 - 1476120869789657611325531908800620198098*x^139 - 1397617529728783996032117665293669602094*x^138 + 7444531079088146122861504126759851290169*x^137 + 7019217139332243816551300478577869566889*x^136 - 35504784110714310958082468247310096728034*x^135 - 33330332146984705895852330007346231454814*x^134 + 160211843496748738095988916914608101111864*x^133 + 149714319094968937624946232470670611810108*x^132 - 684315365094904788348446087123695254810054*x^131 - 636434055078119715219629311964720904811466*x^130 + 2767839795673337577608814407232702163449427*x^129 + 2561396066085640703561706146101264096384671*x^128 - 10604555548190420586684622027429211336313876*x^127 - 9762812243109044134830127868677290652142484*x^126 + 38497352396490093816920423722530446959079660*x^125 + 35250528763473068574618796702605336211736864*x^124 - 132450430146543762498574981739254803381214032*x^123 - 120598966007059581754978211837060225970563436*x^122 + 431951973643053867112128020674017311923517399*x^121 + 391004360898881617001518243100046383907059347*x^120 - 1335462276628820466108060233269944161804377970*x^119 - 1201521038992379581500570105278807240698036126*x^118 + 3914498081846154572615001682312635113883711652*x^117 + 3499646389787245342604520053218046938869741460*x^116 - 10878859867604695819615413255723723709920745900*x^115 - 9662095151622053006304288302328992455171184512*x^114 + 28664795917717450173613259174044037358903545509*x^113 + 25285103206472665226691841771394486393199164601*x^112 - 71605933754608848839639630061828449485326397064*x^111 - 62715841155067763867953959993509830665026314684*x^110 + 169567197433050228265209906520992289565013918083*x^109 + 147422191683632975971811497943444364875246502491*x^108 - 380598446147375410339314159382072036065494489954*x^107 - 328365022030517998579977404391232553156194914102*x^106 + 809554327970609341493715951504061613720632730006*x^105 + 692908778130462711309191048463219199175474278906*x^104 - 1631481515954562690239620805399902595527975096398*x^103 - 1384900363980492745788557392243306702998887739794*x^102 + 3114301780842297264752238203352156537572214705307*x^101 + 2620980297989801199370106344203374401137151789291*x^100 - 5629224704752084484873803888413498140541567221726*x^99 - 4695397590477469501285592478033863876696563835974*x^98 + 9631510990722836276585439287592164597284578645706*x^97 + 7959502462793319607721237716683471758277791335790*x^96 - 15592947028183786942148820642063305824497698271128*x^95 - 12762228947059038424373042452987907991734210125488*x^94 + 23875969803616151322448401432697923353738008681202*x^93 + 19346237050118859111518712401149507131165558550822*x^92 - 34560874928216934167764136291110128702622088277022*x^91 - 27712634746665567072628342685956924274163364165358*x^90 + 47268465548100535265316774427838725242530330580043*x^89 + 37491388629293643807727985507646860430013491626219*x^88 - 61048269440187534571414929707507238486877252872098*x^87 - 47873709152355746403920324406129294327126336179378*x^86 + 74408329562239318962641628204142798943925177314600*x^85 + 57662240045864588654595338527487945710335837621924*x^84 - 85531477152928874558117855884829182175915722909948*x^83 - 65464905899212739533023834757292824647125683470904*x^82 + 92656173124659686028414088768213607099853694290437*x^81 + 70003146667529567699360119080720488308757546966913*x^80 - 94521697174637981397599789247801013869278638560250*x^79 - 70446982410824410537923993224113657102560020767694*x^78 + 90727374956581186426277265509159456831405536655050*x^77 + 66659189743214147498893372820158739179878862365170*x^76 - 81867374522651962216415073650265121856968530171590*x^75 - 59251464523347122280183565126838213623921970098966*x^74 + 69380748759468835293116984783643634082168036269097*x^73 + 49424026515674095719993689646092905065499802282849*x^72 - 55167745408017754840881010657909913923257508349016*x^71 - 38645923140683987598223485116496459258348652734364*x^70 + 41113390384972925589405875892684720052450430287255*x^69 + 28293594748527093909420678614139574734316604620999*x^68 - 28683774014969019145286706541184240216365653709644*x^67 - 19370779845143650083888476008581673996580719419628*x^66 + 18711773421401472778844653450016378533426776002537*x^65 + 12385019677678072898819966056871130386817340796321*x^64 - 11398701474469804123821163882927460213154373518100*x^63 - 7384313782240562947561831006765308426578464356752*x^62 + 6475250789951495526094624835561021114551718724601*x^61 + 4099340549054595834987650423867016967790088471525*x^60 - 3425134206919123693765574175636177090512951757660*x^59 - 2115357439645767647023014447038921920225644412524*x^58 + 1684356323113760374747294149318960702925959089144*x^57 + 1012835007069715077074587817227484082336501221740*x^56 - 768765532914472512569814333836175708531500591214*x^55 - 449092508827856053950793745369344729311960459578*x^54 + 325067379811175816407267128569972818912544752010*x^53 + 184018981950071946919226302360852763202832935518*x^52 - 127095613611382382311589544196576982702403258200*x^51 - 69523029570013831361851314919152595765869425560*x^50 + 45852056627879179288888045855928311346181383630*x^49 + 24157683427819953582018927498072490958194874186*x^48 - 15229250113011490328410627500630998958710286248*x^47 - 7699507836396361389165554955288813665033469132*x^46 + 4645439614335876005170159307939684128856368263*x^45 + 2244172740073720370361337085337585279058438159*x^44 - 1297911945824200806487455837426407860537084008*x^43 - 596217726439003160354637043977186483234502256*x^42 + 331180109301987797551769700129749942913641075*x^41 + 143853282989494212973031642525573038137845671*x^40 - 76927971765568288366229137539726145693918454*x^39 - 31392299092624544052146681505713983108544670*x^38 + 16208838747864434800021813999302693264574250*x^37 + 6167499247168774442598407293684028368196018*x^36 - 3085531352120701886147352986563267741694498*x^35 - 1085156064118900277998640834898223884430750*x^34 + 528274803012934888432737654781692535828721*x^33 + 169956227151761390680872710174451313830221*x^32 - 80930751274768145994277138856986010364470*x^31 - 23526680036112667521630390028982292864954*x^30 + 11028875003119002833791262172250943166017*x^29 + 2854235764495528630924194649516935214413*x^28 - 1327822806794234646835321448147202154674*x^27 - 300362069567667966208093924309494336110*x^26 + 140102609999290813280810819276762519879*x^25 + 27063826066971322980276381442304905343*x^24 - 12831747439964297846439917587973553648*x^23 - 2052626144241413383937688154147633784*x^22 + 1008361694338200184679625735694737153*x^21 + 127940037750481390312064878939365357*x^20 - 67020789718382345390821688084212404*x^19 - 6313993375277974303041144588755744*x^18 + 3699793374005130894391251431381271*x^17 + 230216549049557880626206128775703*x^16 - 165650256751416200646737232197110*x^15 - 5155144430208078362765995323286*x^14 + 5822178574905047139637511138554*x^13 + 5481073924800127954410590434*x^12 - 153117698829001851595237827756*x^11 + 4383171520925131372615180220*x^10 + 2784368551831239381889087153*x^9 - 163985745163703706009406091*x^8 - 29817325465522399865126424*x^7 + 2845000236993117985193328*x^6 + 105751282870331280890112*x^5 - 20470501152827091729312*x^4 + 670040860893002282880*x^3 - 213776079305603328*x^2 - 132464511631984896*x + 603724639714560 time = 47.24 Factoring characteristic polynomial. [ , , , ] time = 1.42 Cutting out subspace using f(T_2), where f=x^43 + 4*x^42 - 49*x^41 - 208*x^40 + 1088*x^39 + 4964*x^38 - 14465*x^37 - 72153*x^36 + 128006*x^35 + 714826*x^34 - 790663*x^33 - 5118521*x^32 + 3455195*x^31 + 27412048*x^30 - 10423964*x^29 - 112089335*x^28 + 19219609*x^27 + 354184177*x^26 - 7323286*x^25 - 869842248*x^24 - 77300540*x^23 + 1661514451*x^22 + 278805587*x^21 - 2458854565*x^20 - 548647998*x^19 + 2795379858*x^18 + 725424191*x^17 - 2408608108*x^16 - 674099391*x^15 + 1542903346*x^14 + 440791060*x^13 - 715849278*x^12 - 198270555*x^11 + 232486602*x^10 + 58659145*x^9 - 50604258*x^8 - 10615388*x^7 + 6965938*x^6 + 1044366*x^5 - 545989*x^4 - 42007*x^3 + 18543*x^2 - 40*x - 4. Cutting out subspace using f(T_2), where f=x^44 + 3*x^43 - 57*x^42 - 175*x^41 + 1490*x^40 + 4704*x^39 - 23677*x^38 - 77330*x^37 + 255547*x^36 + 870168*x^35 - 1981941*x^34 - 7108160*x^33 + 11390690*x^32 + 43621953*x^31 - 49263394*x^30 - 205328541*x^29 + 160881882*x^28 + 750291410*x^27 - 393090149*x^26 - 2140836548*x^25 + 698127846*x^24 + 4773992247*x^23 - 835338054*x^22 - 8290490020*x^21 + 505216923*x^20 + 11124475176*x^19 + 246326439*x^18 - 11393175935*x^17 - 890027471*x^16 + 8753840497*x^15 + 957587944*x^14 - 4931449958*x^13 - 580338083*x^12 + 1976803147*x^11 + 207515545*x^10 - 542130611*x^9 - 40430902*x^8 + 96379178*x^7 + 3053660*x^6 - 10225107*x^5 + 167094*x^4 + 557214*x^3 - 33285*x^2 - 11124*x + 972. Cutting out subspace using f(T_2), where f=x^57 - 4*x^56 - 84*x^55 + 348*x^54 + 3302*x^53 - 14242*x^52 - 80689*x^51 + 364625*x^50 + 1373043*x^49 - 6551545*x^48 - 17267694*x^47 + 87857776*x^46 + 166175337*x^45 - 912987660*x^44 - 1249204887*x^43 + 7535136027*x^42 + 7414468537*x^41 - 50226848964*x^40 - 34806753658*x^39 + 273531489498*x^38 + 128012419556*x^37 - 1226577039095*x^36 - 357835971880*x^35 + 4551558501133*x^34 + 695328638798*x^33 - 14014530094433*x^32 - 606218039532*x^31 + 35833409781274*x^30 - 1516745784510*x^29 - 76011047883276*x^28 + 8208686663590*x^27 + 133420462924173*x^26 - 20911347198588*x^25 - 192972262961568*x^24 + 36833337290185*x^23 + 228621182935320*x^22 - 48547181724585*x^21 - 220128727003907*x^20 + 49069341516054*x^19 + 170522899944845*x^18 - 38256373223215*x^17 - 104909376180372*x^16 + 22935749704876*x^15 + 50411468647678*x^14 - 10486156171529*x^13 - 18510400943234*x^12 + 3610983296655*x^11 + 5041613767726*x^10 - 920430749432*x^9 - 976187901798*x^8 + 169024338659*x^7 + 125737899090*x^6 - 21278042403*x^5 - 9548773178*x^4 + 1651824885*x^3 + 317565335*x^2 - 59552376*x + 294060. Cutting out subspace using f(T_2), where f=x^57 - 2*x^56 - 90*x^55 + 178*x^54 + 3818*x^53 - 7462*x^52 - 101535*x^51 + 195963*x^50 + 1899049*x^49 - 3616895*x^48 - 26565640*x^47 + 49896638*x^46 + 288582787*x^45 - 534184624*x^44 - 2494926917*x^43 + 4548587173*x^42 + 17454964961*x^41 - 31323528234*x^40 - 99953606294*x^39 + 176449980216*x^38 + 472057798256*x^37 - 819262859145*x^36 - 1847343114740*x^35 + 3149891293093*x^34 + 6004400543452*x^33 - 10051081736991*x^32 - 16214191985886*x^31 + 26621772639486*x^30 + 36321415960686*x^29 - 58423301241998*x^28 - 67275756468168*x^27 + 105840886561139*x^26 + 102526013225748*x^25 - 157392803725036*x^24 - 127704171191463*x^23 + 190640035810464*x^22 + 128927855981245*x^21 - 186187125248153*x^20 - 104447113859474*x^19 + 144741454596935*x^18 + 67108463436113*x^17 - 88114177850672*x^16 - 33747171086824*x^15 + 41135320600720*x^14 + 13086586567077*x^13 - 14325613944932*x^12 - 3846053909341*x^11 + 3581860938426*x^10 + 836827765148*x^9 - 607036059318*x^8 - 129481669707*x^7 + 63264863026*x^6 + 13082663123*x^5 - 3323446342*x^4 - 697066433*x^3 + 49275711*x^2 + 8158360*x - 528052. Computing representation of Modular symbols space of level 2501, weight 2, and dimension 43. Goal dimension = 43. Computing T_2 on dual space of dimension 43. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^43 + 4*x^42 - 49*x^41 - 208*x^40 + 1088*x^39 + 4964*x^38 - 14465*x^37 - 72153*x^36 + 128006*x^35 + 714826*x^34 - 790663*x^33 - 5118521*x^32 + 3455195*x^31 + 27412048*x^30 - 10423964*x^29 - 112089335*x^28 + 19219609*x^27 + 354184177*x^26 - 7323286*x^25 - 869842248*x^24 - 77300540*x^23 + 1661514451*x^22 + 278805587*x^21 - 2458854565*x^20 - 548647998*x^19 + 2795379858*x^18 + 725424191*x^17 - 2408608108*x^16 - 674099391*x^15 + 1542903346*x^14 + 440791060*x^13 - 715849278*x^12 - 198270555*x^11 + 232486602*x^10 + 58659145*x^9 - 50604258*x^8 - 10615388*x^7 + 6965938*x^6 + 1044366*x^5 - 545989*x^4 - 42007*x^3 + 18543*x^2 - 40*x - 4 p = %o, dimension = %o. 2 43 Computing representation of Modular symbols space of level 2501, weight 2, and dimension 44. Goal dimension = 44. Computing T_2 on dual space of dimension 44. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^44 + 3*x^43 - 57*x^42 - 175*x^41 + 1490*x^40 + 4704*x^39 - 23677*x^38 - 77330*x^37 + 255547*x^36 + 870168*x^35 - 1981941*x^34 - 7108160*x^33 + 11390690*x^32 + 43621953*x^31 - 49263394*x^30 - 205328541*x^29 + 160881882*x^28 + 750291410*x^27 - 393090149*x^26 - 2140836548*x^25 + 698127846*x^24 + 4773992247*x^23 - 835338054*x^22 - 8290490020*x^21 + 505216923*x^20 + 11124475176*x^19 + 246326439*x^18 - 11393175935*x^17 - 890027471*x^16 + 8753840497*x^15 + 957587944*x^14 - 4931449958*x^13 - 580338083*x^12 + 1976803147*x^11 + 207515545*x^10 - 542130611*x^9 - 40430902*x^8 + 96379178*x^7 + 3053660*x^6 - 10225107*x^5 + 167094*x^4 + 557214*x^3 - 33285*x^2 - 11124*x + 972 p = %o, dimension = %o. 2 44 Computing representation of Modular symbols space of level 2501, weight 2, and dimension 57. Goal dimension = 57. Computing T_2 on dual space of dimension 57. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^57 - 4*x^56 - 84*x^55 + 348*x^54 + 3302*x^53 - 14242*x^52 - 80689*x^51 + 364625*x^50 + 1373043*x^49 - 6551545*x^48 - 17267694*x^47 + 87857776*x^46 + 166175337*x^45 - 912987660*x^44 - 1249204887*x^43 + 7535136027*x^42 + 7414468537*x^41 - 50226848964*x^40 - 34806753658*x^39 + 273531489498*x^38 + 128012419556*x^37 - 1226577039095*x^36 - 357835971880*x^35 + 4551558501133*x^34 + 695328638798*x^33 - 14014530094433*x^32 - 606218039532*x^31 + 35833409781274*x^30 - 1516745784510*x^29 - 76011047883276*x^28 + 8208686663590*x^27 + 133420462924173*x^26 - 20911347198588*x^25 - 192972262961568*x^24 + 36833337290185*x^23 + 228621182935320*x^22 - 48547181724585*x^21 - 220128727003907*x^20 + 49069341516054*x^19 + 170522899944845*x^18 - 38256373223215*x^17 - 104909376180372*x^16 + 22935749704876*x^15 + 50411468647678*x^14 - 10486156171529*x^13 - 18510400943234*x^12 + 3610983296655*x^11 + 5041613767726*x^10 - 920430749432*x^9 - 976187901798*x^8 + 169024338659*x^7 + 125737899090*x^6 - 21278042403*x^5 - 9548773178*x^4 + 1651824885*x^3 + 317565335*x^2 - 59552376*x + 294060 p = %o, dimension = %o. 2 57 Computing representation of Modular symbols space of level 2501, weight 2, and dimension 57. Goal dimension = 57. Computing T_2 on dual space of dimension 57. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^57 - 2*x^56 - 90*x^55 + 178*x^54 + 3818*x^53 - 7462*x^52 - 101535*x^51 + 195963*x^50 + 1899049*x^49 - 3616895*x^48 - 26565640*x^47 + 49896638*x^46 + 288582787*x^45 - 534184624*x^44 - 2494926917*x^43 + 4548587173*x^42 + 17454964961*x^41 - 31323528234*x^40 - 99953606294*x^39 + 176449980216*x^38 + 472057798256*x^37 - 819262859145*x^36 - 1847343114740*x^35 + 3149891293093*x^34 + 6004400543452*x^33 - 10051081736991*x^32 - 16214191985886*x^31 + 26621772639486*x^30 + 36321415960686*x^29 - 58423301241998*x^28 - 67275756468168*x^27 + 105840886561139*x^26 + 102526013225748*x^25 - 157392803725036*x^24 - 127704171191463*x^23 + 190640035810464*x^22 + 128927855981245*x^21 - 186187125248153*x^20 - 104447113859474*x^19 + 144741454596935*x^18 + 67108463436113*x^17 - 88114177850672*x^16 - 33747171086824*x^15 + 41135320600720*x^14 + 13086586567077*x^13 - 14325613944932*x^12 - 3846053909341*x^11 + 3581860938426*x^10 + 836827765148*x^9 - 607036059318*x^8 - 129481669707*x^7 + 63264863026*x^6 + 13082663123*x^5 - 3323446342*x^4 - 697066433*x^3 + 49275711*x^2 + 8158360*x - 528052 p = %o, dimension = %o. 2 57 Computing cuspidal part of Full Modular symbols space of level 61, weight 2, and dimension 5 Computing cuspidal part of Modular symbols space of level 61, weight 2, and dimension 4 Computing new part of Modular symbols space of level 61, weight 2, and dimension 4. Computing 61-new part of Modular symbols space of level 61, weight 2, and dimension 4. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 61 and dimension 4 using T_2. (will stop at 434) Computing T_2 on dual space of dimension 4. Computing DualVectorSpace of Modular symbols space of level 61, weight 2, and dimension 4. Computing complement of Modular symbols space of level 61, weight 2, and dimension 4 Computing representation of Modular symbols space of level 61, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 5. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 61, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^4 - 4*x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x^3 - x^2 - 3*x + 1. Computing representation of Modular symbols space of level 61, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 61, weight 2, and dimension 3. Computing complement of Modular symbols space of level 61, weight 2, and dimension 3 Computing DualVectorSpace of Modular symbols space of level 61, weight 2, and dimension 2. Goal dimension = 2. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 2. (0 s) %o x^2 - 2*x - 3 p = 2, dimension = 2. Computing complement of Modular symbols space of level 61, weight 2, and dimension 2 Computing cuspidal part of Full Modular symbols space of level 41, weight 2, and dimension 4 Computing cuspidal part of Modular symbols space of level 41, weight 2, and dimension 3 Computing new part of Modular symbols space of level 41, weight 2, and dimension 3. Computing 41-new part of Modular symbols space of level 41, weight 2, and dimension 3. Decomposing space of level 41 and dimension 3 using T_2. (will stop at 434) Computing T_2 on dual space of dimension 3. Computing DualVectorSpace of Modular symbols space of level 41, weight 2, and dimension 3. Computing complement of Modular symbols space of level 41, weight 2, and dimension 3 Computing representation of Modular symbols space of level 41, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 4. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 41, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^3 + x^2 - 5*x - 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x^3 + x^2 - 5*x - 1. Sorting ... 1.719 seconds. Computing T_3 on dual space of dimension 43. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 43. T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 43. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 43. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 43. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). Computing T_17 on dual space of dimension 43. T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 43. T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 43. T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). Computing T_29 on dual space of dimension 43. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 43. T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 43. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 44. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 44. T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 44. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 44. T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 44. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). Computing T_17 on dual space of dimension 44. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). Computing T_19 on dual space of dimension 44. T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 44. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 44. T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 44. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 44. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 57. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 57. T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 57. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 57. T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 57. T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). Computing T_17 on dual space of dimension 57. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 57. T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). Computing T_23 on dual space of dimension 57. T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). Computing T_29 on dual space of dimension 57. T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 57. T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 57. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 57. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 57. T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 57. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 57. T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 57. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 57. T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). Computing T_19 on dual space of dimension 57. T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 57. T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 57. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 57. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 57. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). Computing q-expansion. T_2 sparse... (0.009 s). T_3 sparse... (0 s). T_5 sparse... (0.009 s). T_7 sparse... (0.009 s). T_11 sparse... (0 s). T_13 sparse... (0.009 s). T_17 sparse... (0.009 s). T_19 sparse... (0 s). T_23 sparse... (0.009 s). T_29 sparse... (0.01 s). T_31 sparse... (0.01 s). T_37 sparse... (0.01 s). (0.94 s) Computing q-expansion. (1.01 s) Computing q-expansion. (3 s) Computing q-expansion. (2.831 s) Computing character group of torus of J_0(41*61)/F_41. 338.519 seconds. Computing T_2 on space of dimension 43. (0.199 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing character group of torus of J_0(61*41)/F_61. 335.21 seconds. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 44. (0.241 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 57. (0.279 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 57. (0.289 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_3 on space of dimension 43. Computing T_3 on space of dimension 218. (0.069 s) (0.319 s) Computing T_5 on space of dimension 43. Computing T_5 on space of dimension 218. (0.099 s) (0.369 s) Computing T_7 on space of dimension 43. Computing T_7 on space of dimension 218. (0.121 s) (0.42 s) Computing T_11 on space of dimension 43. Computing T_11 on space of dimension 218. (0.17 s) (0.52 s) Computing T_13 on space of dimension 43. Computing T_13 on space of dimension 218. (0.21 s) (0.57 s) Computing T_17 on space of dimension 43. Computing T_17 on space of dimension 218. (0.27 s) (0.69 s) Computing T_19 on space of dimension 43. Computing T_19 on space of dimension 218. (0.289 s) (0.679 s) Computing T_23 on space of dimension 43. Computing T_23 on space of dimension 218. (0.35 s) (0.75 s) Computing T_29 on space of dimension 43. Computing T_29 on space of dimension 218. (0.451 s) (0.86 s) Computing T_31 on space of dimension 43. Computing T_31 on space of dimension 218. (0.469 s) (0.88 s) Computing T_37 on space of dimension 43. Computing T_37 on space of dimension 218. (0.579 s) (1.069 s) Computing T_3 on space of dimension 44. (0.33 s) Computing T_5 on space of dimension 44. (0.39 s) Computing T_7 on space of dimension 44. (0.42 s) Computing T_11 on space of dimension 44. (0.43 s) Computing T_13 on space of dimension 44. (0.44 s) Computing T_17 on space of dimension 44. (0.43 s) Computing T_19 on space of dimension 44. (0.46 s) Computing T_23 on space of dimension 44. (0.449 s) Computing T_29 on space of dimension 44. (0.489 s) Computing T_31 on space of dimension 44. (0.46 s) Computing T_37 on space of dimension 44. (0.489 s) Computing T_3 on space of dimension 57. (0.341 s) Computing T_5 on space of dimension 57. (0.449 s) Computing T_7 on space of dimension 57. (0.489 s) Computing T_11 on space of dimension 57. (0.539 s) Computing T_13 on space of dimension 57. (0.539 s) Computing T_17 on space of dimension 57. (0.589 s) Computing T_19 on space of dimension 57. (0.571 s) Computing T_23 on space of dimension 57. (0.569 s) Computing T_29 on space of dimension 57. (0.59 s) Computing T_31 on space of dimension 57. (0.619 s) Computing T_37 on space of dimension 57. (0.629 s) Computing T_3 on space of dimension 57. (0.329 s) Computing T_5 on space of dimension 57. (0.449 s) Computing T_7 on space of dimension 57. (0.451 s) Computing T_11 on space of dimension 57. (0.54 s) Computing T_13 on space of dimension 57. (0.519 s) Computing T_17 on space of dimension 57. (0.569 s) Computing T_19 on space of dimension 57. (0.56 s) Computing T_23 on space of dimension 57. (0.57 s) Computing T_29 on space of dimension 57. (0.599 s) Computing T_31 on space of dimension 57. (0.631 s) Computing T_37 on space of dimension 57. (0.709 s) Computing T_1 on space of dimension 218. (0 s) T_2 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_4 on space of dimension 218. (0.029 s) T_5 sparse... (0.009 s). Computing T_6 on space of dimension 218. (0.02 s) T_7 sparse... (0.009 s). Computing T_8 on space of dimension 218. (0.04 s) Computing T_9 on space of dimension 218. (0.039 s) Computing T_10 on space of dimension 218. (0.041 s) T_11 sparse... (0.009 s). Computing T_12 on space of dimension 218. (0.04 s) T_13 sparse... (0.009 s). Computing T_14 on space of dimension 218. (0.05 s) Computing T_15 on space of dimension 218. (0.04 s) Computing T_16 on space of dimension 218. (0.059 s) T_17 sparse... (0.009 s). Computing T_18 on space of dimension 218. (0.03 s) T_19 sparse... (0.01 s). Computing T_20 on space of dimension 218. (0.039 s) Computing T_21 on space of dimension 218. (0.03 s) Computing T_22 on space of dimension 218. (0.03 s) T_23 sparse... (0.01 s). Computing T_24 on space of dimension 218. (0.05 s) Computing T_25 on space of dimension 218. (0.05 s) Computing T_26 on space of dimension 218. (0.03 s) Computing T_27 on space of dimension 218. (0.05 s) Computing T_28 on space of dimension 218. (0.04 s) T_29 sparse... (0 s). Computing T_30 on space of dimension 218. (0.039 s) T_31 sparse... (0.009 s). Computing T_32 on space of dimension 218. (0.06 s) Computing T_33 on space of dimension 218. (0.049 s) Computing T_34 on space of dimension 218. (0.049 s) Computing T_35 on space of dimension 218. (0.039 s) Computing T_36 on space of dimension 218. (0.04 s) T_37 sparse... (0 s). Computing T_38 on space of dimension 218. (0.039 s) Computing T_39 on space of dimension 218. (0.03 s) Computing T_40 on space of dimension 218. (0.05 s) T_41 sparse... (0.009 s). Computing T_42 on space of dimension 218. (0.041 s) T_43 sparse... (0.009 s). Computing T_44 on space of dimension 218. (0.04 s) Computing T_45 on space of dimension 218. (0.049 s) Computing T_46 on space of dimension 218. (0.039 s) T_47 sparse... (0.01 s). Computing T_48 on space of dimension 218. (0.059 s) Computing T_49 on space of dimension 218. (0.079 s) Computing T_50 on space of dimension 218. (0.05 s) Computing T_51 on space of dimension 218. (0.05 s) Computing T_52 on space of dimension 218. (0.039 s) T_53 sparse... (0.02 s). Computing T_54 on space of dimension 218. (0.03 s) Computing T_55 on space of dimension 218. (0.05 s) Computing T_56 on space of dimension 218. (0.05 s) Computing T_57 on space of dimension 218. (0.039 s) Computing T_58 on space of dimension 218. (0.03 s) T_59 sparse... (0.01 s). Computing T_60 on space of dimension 218. (0.04 s) T_61 sparse... (0.009 s). Computing T_62 on space of dimension 218. (0.04 s) Computing T_63 on space of dimension 218. (0.05 s) Computing T_64 on space of dimension 218. (0.06 s) Computing T_65 on space of dimension 218. (0.049 s) Computing T_66 on space of dimension 218. (0.04 s) T_67 sparse... (0.019 s). Computing T_68 on space of dimension 218. (0.05 s) Computing T_69 on space of dimension 218. (0.04 s) Computing T_70 on space of dimension 218. (0.029 s) T_71 sparse... (0.019 s). Computing T_72 on space of dimension 218. (0.049 s) T_73 sparse... (0.019 s). Computing T_74 on space of dimension 218. (0.039 s) Computing T_75 on space of dimension 218. (0.029 s) Computing T_76 on space of dimension 218. (0.049 s) Computing T_77 on space of dimension 218. (0.039 s) Computing T_78 on space of dimension 218. (0.04 s) T_79 sparse... (0.019 s). Computing T_80 on space of dimension 218. (0.071 s) Computing T_81 on space of dimension 218. (0.07 s) Computing T_82 on space of dimension 218. Computing T_41 on space of dimension 218. (1.161 s) (1.201 s) T_83 sparse... (0.02 s). Computing T_84 on space of dimension 218. (0.04 s) Computing T_85 on space of dimension 218. (0.05 s) Computing T_86 on space of dimension 218. Computing T_43 on space of dimension 218. (0.681 s) (0.721 s) Computing T_87 on space of dimension 218. (0.05 s) Computing T_88 on space of dimension 218. (0.07 s) T_89 sparse... (0.03 s). Computing T_90 on space of dimension 218. (0.039 s) Computing T_91 on space of dimension 218. (0.05 s) Computing T_92 on space of dimension 218. (0.039 s) Computing T_93 on space of dimension 218. (0.03 s) Computing T_94 on space of dimension 218. Computing T_47 on space of dimension 218. (0.75 s) (0.78 s) Computing T_95 on space of dimension 218. (0.05 s) Computing T_96 on space of dimension 218. (0.061 s) T_97 sparse... (0.03 s). Computing T_98 on space of dimension 218. (0.029 s) Computing T_99 on space of dimension 218. (0.059 s) Computing T_100 on space of dimension 218. (0.04 s) T_101 sparse... (0.03 s). Computing T_102 on space of dimension 218. (0.041 s) T_103 sparse... (0.02 s). Computing T_104 on space of dimension 218. (0.059 s) Computing T_105 on space of dimension 218. (0.03 s) Computing T_106 on space of dimension 218. Computing T_53 on space of dimension 218. (0.84 s) (0.871 s) T_107 sparse... (0.02 s). Computing T_108 on space of dimension 218. (0.039 s) T_109 sparse... (0.03 s). Computing T_110 on space of dimension 218. (0.029 s) Computing T_111 on space of dimension 218. (0.039 s) Computing T_112 on space of dimension 218. (0.059 s) T_113 sparse... (0.03 s). Computing T_114 on space of dimension 218. (0.049 s) Computing T_115 on space of dimension 218. (0.059 s) Computing T_116 on space of dimension 218. (0.049 s) Computing T_117 on space of dimension 218. (0.069 s) Computing T_118 on space of dimension 218. Computing T_59 on space of dimension 218. (0.92 s) (0.96 s) Computing T_119 on space of dimension 218. (0.05 s) Computing T_120 on space of dimension 218. (0.05 s) Computing T_121 on space of dimension 218. (0.069 s) Computing T_122 on space of dimension 218. Computing T_61 on space of dimension 218. (1.679 s) (1.71 s) Computing T_123 on space of dimension 218. (0.03 s) Computing T_124 on space of dimension 218. (0.04 s) Computing T_125 on space of dimension 218. (0.059 s) Computing T_126 on space of dimension 218. (0.041 s) T_127 sparse... (0.031 s). Computing T_128 on space of dimension 218. (0.049 s) Computing T_129 on space of dimension 218. (0.039 s) Computing T_130 on space of dimension 218. (0.04 s) T_131 sparse... (0.029 s). Computing T_132 on space of dimension 218. (0.061 s) Computing T_133 on space of dimension 218. (0.06 s) Computing T_134 on space of dimension 218. Computing T_67 on space of dimension 218. (1.059 s) (1.099 s) Computing T_135 on space of dimension 218. (0.061 s) Computing T_136 on space of dimension 218. (0.06 s) T_137 sparse... (0.039 s). Computing T_138 on space of dimension 218. (0.039 s) T_139 sparse... (0.041 s). Computing T_140 on space of dimension 218. (0.059 s) Computing T_141 on space of dimension 218. (0.04 s) Computing T_142 on space of dimension 218. Computing T_71 on space of dimension 218. (1.109 s) (1.15 s) Computing T_143 on space of dimension 218. (0.06 s) Computing T_144 on space of dimension 218. (0.079 s) Computing T_145 on space of dimension 218. (0.061 s) Computing T_146 on space of dimension 218. Computing T_73 on space of dimension 218. (1.151 s) (1.181 s) Computing T_147 on space of dimension 218. (0.039 s) Computing T_148 on space of dimension 218. (0.049 s) T_149 sparse... (0.039 s). Computing T_150 on space of dimension 218. (0.04 s) T_151 sparse... (0.039 s). Computing T_152 on space of dimension 218. (0.059 s) Computing T_153 on space of dimension 218. (0.059 s) Computing T_154 on space of dimension 218. (0.03 s) Computing T_155 on space of dimension 218. (0.05 s) Computing T_156 on space of dimension 218. (0.04 s) T_157 sparse... (0.039 s). Computing T_158 on space of dimension 218. Computing T_79 on space of dimension 218. (1.25 s) (1.29 s) Computing T_159 on space of dimension 218. (0.029 s) Computing T_160 on space of dimension 218. (0.07 s) Computing T_161 on space of dimension 218. (0.041 s) Computing T_162 on space of dimension 218. (0.041 s) T_163 sparse... (0.039 s). Computing T_164 on space of dimension 218. (0.039 s) Computing T_165 on space of dimension 218. (0.05 s) Computing T_166 on space of dimension 218. Computing T_83 on space of dimension 218. (1.291 s) (1.32 s) T_167 sparse... (0.039 s). Computing T_168 on space of dimension 218. (0.06 s) Computing T_169 on space of dimension 218. (0.09 s) Computing T_170 on space of dimension 218. (0.039 s) Computing T_171 on space of dimension 218. (0.06 s) Computing T_172 on space of dimension 218. (0.039 s) T_173 sparse... (0.04 s). Computing T_174 on space of dimension 218. (0.041 s) Computing T_175 on space of dimension 218. (0.06 s) Computing T_176 on space of dimension 218. (0.06 s) Computing T_177 on space of dimension 218. (0.039 s) Computing T_178 on space of dimension 218. Computing T_89 on space of dimension 218. (1.391 s) (1.431 s) T_179 sparse... (0.05 s). Computing T_180 on space of dimension 218. (0.05 s) T_181 sparse... (0.05 s). Computing T_182 on space of dimension 218. (0.04 s) Computing T_183 on space of dimension 218. (0.039 s) Computing T_184 on space of dimension 218. (0.05 s) Computing T_185 on space of dimension 218. (0.051 s) Computing T_186 on space of dimension 218. (0.03 s) Computing T_187 on space of dimension 218. (0.06 s) Computing T_188 on space of dimension 218. (0.039 s) Computing T_189 on space of dimension 218. (0.081 s) Computing T_190 on space of dimension 218. (0.03 s) T_191 sparse... (0.05 s). Computing T_192 on space of dimension 218. (0.079 s) T_193 sparse... (0.059 s). Computing T_194 on space of dimension 218. Computing T_97 on space of dimension 218. (1.529 s) (1.559 s) Computing T_195 on space of dimension 218. (0.04 s) Computing T_196 on space of dimension 218. (0.039 s) T_197 sparse... (0.05 s). Computing T_198 on space of dimension 218. (0.08 s) T_199 sparse... (0.039 s). Computing T_200 on space of dimension 218. (0.05 s) Computing T_201 on space of dimension 218. (0.041 s) Computing T_202 on space of dimension 218. Computing T_101 on space of dimension 218. (1.57 s) (1.62 s) Computing T_203 on space of dimension 218. (0.049 s) Computing T_204 on space of dimension 218. (0.041 s) Computing T_205 on space of dimension 218. (0.04 s) Computing T_206 on space of dimension 218. Computing T_103 on space of dimension 218. (1.579 s) (1.609 s) Computing T_207 on space of dimension 218. (0.059 s) Computing T_208 on space of dimension 218. (0.069 s) Computing T_209 on space of dimension 218. (0.059 s) Computing T_210 on space of dimension 218. (0.09 s) T_211 sparse... (0.059 s). Computing T_212 on space of dimension 218. (0.049 s) Computing T_213 on space of dimension 218. (0.039 s) Computing T_214 on space of dimension 218. Computing T_107 on space of dimension 218. (1.61 s) (1.641 s) Computing T_215 on space of dimension 218. (0.05 s) Computing T_216 on space of dimension 218. (0.05 s) Computing T_217 on space of dimension 218. (0.05 s) Computing T_218 on space of dimension 218. Computing T_109 on space of dimension 218. (1.66 s) (1.69 s) Computing T_219 on space of dimension 218. (0.041 s) Computing T_220 on space of dimension 218. (0.04 s) Computing T_221 on space of dimension 218. (0.059 s) Computing T_222 on space of dimension 218. (0.069 s) T_223 sparse... (0.05 s). Computing T_224 on space of dimension 218. (0.079 s) Computing T_225 on space of dimension 218. (0.07 s) Computing T_226 on space of dimension 218. Computing T_113 on space of dimension 218. (1.701 s) (1.74 s) T_227 sparse... (0.061 s). Computing T_228 on space of dimension 218. (0.039 s) T_229 sparse... (0.06 s). Computing T_230 on space of dimension 218. (0.03 s) Computing T_231 on space of dimension 218. (0.04 s) Computing T_232 on space of dimension 218. (0.061 s) T_233 sparse... (0.06 s). Computing T_234 on space of dimension 218. (0.079 s) Computing T_235 on space of dimension 218. (0.041 s) Computing T_236 on space of dimension 218. (0.051 s) Computing T_237 on space of dimension 218. (0.04 s) Computing T_238 on space of dimension 218. (0.029 s) T_239 sparse... (0.059 s). Computing T_240 on space of dimension 218. (0.07 s) T_241 sparse... (0.06 s). Computing T_242 on space of dimension 218. (0.04 s) Computing T_243 on space of dimension 218. (0.059 s) Computing T_244 on space of dimension 218. (0.061 s) Computing T_245 on space of dimension 218. (0.06 s) Computing T_246 on space of dimension 218. (0.079 s) Computing T_247 on space of dimension 218. (0.061 s) Computing T_248 on space of dimension 218. (0.06 s) Computing T_249 on space of dimension 218. (0.039 s) Computing T_250 on space of dimension 218. (0.07 s) T_251 sparse... (0.061 s). Computing T_252 on space of dimension 218. (0.04 s) Computing T_253 on space of dimension 218. (0.059 s) Computing T_254 on space of dimension 218. Computing T_127 on space of dimension 218. (1.891 s) (1.92 s) Computing T_255 on space of dimension 218. (0.03 s) Computing T_256 on space of dimension 218. (0.101 s) T_257 sparse... (0.071 s). Computing T_258 on space of dimension 218. (0.089 s) Computing T_259 on space of dimension 218. (0.05 s) Computing T_260 on space of dimension 218. (0.049 s) Computing T_261 on space of dimension 218. (0.049 s) Computing T_262 on space of dimension 218. Computing T_131 on space of dimension 218. (1.911 s) (1.951 s) T_263 sparse... (0.059 s). Computing T_264 on space of dimension 218. (0.059 s) Computing T_265 on space of dimension 218. (0.05 s) Computing T_266 on space of dimension 218. (0.069 s) Computing T_267 on space of dimension 218. (0.039 s) Computing T_268 on space of dimension 218. (0.04 s) T_269 sparse... (0.07 s). Computing T_270 on space of dimension 218. (0.079 s) T_271 sparse... (0.08 s). Computing T_272 on space of dimension 218. (0.081 s) Computing T_273 on space of dimension 218. (0.04 s) Computing T_274 on space of dimension 218. Computing T_137 on space of dimension 218. (2 s) (2.039 s) Computing T_275 on space of dimension 218. (0.08 s) Computing T_276 on space of dimension 218. (0.039 s) T_277 sparse... (0.069 s). Computing T_278 on space of dimension 218. Computing T_139 on space of dimension 218. (2 s) (2.04 s) Computing T_279 on space of dimension 218. (0.049 s) Computing T_280 on space of dimension 218. (0.059 s) T_281 sparse... (0.069 s). Computing T_282 on space of dimension 218. (0.07 s) T_283 sparse... (0.07 s). Computing T_284 on space of dimension 218. (0.049 s) Computing T_285 on space of dimension 218. (0.059 s) Computing T_286 on space of dimension 218. (0.08 s) Computing T_287 on space of dimension 218. (0.039 s) Computing T_288 on space of dimension 218. (0.07 s) Computing T_289 on space of dimension 218. (0.08 s) Computing T_290 on space of dimension 218. (0.079 s) Computing T_291 on space of dimension 218. (0.029 s) Computing T_292 on space of dimension 218. (0.04 s) T_293 sparse... (0.069 s). Computing T_294 on space of dimension 218. (0.09 s) Computing T_295 on space of dimension 218. (0.059 s) Computing T_296 on space of dimension 218. (0.06 s) Computing T_297 on space of dimension 218. (0.079 s) Computing T_298 on space of dimension 218. Computing T_149 on space of dimension 218. (2.109 s) (2.179 s) Computing T_299 on space of dimension 218. (0.059 s) Computing T_300 on space of dimension 218. (0.05 s) Computing T_301 on space of dimension 218. (0.05 s) Computing T_302 on space of dimension 218. Computing T_151 on space of dimension 218. (2.15 s) (2.23 s) Computing T_303 on space of dimension 218. (0.059 s) Computing T_304 on space of dimension 218. (0.079 s) Computing T_305 on space of dimension 218. (0.04 s) Computing T_306 on space of dimension 218. (0.079 s) T_307 sparse... (0.07 s). Computing T_308 on space of dimension 218. (0.039 s) Computing T_309 on space of dimension 218. (0.04 s) Computing T_310 on space of dimension 218. (0.059 s) T_311 sparse... (0.081 s). Computing T_312 on space of dimension 218. (0.059 s) T_313 sparse... (0.079 s). Computing T_314 on space of dimension 218. Computing T_157 on space of dimension 218. (2.201 s) (2.271 s) Computing T_315 on space of dimension 218. (0.061 s) Computing T_316 on space of dimension 218. (0.039 s) T_317 sparse... (0.08 s). Computing T_318 on space of dimension 218. (0.081 s) Computing T_319 on space of dimension 218. (0.05 s) Computing T_320 on space of dimension 218. (0.069 s) Computing T_321 on space of dimension 218. (0.05 s) Computing T_322 on space of dimension 218. (0.081 s) Computing T_323 on space of dimension 218. (0.07 s) Computing T_324 on space of dimension 218. (0.05 s) Computing T_325 on space of dimension 218. (0.069 s) Computing T_326 on space of dimension 218. Computing T_163 on space of dimension 218. (2.259 s) (2.329 s) Computing T_327 on space of dimension 218. (0.04 s) Computing T_328 on space of dimension 218. (0.059 s) Computing T_329 on space of dimension 218. (0.059 s) Computing T_330 on space of dimension 218. (0.079 s) T_331 sparse... (0.081 s). Computing T_332 on space of dimension 218. (0.04 s) Computing T_333 on space of dimension 218. (0.049 s) Computing T_334 on space of dimension 218. Computing T_167 on space of dimension 218. (2.27 s) (2.351 s) Computing T_335 on space of dimension 218. (0.05 s) Computing T_336 on space of dimension 218. (0.07 s) T_337 sparse... (0.081 s). Computing T_338 on space of dimension 218. (0.069 s) Computing T_339 on space of dimension 218. (0.039 s) Computing T_340 on space of dimension 218. (0.05 s) Computing T_341 on space of dimension 218. (0.061 s) Computing T_342 on space of dimension 218. (0.071 s) Computing T_343 on space of dimension 218. (0.07 s) Computing T_344 on space of dimension 218. (0.07 s) Computing T_345 on space of dimension 218. (0.051 s) Computing T_346 on space of dimension 218. Computing T_173 on space of dimension 218. (2.289 s) (2.38 s) T_347 sparse... (0.101 s). Computing T_348 on space of dimension 218. (0.04 s) T_349 sparse... (0.089 s). Computing T_350 on space of dimension 218. (0.07 s) Computing T_351 on space of dimension 218. (0.07 s) Computing T_352 on space of dimension 218. (0.07 s) T_353 sparse... (0.09 s). Computing T_354 on space of dimension 218. (0.08 s) Computing T_355 on space of dimension 218. (0.039 s) Computing T_356 on space of dimension 218. (0.05 s) Computing T_357 on space of dimension 218. (0.039 s) Computing T_358 on space of dimension 218. Computing T_179 on space of dimension 218. (2.37 s) (2.44 s) T_359 sparse... (0.089 s). Computing T_360 on space of dimension 218. (0.06 s) Computing T_361 on space of dimension 218. (0.079 s) Computing T_362 on space of dimension 218. Computing T_181 on space of dimension 218. (2.399 s) (2.469 s) Computing T_363 on space of dimension 218. (0.041 s) Computing T_364 on space of dimension 218. (0.05 s) Computing T_365 on space of dimension 218. (0.04 s) Computing T_366 on space of dimension 218. (0.079 s) T_367 sparse... (0.09 s). Computing T_368 on space of dimension 218. (0.07 s) Computing T_369 on space of dimension 218. (0.05 s) Computing T_370 on space of dimension 218. (0.081 s) Computing T_371 on space of dimension 218. (0.05 s) Computing T_372 on space of dimension 218. (0.04 s) T_373 sparse... (0.09 s). Computing T_374 on space of dimension 218. (0.079 s) Computing T_375 on space of dimension 218. (0.1 s) Computing T_376 on space of dimension 218. (0.059 s) Computing T_377 on space of dimension 218. (0.059 s) Computing T_378 on space of dimension 218. (0.07 s) T_379 sparse... (0.09 s). Computing T_380 on space of dimension 218. (0.039 s) Computing T_381 on space of dimension 218. (0.04 s) Computing T_382 on space of dimension 218. Computing T_191 on space of dimension 218. (2.529 s) (2.61 s) T_383 sparse... (0.101 s). Computing T_384 on space of dimension 218. (0.369 s) Computing T_385 on space of dimension 218. (0.049 s) Computing T_386 on space of dimension 218. Computing T_193 on space of dimension 218. (2.489 s) (2.559 s) Computing T_387 on space of dimension 218. (0.06 s) Computing T_388 on space of dimension 218. (0.039 s) T_389 sparse... (0.099 s). Computing T_390 on space of dimension 218. (0.069 s) Computing T_391 on space of dimension 218. (0.07 s) Computing T_392 on space of dimension 218. (0.061 s) Computing T_393 on space of dimension 218. (0.039 s) Computing T_394 on space of dimension 218. Computing T_197 on space of dimension 218. (2.57 s) (2.65 s) Computing T_395 on space of dimension 218. (0.04 s) Computing T_396 on space of dimension 218. (0.13 s) T_397 sparse... (0.099 s). Computing T_398 on space of dimension 218. Computing T_199 on space of dimension 218. (2.56 s) (2.639 s) Computing T_399 on space of dimension 218. (0.099 s) Computing T_400 on space of dimension 218. (0.07 s) T_401 sparse... (0.101 s). Computing T_402 on space of dimension 218. (0.069 s) Computing T_403 on space of dimension 218. (0.059 s) Computing T_404 on space of dimension 218. (0.039 s) Computing T_405 on space of dimension 218. (0.079 s) Computing T_406 on space of dimension 218. (0.08 s) Computing T_407 on space of dimension 218. (0.07 s) Computing T_408 on space of dimension 218. (0.059 s) T_409 sparse... (0.099 s). Computing T_410 on space of dimension 218. (0.07 s) Computing T_411 on space of dimension 218. (0.04 s) Computing T_412 on space of dimension 218. (0.049 s) Computing T_413 on space of dimension 218. (0.039 s) Computing T_414 on space of dimension 218. (0.07 s) Computing T_415 on space of dimension 218. (0.04 s) Computing T_416 on space of dimension 218. (0.079 s) Computing T_417 on space of dimension 218. (0.04 s) Computing T_418 on space of dimension 218. (0.079 s) T_419 sparse... (0.099 s). Computing T_420 on space of dimension 218. (0.13 s) T_421 sparse... (0.109 s). Computing T_422 on space of dimension 218. Computing T_211 on space of dimension 218. (2.69 s) (2.77 s) Computing T_423 on space of dimension 218. (0.059 s) Computing T_424 on space of dimension 218. (0.069 s) Computing T_425 on space of dimension 218. (0.069 s) Computing T_426 on space of dimension 218. (0.079 s) Computing T_427 on space of dimension 218. (0.049 s) Computing T_428 on space of dimension 218. (0.049 s) Computing T_429 on space of dimension 218. (0.099 s) Computing T_430 on space of dimension 218. (0.069 s) T_431 sparse... (0.109 s). Computing T_432 on space of dimension 218. (0.07 s) T_433 sparse... (0.099 s). Computing T_434 on space of dimension 218. (0.07 s) Total time: 3191.429 seconds Magma V2.7-1 Mon Jan 29 2001 03:49:23 on modular [Seed = 1377599593] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2503 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.78 s) III. 3-term relations. Computing quotient by 836 relations. Form quot and then images (0.5 s) (total time to create space = 1.32 s) Computing cuspidal part of Full Modular symbols space of level 2503, weight 2, and dimension 209 Computing new part of Modular symbols space of level 2503, weight 2, and dimension 208. Computing 2503-new part of Modular symbols space of level 2503, weight 2, and dimension 208. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2503, weight 2, and dimension 208. Computing 2503-new part of Modular symbols space of level 2503, weight 2, and dimension 208. Computing cuspidal part of Modular symbols space of level 2503, weight 2, and dimension 208 Decomposing space of level 2503 and dimension 208 using T_2. (will stop at 418) Computing T_2 on dual space of dimension 208. Computing DualVectorSpace of Modular symbols space of level 2503, weight 2, and dimension 208. Computing complement of Modular symbols space of level 2503, weight 2, and dimension 208 Computing representation of Modular symbols space of level 2503, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 209. (0.491 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2503, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing characteristic polynomial of T_2. x^208 + x^207 - 311*x^206 - 311*x^205 + 47584*x^204 + 47582*x^203 - 4774882*x^202 - 4774276*x^201 + 353458665*x^200 + 353368345*x^199 - 20584324494*x^198 - 20575497360*x^197 + 982206154768*x^196 + 981569875562*x^195 - 39489961658458*x^194 - 39453886355628*x^193 + 1365392035913580*x^192 + 1363716527608558*x^191 - 41234989875748655*x^190 - 41169435558777849*x^189 + 1101075903177187284*x^188 + 1098870763035109255*x^187 - 26253319127944930675*x^186 - 26188545861895653353*x^185 + 563477779862176935127*x^184 + 561795965646506644598*x^183 - 10960370312067292600832*x^182 - 10921389732721834315254*x^181 + 194315988637010771462632*x^180 + 193502954062998504440249*x^179 - 3155349850745547452565055*x^178 - 3139986621099089053477768*x^177 + 47127421132474208118140430*x^176 + 46862912635038780912765096*x^175 - 649802495602051766353528359*x^174 - 645632912602832393860277833*x^173 + 8297897308810508419329615002*x^172 + 8237465694679633186489470426*x^171 - 98415997813608470650640139943*x^170 - 97607759216736471304009223202*x^169 + 1086840518451432397132877317758*x^168 + 1076833451773837419259714683311*x^167 - 11200555133193051158633905599666*x^166 - 11085531248283337427823871556678*x^165 + 107932925303615139524969031144950*x^164 + 106702473192620934640412151810810*x^163 - 974283655335557612575165597470681*x^162 - 962006506037436749744297249370955*x^161 + 8251459455869536399868903997543264*x^160 + 8136975987804522517838583294935280*x^159 - 65662360802962911639742428891658172*x^158 - 64662900176553103732077285456317468*x^157 + 491593936041196793897515673859586855*x^156 + 483412084759707570364327657485713677*x^155 - 3466640394571750359851731760137147848*x^154 - 3403745549776364012510453413160032969*x^153 + 23050528384855554440010956280522269706*x^152 + 22595951079926642709821195252929007383*x^151 - 144655432271214327529372282922781102658*x^150 - 141562823722658497591257947462471110139*x^149 + 857513229636731540980072506564908504866*x^148 + 837688324217326504114235769634237830306*x^147 - 4805422838733409750521180082793972918092*x^146 - 4685565483222016487863228314260373325203*x^145 + 25474440142496331221517108489727534805735*x^144 + 24790462155395609969318433657329435437669*x^143 - 127827779866620676190595761280489173804733*x^142 - 124140879024505692815363586021926814917788*x^141 + 607475449456483488120080767244404815050028*x^140 + 588690703688733209898137963961395854215561*x^139 - 2735410204170198535819132812959470451122689*x^138 - 2644894574938491013665634944604374339069957*x^137 + 11675824762282000001572083764704819927235229*x^136 + 11263123709948994707417736088123110220387524*x^135 - 47258556421080096079888266009764994871491107*x^134 - 45477276549138007213734426351344690210913864*x^133 + 181440444483110920968314114421057402243644980*x^132 + 174159673889939243257273605899297971499672341*x^131 - 660935718945037014434780431092973245274256992*x^130 - 632744761775257093214765741641438662631512585*x^129 + 2284784335552369836371084352670280711957353038*x^128 + 2181354886307512797805251102051082928698547143*x^127 - 7496542129487711563036983263012095308922917198*x^126 - 7136898653227230340394268086879291363453046228*x^125 + 23348322497293605917876155304760016486416887726*x^124 + 22162926676716002148818269406120105401160394056*x^123 - 69033398427140826196141001727718554299147074416*x^122 - 65329438825187246504885981971294486989460372264*x^121 + 193768390842460348322017178415650432893071734664*x^120 + 182795815301900940236964980897168375939083007712*x^119 - 516320798550362276000845593705839465151134283928*x^118 - 485503240820305844116717667835529738227867496740*x^117 + 1306002961037175243994238981056054678075265159337*x^116 + 1223944500312486621462405818500304477075321964125*x^115 - 3135548671603489173531389814142043727693840629622*x^114 - 2928413927919844609449175653910088992030187697821*x^113 + 7144420598559228749433347061919346613566683387192*x^112 + 6648814265922433777023844134866171155918587282426*x^111 - 15446357493840031305638196201782159226801702582638*x^110 - 14322513566568161315158775631441997178992349353083*x^109 + 31680680014554511274040074795936027036620251959167*x^108 + 29265928270707394145839442925643858347682273234976*x^107 - 61625164549327652060326872832929392516054074343468*x^106 - 56710097536449588581003737669834980592631067460645*x^105 + 113653966459123772931755241239549704542643197699680*x^104 + 104179583169330488147032482564436310004258399762090*x^103 - 198665900797824640311949297056845138549792645477173*x^102 - 181376027336926571927899936786105471620259588746009*x^101 + 329006775873542309833345106651950926905591760132421*x^100 + 299146950390051488143436180221772555928954948243715*x^99 - 515989018053584742068295372771710418767761628753424*x^98 - 467207808584258147267843320719268308441134052706632*x^97 + 765987619461884433276489799588452691433673984250036*x^96 + 690637744963824805577302479497580064205391103984043*x^95 - 1075771192957577114614152416972302543186966389859785*x^94 - 965781752913767989879341863289121630023529614341854*x^93 + 1428515777093143607706406855525351317107268137458351*x^92 + 1276877062424224849711952007625191829128610270078536*x^91 - 1792442957406007526186306059866722801500687028034826*x^90 - 1595114559373031088524754376709015961075392474691560*x^89 + 2123763763644943100326911017774278912802205376504251*x^88 + 1881551591596941240276361191455914086997162569933319*x^87 - 2374374318601846951543830913187256982015785501940212*x^86 - 2094146341191298705990991559934626309904195286145310*x^85 + 2502827226266152818086943344200359730878106884466261*x^84 + 2197480560632051928381740145292103535907426696588946*x^83 - 2485316009713399254140748164739454475425001883943965*x^82 - 2172224271953740598616935378966316206849511933300934*x^81 + 2322759038839003256248558572412302846937081142411297*x^80 + 2020937917167739161756402914572042958820344898344753*x^79 - 2041136553011241065752026802223221852034120127079131*x^78 - 1767860861977897416621604537057512428378445469366254*x^77 + 1684721123676504119408435745576911575032127342300507*x^76 + 1452571030275170922596474946124450153465139822074613*x^75 - 1304613908869099130697958286940657103336053010234602*x^74 - 1119787462422916420943165159736271511159745381398842*x^73 + 946693022211843924962093553398999905441032910397281*x^72 + 808951877811645995413489237567140087610874302721228*x^71 - 642906243688044975833338799450254767698883797854299*x^70 - 546942159121383957221438731310869508468235486999157*x^69 + 408033637037797666693616696672308226327134737546174*x^68 + 345616667064909781813280846189874076355443273667357*x^67 - 241663145812258026454695328920645794736119700972202*x^66 - 203818069072159408498009424548205770907296633580669*x^65 + 133352762196093396411619772886301070204855237095403*x^64 + 111995226856610997676130499694960267191154425343524*x^63 - 68443650202460252042116394917269811622840684212303*x^62 - 57243939248306134166034170457937545713888784242126*x^61 + 32614753527992789875739509899672565204473588542541*x^60 + 27167089501158328491002438169608727103104003476320*x^59 - 14401207867840084328100439490202056489023012627928*x^58 - 11947916004503154111780731277324904303094636084710*x^57 + 5880052938141279791747820577006468123891282011273*x^56 + 4859197871274255421030579049203474747438758900252*x^55 - 2215080335446581040134954060592505359574837078454*x^54 - 1823384802351884356576166535313139047746750913381*x^53 + 768036347771601785082910998300565294115812803462*x^52 + 629759011979181960724327758480962844814777424181*x^51 - 244478338620094962307473131214213017856797577641*x^50 - 199668125830033345770494968933918267975659682500*x^49 + 71246874224898892358228727079093340482197270854*x^48 + 57948601205794214606676281236022131694627718963*x^47 - 18952674165203840726963410972406212979022828072*x^46 - 15347342839355027370912353295156471425812173041*x^45 + 4587459129647168840348499551784188382750265860*x^44 + 3696725015531764173316309954331810771770580240*x^43 - 1006902199673106474006342212878841845983958345*x^42 - 806860483577052663179623167339175124731614600*x^41 + 199675027842615481844588561825271301145362346*x^40 + 158938035230413334555187116159613792225302073*x^39 - 35634804313805048762251517471846958117205866*x^38 - 28130677168363774497128365467346921271489234*x^37 + 5699144674096465507929184181963212385571802*x^36 + 4451701312439711436101569032036619768135385*x^35 - 813149241807705453219944609733484952939678*x^34 - 626463652031085168529002897842725332006326*x^33 + 103004693293572756672191455555967185718341*x^32 + 77917486660304624320111199739907781663880*x^31 - 11524333741929679124277902686288497239565*x^30 - 8506369270786280338191420716044882141823*x^29 + 1132425902122250804163020063133118664365*x^28 + 808729497657171693202054361388954573573*x^27 - 97132821882799823257138646063115899814*x^26 - 66353856676079153326735194700377144155*x^25 + 7222291083152153708678393506926692536*x^24 + 4648569370152038041094138895273885147*x^23 - 461752415140551050736998689916512509*x^22 - 274588951470836779074652495385894842*x^21 + 25131290501859039005267341817629279*x^20 + 13468822417897602458600116191453543*x^19 - 1149272804010946895794055418056105*x^18 - 538363709543126310580930532779446*x^17 + 43383372666304358649270934102870*x^16 + 17123322911079048715838153373602*x^15 - 1318634907048518420212522668352*x^14 - 420259656540212950330002207193*x^13 + 31150695716285076520830740173*x^12 + 7643614234801694013319572536*x^11 - 543425101088619233070535218*x^10 - 97674088476256146238650331*x^9 + 6488905209492176016200347*x^8 + 820429060006731851701947*x^7 - 47156766878069733909597*x^6 - 4238729868420183532386*x^5 + 171919384712188936778*x^4 + 12854812902983945443*x^3 - 206308078530365139*x^2 - 18123126975829737*x - 170216895460797 time = 5.51 Factoring characteristic polynomial. [ , ] time = 1.15 Cutting out subspace using f(T_2), where f=x^94 + 20*x^93 + 63*x^92 - 1362*x^91 - 10791*x^90 + 27983*x^89 + 543426*x^88 + 499378*x^87 - 15295342*x^86 - 45297591*x^85 + 272037927*x^84 + 1401807234*x^83 - 2927185284*x^82 - 27803972886*x^81 + 8934938308*x^80 + 401185931970*x^79 + 332378429600*x^78 - 4416262831095*x^77 - 7949529148957*x^76 + 37602061923823*x^75 + 107428540875386*x^74 - 242979959637341*x^73 - 1067001911401402*x^72 + 1082175614337967*x^71 + 8389060001441325*x^70 - 1743923852262248*x^69 - 53882995614660237*x^68 - 21850645200940877*x^67 + 286821220827899411*x^66 + 270254664109311523*x^65 - 1270053262922336119*x^64 - 1885000165546830588*x^63 + 4646343721104178704*x^62 + 9889320508961929138*x^61 - 13705930050224364730*x^60 - 42033438132451815062*x^59 + 30395977233728116624*x^58 + 149153780981172634215*x^57 - 37897695442555966324*x^56 - 448095904090339674291*x^55 - 51164001605660670615*x^54 + 1146621439861642631685*x^53 + 494152536730985228008*x^52 - 2500708834171943933144*x^51 - 1825670680093115332366*x^50 + 4628015531006857712250*x^49 + 4830883494896863896831*x^48 - 7188159625077893933777*x^47 - 10190435184555686715493*x^46 + 9156164927109930092612*x^45 + 17781306042697773654016*x^44 - 9076060065853650222388*x^43 - 26059795278668871113879*x^42 + 5949398104119416480987*x^41 + 32263392767523237555642*x^40 - 245776019061141966557*x^39 - 33754027832339517628670*x^38 - 5944960996705610013638*x^37 + 29735099383556538865485*x^36 + 10075271862169310989622*x^35 - 21900681607636134281439*x^34 - 10800725590488107536357*x^33 + 13337897014822248233923*x^32 + 8700307309463427299979*x^31 - 6607470239902223556095*x^30 - 5514884321811868175136*x^29 + 2596722046414970913399*x^28 + 2788949642746441952165*x^27 - 776064830928046191447*x^26 - 1126133382288902707735*x^25 + 161426992204660297801*x^24 + 360928441767896009405*x^23 - 17161133373893594316*x^22 - 90923778715760667807*x^21 - 1702131171413413647*x^20 + 17787508206698627920*x^19 + 1074643403101060513*x^18 - 2666316121916599408*x^17 - 213448645834308721*x^16 + 301681811173560370*x^15 + 23938013976578768*x^14 - 25268463137206739*x^13 - 1538811827763847*x^12 + 1519093721345121*x^11 + 44710362307090*x^10 - 62093014314691*x^9 + 528483045464*x^8 + 1563094445371*x^7 - 72676267471*x^6 - 19806353613*x^5 + 1593594454*x^4 + 71478313*x^3 - 8254961*x^2 - 58590*x + 12717. Cutting out subspace using f(T_2), where f=x^114 - 19*x^113 + 6*x^112 + 2128*x^111 - 10441*x^110 - 102502*x^109 + 884274*x^108 + 2398294*x^107 - 40517888*x^106 - 1634511*x^105 + 1248297676*x^104 - 1985044680*x^103 - 28028235586*x^102 + 82790198836*x^101 + 473154108208*x^100 - 2113599404046*x^99 - 5956169709202*x^98 + 40083645205991*x^97 + 51141109338850*x^96 - 603991933489029*x^95 - 157439574363901*x^94 + 7473735730400297*x^93 - 3829086687838461*x^92 - 77338282576095201*x^91 + 91133424425942098*x^90 + 675613687495306105*x^89 - 1233653570974335779*x^88 - 4993182713641658514*x^87 + 12693111857160373493*x^86 + 31007881217763104280*x^85 - 107232880552918784036*x^84 - 158116437031162158703*x^83 + 768952680830806444837*x^82 + 619613875452834873643*x^81 - 4763570555603548194933*x^80 - 1424077271503913697451*x^79 + 25757534142973023425299*x^78 - 2955817114358704035554*x^77 - 122314552397039256790161*x^76 + 58185038294458748674481*x^75 + 511764292019555793102441*x^74 - 415576497517959445362022*x^73 - 1888195257669340347283153*x^72 + 2167869539193293877910719*x^71 + 6133021919542191421749352*x^70 - 9266455727283362412936281*x^69 - 17448917034398728505172650*x^68 + 33831575634896926384090984*x^67 + 43031787939187916376384392*x^66 - 107594331390283855373635987*x^65 - 90056076752534821832483614*x^64 + 301249055646559003197677443*x^63 + 152363229800203706503125684*x^62 - 747086562119137128792233309*x^61 - 179399887024045691918679459*x^60 + 1646715380896700067377458820*x^59 + 29121942737201427788802752*x^58 - 3231516627296307422752438136*x^57 + 568857233797536147925571280*x^56 + 5648208149890645866534035906*x^55 - 1984308880424533789668662614*x^54 - 8786896307754784800843995946*x^53 + 4537238286498786431490680176*x^52 + 12146022078675890280188781037*x^51 - 8243234332615330957449487564*x^50 - 14875459524803706571055073532*x^49 + 12588963629324288927563690763*x^48 + 16073386253853922314233726539*x^47 - 16544557900738028948614702563*x^46 - 15229167086167802094937412325*x^45 + 18922451916858090424401167790*x^44 + 12537548550395300105181558189*x^43 - 18939208623458091977122935013*x^42 - 8840208075317683256362103973*x^41 + 16628719778154176167529820279*x^40 + 5205294684581749580904450335*x^39 - 12813966572316707215809752967*x^38 - 2426899474479394456460089149*x^37 + 8659282032288278426345237658*x^36 + 764602705409603334474406445*x^35 - 5122425757247609149989653323*x^34 - 24445523870014029946268325*x^33 + 2645734550595349901367024699*x^32 - 170713722991229190746550395*x^31 - 1189272283920440110889209312*x^30 + 144900653461212617993804476*x^29 + 463443971671917488805110848*x^28 - 78157947100845831292296296*x^27 - 155862255571607634647018394*x^26 + 32080147476066320638011028*x^25 + 45005667262315916717131237*x^24 - 10521617702910996195239243*x^23 - 11091298465533462890794683*x^22 + 2801240367568855533748377*x^21 + 2316524096884130493688613*x^20 - 606726027290086544206374*x^19 - 406571166115370386972236*x^18 + 106295524304646379019289*x^17 + 59324054132801243405621*x^16 - 14878773839989069292264*x^15 - 7095878121606179087438*x^14 + 1631488650487710497498*x^13 + 682453552638399251491*x^12 - 135968786996328138968*x^11 - 51335698196777273259*x^10 + 8207394716036746371*x^9 + 2897305896892155772*x^8 - 329233310640582324*x^7 - 114731464337605853*x^6 + 7191068280228740*x^5 + 2818712603411215*x^4 - 25371520947095*x^3 - 31761496143590*x^2 - 1486777812131*x - 13384988241. Computing representation of Modular symbols space of level 2503, weight 2, and dimension 94. Goal dimension = 94. Computing T_2 on dual space of dimension 94. T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). %o x^94 + 19*x^93 + 47*x^92 - 1348*x^91 - 9214*x^90 + 33583*x^89 + 477682*x^88 + 70916*x^87 - 13925622*x^86 - 29028415*x^85 + 265348349*x^84 + 1002208623*x^83 - 3395378033*x^82 - 20863034480*x^81 + 25865871928*x^80 + 313270105777*x^79 - 4664159738*x^78 - 3619669147889*x^77 - 3157716010944*x^76 + 33141087978533*x^75 + 54804857354008*x^74 - 242877784025237*x^73 - 604653979991923*x^72 + 1412007161006328*x^71 + 5084540441192187*x^70 - 6224879456552713*x^69 - 34584486026147944*x^68 + 17419661912384014*x^67 + 195570868030156013*x^66 + 5692994921512518*x^65 - 932635773919252809*x^64 - 435123118429990745*x^63 + 3776796730140121670*x^62 + 3259056020921246414*x^61 - 13007209476485872449*x^60 - 16407302590868303814*x^59 + 37936195736042718396*x^58 + 64948959216441592359*x^57 - 92517660401955806679*x^56 - 212681998501136561453*x^55 + 183129405106742201556*x^54 + 589114671576442855944*x^53 - 271958725562408671420*x^52 - 1395491719916990956993*x^51 + 216898786041014883084*x^50 + 2841371549194961464280*x^49 + 269129750633396488025*x^48 - 4979897931388268024668*x^47 - 1550543701581023749152*x^46 + 7502182252511082305177*x^45 + 3830954944195137871648*x^44 - 9674575843923189896361*x^43 - 6838430016247418896212*x^42 + 10601469923708405716633*x^41 + 9714027338904290231572*x^40 - 9754727573481262744705*x^39 - 11347863873715608962294*x^38 + 7388744642935399888483*x^37 + 11039680783142007098355*x^36 - 4441184652059810282040*x^35 - 8975068843839017341139*x^34 + 1945745747084217279833*x^33 + 6087367266896323011696*x^32 - 445069545570770446244*x^31 - 3426555362723472286725*x^30 - 140744182899865979219*x^29 + 1587848141478080210099*x^28 + 211518938449588792018*x^27 - 599350876897132647737*x^26 - 124553687543800179990*x^25 + 181929269900648638386*x^24 + 48641279992571277446*x^23 - 43763683414608745841*x^22 - 13679911176131936775*x^21 + 8212956423412555318*x^20 + 2811916519557189203*x^19 - 1183801054499787665*x^18 - 418688792331901002*x^17 + 129139164394077795*x^16 + 44193883571957909*x^15 - 10498468086845627*x^14 - 3205728333178974*x^13 + 622136832807562*x^12 + 153365121900416*x^11 - 25984915592500*x^10 - 4563912559742*x^9 + 731391460003*x^8 + 75770145251*x^7 - 13064302157*x^6 - 474655927*x^5 + 126350628*x^4 - 2747849*x^3 - 254086*x^2 + 9504*x p = %o, dimension = %o. 2 0 Computing representation of Modular symbols space of level 2503, weight 2, and dimension 114. Computing complement of Modular symbols space of level 2503, weight 2, and dimension 114 Computing DualVectorSpace of Modular symbols space of level 2503, weight 2, and dimension 95. Goal dimension = 95. T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... 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T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 95. (0.569 s) %o x^95 + 17*x^94 + 3*x^93 - 1551*x^92 - 6705*x^91 + 60356*x^90 + 459477*x^89 - 1130900*x^88 - 16793476*x^87 + 588435*x^86 + 407930700*x^85 + 585693453*x^84 - 7132606986*x^83 - 19022417034*x^82 + 92346856966*x^81 + 374381117046*x^80 - 871179366310*x^79 - 5413398119895*x^78 + 5299259344328*x^77 + 61450649370694*x^76 - 5377644896083*x^75 - 565265582263499*x^74 - 338062032489379*x^73 + 4283181348542173*x^72 + 5142533158427424*x^71 - 26911103856586223*x^70 - 48651224057873493*x^69 + 139798341643039834*x^68 + 352373156430722042*x^67 - 590208998374386710*x^66 - 2080817255250270688*x^65 + 1925159623220177769*x^64 + 10301344217744670468*x^63 - 4049710654350606974*x^62 - 43373891577110152144*x^61 - 915647981778720872*x^60 + 156496291631083561810*x^59 + 57965849279988284343*x^58 - 485359038386073868969*x^57 - 334402817762671775319*x^56 + 1293123710665358352258*x^55 + 1300113444678624643530*x^54 - 2945711782853942667047*x^53 - 3983166444364899617168*x^52 + 5676455822422716467066*x^51 + 10105027571286203709348*x^50 - 9053163098123709239919*x^49 - 21680810109768485624270*x^48 + 11374043690677995085838*x^47 + 39727470480776990239091*x^46 - 9687188738632016623820*x^45 - 62419978193946971184436*x^44 + 1168384918892079553285*x^43 + 84128783940126029822624*x^42 + 14415198455164988112681*x^41 - 97035954321630854633483*x^40 - 33016699775156091728999*x^39 + 95317122500312942872372*x^38 + 47569982373673368906399*x^37 - 79130026288500305606833*x^36 - 52126497194144067250305*x^35 + 54901319232420295307960*x^34 + 45740073786286570842994*x^33 - 31313383735003317401790*x^32 - 32708392168292505456032*x^31 + 14307526397894802493149*x^30 + 19141375011850575438807*x^29 - 5001216496498470788032*x^28 - 9142913759167372047942*x^27 + 1202061110495235866606*x^26 + 3539827139071368421006*x^25 - 123352534846084883998*x^24 - 1099946458677581622531*x^23 - 39440378594079884859*x^22 + 271069204975868589774*x^21 + 22893901720938868861*x^20 - 52287881216994823247*x^19 - 5890246331219780947*x^18 + 7785499719915489503*x^17 + 942027748676486533*x^16 - 881107419544102342*x^15 - 97082505066943043*x^14 + 74266577583856370*x^13 + 6135529204636662*x^12 - 4512570801728273*x^11 - 196224101235961*x^10 + 186807525989537*x^9 - 22354691021*x^8 - 4761959603584*x^7 + 198222448800*x^6 + 61012655293*x^5 - 4709305049*x^4 - 222689900*x^3 + 24706293*x^2 + 188487*x - 38151 p = 2, dimension = 95. Computing complement of Modular symbols space of level 2503, weight 2, and dimension 95 Sorting ... 0 seconds. J0( N: 2503 ) IntersectionGroup( M1: Modular symbols space of level 2503, weight 2, and dimension..., M2: Modular symbols space of level 2503, weight 2, and dimension... ) IntersectionGroup( S: [ Modular symbols space of level 2503, weight 2, and dimensi... ) IntegralRepresentation( M: Modular symbols space of level 2503, weight 2, and dimension... ) SaturateWithRespectToBasis( V: Vector space of degree 209, dimension 0 over Rational Field, B: [ (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0... ) Saturate( B: [] ) In file "/home/was/modsym/linalg.m", line 166, column 13: >> if Type(B[1]) eq SeqEnum then ^ Runtime error in '[]': Sequence element 1 not defined >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2503, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 341.449 seconds Magma V2.7-1 Mon Jan 29 2001 03:55:05 on modular [Seed = 1444447671] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2505 and weight 2.... I. Manin symbols list. (0.06 s) II. 2-term relations. (1.279 s) III. 3-term relations. Computing quotient by 1344 relations. Form quot and then images (1.171 s) (total time to create space = 2.541 s) Computing cuspidal part of Full Modular symbols space of level 2505, weight 2, and dimension 340 Computing new part of Modular symbols space of level 2505, weight 2, and dimension 333. Computing 3-new part of Modular symbols space of level 2505, weight 2, and dimension 333. Computing space of modular symbols of level 835 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.3 s) III. 3-term relations. Computing quotient by 336 relations. Form quot and then images (0.15 s) (total time to create space = 0.46 s) Computing index-1 degeneracy map from level 2505 to 835. (1.15 s) Computing index-3 degeneracy map from level 2505 to 835. (1.089 s) Computing index-1 degeneracy map from level 835 to 2505. (1.111 s) Computing index-3 degeneracy map from level 835 to 2505. (1.029 s) Computing DualVectorSpace of Modular symbols space of level 2505, weight 2, and dimension 333. Computing complement of Modular symbols space of level 2505, weight 2, and dimension 333 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 340. (0.269 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). %o x^7 - 21*x^6 + 189*x^5 - 945*x^4 + 2835*x^3 - 5103*x^2 + 5103*x - 2187 p = %o, dimension = %o. 2 7 Computing complement of Modular symbols space of level 2505, weight 2, and dimension 7 Computing 5-new part of Modular symbols space of level 2505, weight 2, and dimension 333. Computing space of modular symbols of level 501 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.18 s) III. 3-term relations. Computing quotient by 224 relations. Form quot and then images (0.091 s) (total time to create space = 0.28 s) Computing index-1 degeneracy map from level 2505 to 501. (0.42 s) Computing index-5 degeneracy map from level 2505 to 501. (0.53 s) Computing index-1 degeneracy map from level 501 to 2505. (1.16 s) Computing index-5 degeneracy map from level 501 to 2505. (1.31 s) Computing 167-new part of Modular symbols space of level 2505, weight 2, and dimension 333. Computing space of modular symbols of level 15 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 8 relations. Form quot and then images (0.009 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 2505 to 15. (0.069 s) Computing index-167 degeneracy map from level 2505 to 15. (14.66 s) Computing index-1 degeneracy map from level 15 to 2505. (3.059 s) Computing index-167 degeneracy map from level 15 to 2505. (3.331 s) Finding newform decomposition of Modular symbols space of level 2505, weight 2, and dimension 333. Computing cuspidal part of Modular symbols space of level 2505, weight 2, and dimension 333 Decomposing space of level 2505 and dimension 111 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 111. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). 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T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^111 - 5*x^110 - 157*x^109 + 817*x^108 + 11894*x^107 - 64710*x^106 - 578854*x^105 + 3310254*x^104 + 20324003*x^103 - 122952191*x^102 - 547973295*x^101 + 3534300563*x^100 + 11787381460*x^99 - 81838161196*x^98 - 207384041476*x^97 + 1568832929260*x^96 + 3032973877223*x^95 - 25395292425939*x^94 - 37225499035871*x^93 + 352321884376739*x^92 + 384614936096802*x^91 - 4237666230301418*x^90 - 3327201933399054*x^89 + 44591778256538550*x^88 + 23600403447064581*x^87 - 413505412075766889*x^86 - 129070374726423261*x^85 + 3399083632765427785*x^84 + 425965881545605148*x^83 - 24887293033861706324*x^82 + 932013385279460408*x^81 + 162939110126143349304*x^80 - 29472623558228094624*x^79 - 956937980648121426264*x^78 + 295331172208684511652*x^77 + 5054327847610313288804*x^76 - 2140733897880038451462*x^75 - 24057083595837523701922*x^74 + 12701470863014560784658*x^73 + 103346876752591409723982*x^72 - 64469601616057662345628*x^71 - 401160399710521175667044*x^70 + 285907188856676307772088*x^69 + 1408082660173609482473560*x^68 - 1120876251143431735858866*x^67 - 4470874589141324968264182*x^66 + 3912350192585581879363022*x^65 + 12841736433155348135056770*x^64 - 12212757083139609659717744*x^63 - 33356821563827655216025728*x^62 + 34191645918660823529061992*x^61 + 78304416109577671876505952*x^60 - 86000606504919158794852694*x^59 - 165951771872945619628622410*x^58 + 194509824869588430907278610*x^57 + 317070734688755196241709366*x^56 - 395674188195699513694532640*x^55 - 545138923873395531683088408*x^54 + 723682484279088147019939388*x^53 + 841433837274250414357761156*x^52 - 1189100596761051426592664058*x^51 - 1162589153489285522480068478*x^50 + 1753068121884741868087236982*x^49 + 1432662103746542368286967426*x^48 - 2314985342788161777040045292*x^47 - 1567403239739944480321346396*x^46 + 2732351572973117934434616600*x^45 + 1513489701519622196613270232*x^44 - 2874997483004919799591869792*x^43 - 1279803310844676697356497064*x^42 + 2688543424256326779351351204*x^41 + 937388165845038281919023412*x^40 - 2226467875754057683859891227*x^39 - 584938342790152244103897017*x^38 + 1626025329639304045107138195*x^37 + 302271430003822674678615609*x^36 - 1042219573228031246450992058*x^35 - 121914940980087140444271958*x^34 + 583036655531857907624374966*x^33 + 32019177702624008727767154*x^32 - 282837103452858518981773841*x^31 + 340015567163716351668277*x^30 + 118090735215008510665135081*x^29 - 6167899437319940355372637*x^28 - 42062467988473363448102180*x^27 + 4163371054719784953287116*x^26 + 12647427837842985653448860*x^25 - 1799646267421742354632012*x^24 - 3169600872316577493624665*x^23 + 580411311821916690689413*x^22 + 651702981953643032928621*x^21 - 145108989254194494984697*x^20 - 107742214734664905304074*x^19 + 28301860220044065131850*x^18 + 13942255025941357325234*x^17 - 4268590858088192512954*x^16 - 1359053294990999819731*x^15 + 488057897892396633583*x^14 + 93888395469531018119*x^13 - 40990481028764043147*x^12 - 4079668483651830712*x^11 + 2412701493292579832*x^10 + 75146825293416560*x^9 - 92754155708556336*x^8 + 1639928139328000*x^7 + 2091089480154752*x^6 - 102814684153856*x^5 - 23498884146688*x^4 + 1502310359040*x^3 + 101224988672*x^2 - 5322403840*x - 180596736 time = 20.76 Factoring characteristic polynomial. [ , , , , , , , , , , ] time = 0.541 Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x^2 - 3*x + 1. Cutting out subspace using f(T_2), where f=x^3 - 4*x + 1. Cutting out subspace using f(T_2), where f=x^8 + 3*x^7 - 5*x^6 - 17*x^5 + 7*x^4 + 25*x^3 - 5*x^2 - 7*x - 1. Cutting out subspace using f(T_2), where f=x^9 - 10*x^7 + 32*x^5 + 2*x^4 - 36*x^3 - 4*x^2 + 8*x - 1. Cutting out subspace using f(T_2), where f=x^10 - 6*x^9 + 2*x^8 + 47*x^7 - 71*x^6 - 80*x^5 + 199*x^4 - 35*x^3 - 88*x^2 + 34*x + 1. Cutting out subspace using f(T_2), where f=x^13 - 2*x^12 - 18*x^11 + 34*x^10 + 121*x^9 - 212*x^8 - 382*x^7 + 596*x^6 + 606*x^5 - 749*x^4 - 502*x^3 + 360*x^2 + 186*x - 23. Cutting out subspace using f(T_2), where f=x^14 - 21*x^12 + 170*x^10 - 666*x^8 + 1286*x^6 - 13*x^5 - 1072*x^4 + 51*x^3 + 238*x^2 - 24*x - 8. Cutting out subspace using f(T_2), where f=x^14 + 4*x^13 - 13*x^12 - 62*x^11 + 56*x^10 + 360*x^9 - 84*x^8 - 982*x^7 + 10*x^6 + 1299*x^5 + 36*x^4 - 725*x^3 + 18*x^2 + 80*x - 8. Cutting out subspace using f(T_2), where f=x^18 + x^17 - 32*x^16 - 31*x^15 + 423*x^14 + 396*x^13 - 2985*x^12 - 2693*x^11 + 12127*x^10 + 10505*x^9 - 28504*x^8 - 23593*x^7 + 36891*x^6 + 29034*x^5 - 23047*x^4 - 17331*x^3 + 4686*x^2 + 3680*x + 216. Cutting out subspace using f(T_2), where f=x^19 - 3*x^18 - 27*x^17 + 83*x^16 + 295*x^15 - 937*x^14 - 1681*x^13 + 5587*x^12 + 5358*x^11 - 19039*x^10 - 9461*x^9 + 37523*x^8 + 8393*x^7 - 41427*x^6 - 2483*x^5 + 23755*x^4 - 763*x^3 - 6166*x^2 + 296*x + 568. Computing representation of Modular symbols space of level 2505, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). %o x^2 - 3*x + 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^3 - 4*x + 1 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^8 + 3*x^7 - 5*x^6 - 17*x^5 + 7*x^4 + 25*x^3 - 5*x^2 - 7*x - 1 p = %o, dimension = %o. 2 8 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 9. Goal dimension = 9. Computing T_2 on dual space of dimension 9. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^9 - 10*x^7 + 32*x^5 + 2*x^4 - 36*x^3 - 4*x^2 + 8*x - 1 p = %o, dimension = %o. 2 9 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 10. Goal dimension = 10. Computing T_2 on dual space of dimension 10. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^10 - 6*x^9 + 2*x^8 + 47*x^7 - 71*x^6 - 80*x^5 + 199*x^4 - 35*x^3 - 88*x^2 + 34*x + 1 p = %o, dimension = %o. 2 10 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 13. Goal dimension = 13. Computing T_2 on dual space of dimension 13. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^13 - 2*x^12 - 18*x^11 + 34*x^10 + 121*x^9 - 212*x^8 - 382*x^7 + 596*x^6 + 606*x^5 - 749*x^4 - 502*x^3 + 360*x^2 + 186*x - 23 p = %o, dimension = %o. 2 13 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 14. Goal dimension = 14. Computing T_2 on dual space of dimension 14. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^14 - 21*x^12 + 170*x^10 - 666*x^8 + 1286*x^6 - 13*x^5 - 1072*x^4 + 51*x^3 + 238*x^2 - 24*x - 8 p = %o, dimension = %o. 2 14 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 14. Goal dimension = 14. Computing T_2 on dual space of dimension 14. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^14 + 4*x^13 - 13*x^12 - 62*x^11 + 56*x^10 + 360*x^9 - 84*x^8 - 982*x^7 + 10*x^6 + 1299*x^5 + 36*x^4 - 725*x^3 + 18*x^2 + 80*x - 8 p = %o, dimension = %o. 2 14 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 18. Goal dimension = 18. Computing T_2 on dual space of dimension 18. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^18 + x^17 - 32*x^16 - 31*x^15 + 423*x^14 + 396*x^13 - 2985*x^12 - 2693*x^11 + 12127*x^10 + 10505*x^9 - 28504*x^8 - 23593*x^7 + 36891*x^6 + 29034*x^5 - 23047*x^4 - 17331*x^3 + 4686*x^2 + 3680*x + 216 p = %o, dimension = %o. 2 18 Computing representation of Modular symbols space of level 2505, weight 2, and dimension 19. Goal dimension = 19. Computing T_2 on dual space of dimension 19. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^19 - 3*x^18 - 27*x^17 + 83*x^16 + 295*x^15 - 937*x^14 - 1681*x^13 + 5587*x^12 + 5358*x^11 - 19039*x^10 - 9461*x^9 + 37523*x^8 + 8393*x^7 - 41427*x^6 - 2483*x^5 + 23755*x^4 - 763*x^3 - 6166*x^2 + 296*x + 568 p = %o, dimension = %o. 2 19 Computing cuspidal part of Full Modular symbols space of level 835, weight 2, and dimension 86 Computing cuspidal part of Modular symbols space of level 835, weight 2, and dimension 83 Computing new part of Modular symbols space of level 835, weight 2, and dimension 83. Computing 5-new part of Modular symbols space of level 835, weight 2, and dimension 83. Computing space of modular symbols of level 167 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.05 s) III. 3-term relations. Computing quotient by 56 relations. Form quot and then images (0.009 s) (total time to create space = 0.07 s) Computing index-1 degeneracy map from level 835 to 167. (0.029 s) Computing index-5 degeneracy map from level 835 to 167. (0.05 s) Computing index-1 degeneracy map from level 167 to 835. (0.269 s) Computing index-5 degeneracy map from level 167 to 835. (0.279 s) Computing DualVectorSpace of Modular symbols space of level 835, weight 2, and dimension 83. Computing complement of Modular symbols space of level 835, weight 2, and dimension 83 Computing representation of Modular symbols space of level 835, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 86. (0.01 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 835, weight 2, and dimension 3 Computing 167-new part of Modular symbols space of level 835, weight 2, and dimension 83. Computing space of modular symbols of level 5 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 835 to 5. (0.019 s) Computing index-167 degeneracy map from level 835 to 5. (5.359 s) Computing index-1 degeneracy map from level 5 to 835. (1.07 s) Computing index-167 degeneracy map from level 5 to 835. (1 s) Decomposing space of level 835 and dimension 55 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 55. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^55 + 3*x^54 - 77*x^53 - 235*x^52 + 2772*x^51 + 8632*x^50 - 61988*x^49 - 197664*x^48 + 964844*x^47 + 3164424*x^46 - 11099534*x^45 - 37647996*x^44 + 97794234*x^43 + 345427062*x^42 - 674615040*x^41 - 2503627874*x^40 + 3692195712*x^39 + 14566340136*x^38 - 16137947344*x^37 - 68760863156*x^36 + 56353389641*x^35 + 265155078595*x^34 - 156141012894*x^33 - 838446667918*x^32 + 337046114030*x^31 + 2176870405714*x^30 - 542930335865*x^29 - 4636368356475*x^28 + 576705135144*x^27 + 8076350162444*x^26 - 177880949808*x^25 - 11448268997686*x^24 - 702085289684*x^23 + 13109100529292*x^22 + 1683817466498*x^21 - 12006568152362*x^20 - 2179049424016*x^19 + 8682034998348*x^18 + 1928444379154*x^17 - 4872660557864*x^16 - 1225705559784*x^15 + 2075103034896*x^14 + 561121574205*x^13 - 650403356033*x^12 - 181077099759*x^11 + 143786314523*x^10 + 39336869727*x^9 - 21078642615*x^8 - 5283015045*x^7 + 1866229341*x^6 + 368618744*x^5 - 86413600*x^4 - 7971984*x^3 + 1715504*x^2 - 62080*x + 448 time = 0.119 Factoring characteristic polynomial. [ , , , ] time = 0.09 Cutting out subspace using f(T_2), where f=x^6 + 2*x^5 - 4*x^4 - 8*x^3 + 2*x^2 + 5*x + 1. Cutting out subspace using f(T_2), where f=x^11 - 2*x^10 - 13*x^9 + 24*x^8 + 58*x^7 - 97*x^6 - 97*x^5 + 147*x^4 + 37*x^3 - 64*x^2 - 4*x + 8. Cutting out subspace using f(T_2), where f=x^16 + 5*x^15 - 11*x^14 - 85*x^13 + 9*x^12 + 550*x^11 + 301*x^10 - 1721*x^9 - 1443*x^8 + 2713*x^7 + 2643*x^6 - 2042*x^5 - 2018*x^4 + 650*x^3 + 474*x^2 - 108*x + 1. Cutting out subspace using f(T_2), where f=x^22 - 2*x^21 - 35*x^20 + 68*x^19 + 522*x^18 - 975*x^17 - 4349*x^16 + 7693*x^15 + 22323*x^14 - 36594*x^13 - 73484*x^12 + 108227*x^11 + 156372*x^10 - 198065*x^9 - 210582*x^8 + 215538*x^7 + 169195*x^6 - 127037*x^5 - 71905*x^4 + 32761*x^3 + 12312*x^2 - 1964*x + 56. Computing representation of Modular symbols space of level 835, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^6 + 2*x^5 - 4*x^4 - 8*x^3 + 2*x^2 + 5*x + 1 p = %o, dimension = %o. 2 6 Computing representation of Modular symbols space of level 835, weight 2, and dimension 11. Goal dimension = 11. Computing T_2 on dual space of dimension 11. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^11 - 2*x^10 - 13*x^9 + 24*x^8 + 58*x^7 - 97*x^6 - 97*x^5 + 147*x^4 + 37*x^3 - 64*x^2 - 4*x + 8 p = %o, dimension = %o. 2 11 Computing representation of Modular symbols space of level 835, weight 2, and dimension 16. Goal dimension = 16. Computing T_2 on dual space of dimension 16. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^16 + 5*x^15 - 11*x^14 - 85*x^13 + 9*x^12 + 550*x^11 + 301*x^10 - 1721*x^9 - 1443*x^8 + 2713*x^7 + 2643*x^6 - 2042*x^5 - 2018*x^4 + 650*x^3 + 474*x^2 - 108*x + 1 p = %o, dimension = %o. 2 16 Computing representation of Modular symbols space of level 835, weight 2, and dimension 22. Goal dimension = 22. Computing T_2 on dual space of dimension 22. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^22 - 2*x^21 - 35*x^20 + 68*x^19 + 522*x^18 - 975*x^17 - 4349*x^16 + 7693*x^15 + 22323*x^14 - 36594*x^13 - 73484*x^12 + 108227*x^11 + 156372*x^10 - 198065*x^9 - 210582*x^8 + 215538*x^7 + 169195*x^6 - 127037*x^5 - 71905*x^4 + 32761*x^3 + 12312*x^2 - 1964*x + 56 p = %o, dimension = %o. 2 22 Computing cuspidal part of Full Modular symbols space of level 501, weight 2, and dimension 58 Computing cuspidal part of Modular symbols space of level 501, weight 2, and dimension 55 Computing new part of Modular symbols space of level 501, weight 2, and dimension 55. Computing 3-new part of Modular symbols space of level 501, weight 2, and dimension 55. Computing index-1 degeneracy map from level 501 to 167. (0.021 s) Computing index-3 degeneracy map from level 501 to 167. (0.03 s) Computing index-1 degeneracy map from level 167 to 501. (0.129 s) Computing index-3 degeneracy map from level 167 to 501. (0.201 s) Computing DualVectorSpace of Modular symbols space of level 501, weight 2, and dimension 55. Computing complement of Modular symbols space of level 501, weight 2, and dimension 55 Computing representation of Modular symbols space of level 501, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 58. (0.009 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 501, weight 2, and dimension 3 Computing 167-new part of Modular symbols space of level 501, weight 2, and dimension 55. Computing space of modular symbols of level 3 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 501 to 3. (0.01 s) Computing index-167 degeneracy map from level 501 to 3. (4.339 s) Computing index-1 degeneracy map from level 3 to 501. (1.081 s) Computing index-167 degeneracy map from level 3 to 501. (0.809 s) Decomposing space of level 501 and dimension 27 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 27. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing characteristic polynomial of T_2. x^27 + 3*x^26 - 35*x^25 - 105*x^24 + 533*x^23 + 1591*x^22 - 4651*x^21 - 13701*x^20 + 25791*x^19 + 74041*x^18 - 95271*x^17 - 261849*x^16 + 238553*x^15 + 614247*x^14 - 401869*x^13 - 951187*x^12 + 437972*x^11 + 954068*x^10 - 281938*x^9 - 598886*x^8 + 86243*x^7 + 219637*x^6 - 1211*x^5 - 40793*x^4 - 4569*x^3 + 2769*x^2 + 595*x + 21 time = 0.01 Factoring characteristic polynomial. [ , , , , ] time = 0.019 Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x^5 - 5*x^3 + 4*x + 1. Cutting out subspace using f(T_2), where f=x^5 + 4*x^4 + x^3 - 8*x^2 - 2*x + 3. Cutting out subspace using f(T_2), where f=x^8 - 3*x^7 - 8*x^6 + 28*x^5 + 9*x^4 - 64*x^3 + 17*x^2 + 23*x + 1. Cutting out subspace using f(T_2), where f=x^8 + 3*x^7 - 10*x^6 - 34*x^5 + 17*x^4 + 100*x^3 + 43*x^2 - 21*x - 7. Computing representation of Modular symbols space of level 501, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 501, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^5 - 5*x^3 + 4*x + 1 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 501, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^5 + 4*x^4 + x^3 - 8*x^2 - 2*x + 3 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 501, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^8 - 3*x^7 - 8*x^6 + 28*x^5 + 9*x^4 - 64*x^3 + 17*x^2 + 23*x + 1 p = %o, dimension = %o. 2 8 Computing representation of Modular symbols space of level 501, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^8 + 3*x^7 - 10*x^6 - 34*x^5 + 17*x^4 + 100*x^3 + 43*x^2 - 21*x - 7 p = %o, dimension = %o. 2 8 Computing cuspidal part of Full Modular symbols space of level 167, weight 2, and dimension 15 Computing cuspidal part of Modular symbols space of level 167, weight 2, and dimension 14 Computing new part of Modular symbols space of level 167, weight 2, and dimension 14. Computing 167-new part of Modular symbols space of level 167, weight 2, and dimension 14. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 167 and dimension 14 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 14. Computing DualVectorSpace of Modular symbols space of level 167, weight 2, and dimension 14. Computing complement of Modular symbols space of level 167, weight 2, and dimension 14 Computing representation of Modular symbols space of level 167, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 15. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 167, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^14 - x^13 - 20*x^12 + 18*x^11 + 153*x^10 - 119*x^9 - 569*x^8 + 359*x^7 + 1087*x^6 - 517*x^5 - 1001*x^4 + 348*x^3 + 334*x^2 - 111*x - 9 time = 0 Factoring characteristic polynomial. [ , ] time = 0.01 Cutting out subspace using f(T_2), where f=x^2 + x - 1. Cutting out subspace using f(T_2), where f=x^12 - 2*x^11 - 17*x^10 + 33*x^9 + 103*x^8 - 189*x^7 - 277*x^6 + 447*x^5 + 363*x^4 - 433*x^3 - 205*x^2 + 120*x + 9. Computing representation of Modular symbols space of level 167, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 + x - 1 p = %o, dimension = %o. 2 2 Computing index-1 degeneracy map from level 167 to 2505. (1.23 s) Computing index-3 degeneracy map from level 167 to 2505. (1.21 s) Computing index-5 degeneracy map from level 167 to 2505. (1.319 s) Computing index-15 degeneracy map from level 167 to 2505. (1.329 s) Computing representation of Modular symbols space of level 167, weight 2, and dimension 12. Computing complement of Modular symbols space of level 167, weight 2, and dimension 12 Computing DualVectorSpace of Modular symbols space of level 167, weight 2, and dimension 3. Goal dimension = 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 3. (0 s) %o x^3 - 2*x^2 - 4*x + 3 p = 2, dimension = 3. Computing complement of Modular symbols space of level 167, weight 2, and dimension 3 Computing cuspidal part of Full Modular symbols space of level 15, weight 2, and dimension 4 Computing cuspidal part of Modular symbols space of level 15, weight 2, and dimension 1 Computing new part of Modular symbols space of level 15, weight 2, and dimension 1. Computing 3-new part of Modular symbols space of level 15, weight 2, and dimension 1. Computing index-1 degeneracy map from level 15 to 5. (0 s) Computing index-3 degeneracy map from level 15 to 5. (0.009 s) Computing index-1 degeneracy map from level 5 to 15. (0.02 s) Computing index-3 degeneracy map from level 5 to 15. (0.01 s) Computing DualVectorSpace of Modular symbols space of level 15, weight 2, and dimension 1. Goal dimension = 1. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 1. Computing T_2 on space of dimension 4. (0 s) (0 s) %o x + 1 p = 2, dimension = 1. Computing 5-new part of Modular symbols space of level 15, weight 2, and dimension 1. Computing index-1 degeneracy map from level 15 to 3. (0 s) Computing index-5 degeneracy map from level 15 to 3. (0.01 s) Computing index-1 degeneracy map from level 3 to 15. (0.019 s) Computing index-5 degeneracy map from level 3 to 15. (0.009 s) Decomposing space of level 15 and dimension 1 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Sorting ... 4.19 seconds. Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.019 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.019 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.02 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 3. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 3. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 3. T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 3. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 3. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 3. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 3. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 3. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). Computing T_37 on dual space of dimension 3. T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 8. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 8. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 8. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 8. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 8. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 8. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 8. T_19 sparse... (0.019 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 8. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 8. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.021 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 8. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.02 s). Computing T_37 on dual space of dimension 8. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). Computing T_3 on dual space of dimension 9. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 9. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 9. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 9. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.011 s). Computing T_13 on dual space of dimension 9. T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 9. T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 9. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.019 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 9. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.02 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). Computing T_29 on dual space of dimension 9. T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 9. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.021 s). Computing T_37 on dual space of dimension 9. T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 10. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 10. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 10. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 10. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 10. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 10. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.02 s). Computing T_19 on dual space of dimension 10. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 10. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.02 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 10. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). Computing T_31 on dual space of dimension 10. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 10. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 13. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 13. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 13. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 13. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.011 s). Computing T_13 on dual space of dimension 13. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 13. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 13. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.021 s). T_19 sparse... (0.009 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 13. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 13. T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.021 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 13. T_31 sparse... (0.009 s). T_31 sparse... (0.02 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.021 s). T_31 sparse... (0.009 s). T_31 sparse... (0.011 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 13. T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 14. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 14. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 14. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 14. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 14. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.011 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 14. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.02 s). Computing T_19 on dual space of dimension 14. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.02 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 14. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.02 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 14. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.011 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 14. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.02 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 14. T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). Computing T_3 on dual space of dimension 14. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 14. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 14. T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 14. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 14. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 14. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 14. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.019 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.011 s). Computing T_23 on dual space of dimension 14. T_23 sparse... (0.009 s). T_23 sparse... (0.02 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 14. T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.011 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). Computing T_31 on dual space of dimension 14. T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.02 s). Computing T_37 on dual space of dimension 14. T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.021 s). T_37 sparse... (0.009 s). T_37 sparse... (0.011 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 18. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 18. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 18. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 18. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 18. T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 18. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.019 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 18. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.019 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 18. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 18. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.011 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 18. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.02 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 18. T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 19. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 19. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 19. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 19. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 19. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 19. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.019 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 19. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.019 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 19. T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 19. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.021 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 19. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.021 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.02 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 19. T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). Computing q-expansion. T_2 sparse... (0.01 s). T_3 sparse... (0.009 s). T_5 sparse... (0.011 s). T_7 sparse... (0.009 s). T_11 sparse... (0.01 s). T_13 sparse... (0.009 s). T_17 sparse... (0.01 s). T_19 sparse... (0.009 s). T_23 sparse... (0.01 s). T_29 sparse... (0.019 s). T_31 sparse... (0.009 s). T_37 sparse... (0.01 s). (0.161 s) Computing q-expansion. T_2 sparse... (0 s). T_3 sparse... (0 s). T_5 sparse... (0.01 s). T_7 sparse... (0.009 s). T_11 sparse... (0.01 s). T_13 sparse... (0.009 s). T_17 sparse... (0.01 s). T_19 sparse... (0.009 s). T_23 sparse... (0.021 s). T_29 sparse... (0.009 s). T_31 sparse... (0.011 s). T_37 sparse... (0.009 s). (0.17 s) Computing q-expansion. (0.04 s) Computing q-expansion. T_2 sparse... (0 s). T_3 sparse... (0 s). T_5 sparse... (0.01 s). T_7 sparse... (0.01 s). T_11 sparse... (0.009 s). T_13 sparse... (0.011 s). T_17 sparse... (0.01 s). T_19 sparse... (0.009 s). T_23 sparse... (0.01 s). T_29 sparse... (0.009 s). T_31 sparse... (0.02 s). T_37 sparse... (0.01 s). (0.201 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.17 s) Computing q-expansion. (0.079 s) Computing q-expansion. (0.109 s) Computing q-expansion. (0.049 s) Computing q-expansion. (0.331 s) Computing q-expansion. (0.119 s) Computing character group of torus of J_0(3*835)/F_3. 234.3 seconds. Computing T_2 on space of dimension 1. (0.01 s) Computing T_3 on space of dimension 1. Computing T_3 on space of dimension 340. (0.181 s) (0.19 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing character group of torus of J_0(5*501)/F_5. 418.94 seconds. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing character group of torus of J_0(167*15)/F_167. 830.88 seconds. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 2. (0.03 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 3. (0.039 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 8. (0.17 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 9. (0.13 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 10. (0.229 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 13. (0.191 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 14. (0.261 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 14. (0.22 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 18. (0.48 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 19. (0.259 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_7 on space of dimension 1. Computing T_7 on space of dimension 340. (0.289 s) (0.299 s) Computing T_11 on space of dimension 1. Computing T_11 on space of dimension 340. (0.41 s) (0.43 s) Computing T_13 on space of dimension 1. Computing T_13 on space of dimension 340. (0.489 s) (0.52 s) Computing T_17 on space of dimension 1. Computing T_17 on space of dimension 340. (0.619 s) (0.649 s) Computing T_19 on space of dimension 1. Computing T_19 on space of dimension 340. (0.67 s) (0.699 s) Computing T_23 on space of dimension 1. Computing T_23 on space of dimension 340. (0.841 s) (0.871 s) Computing T_29 on space of dimension 1. Computing T_29 on space of dimension 340. (1.061 s) (1.091 s) Computing T_31 on space of dimension 1. Computing T_31 on space of dimension 340. (1.15 s) (1.181 s) Computing T_37 on space of dimension 1. Computing T_37 on space of dimension 340. (1.369 s) (1.399 s) Computing T_7 on space of dimension 2. (0.041 s) Computing T_11 on space of dimension 2. (0.041 s) Computing T_13 on space of dimension 2. (0.051 s) Computing T_17 on space of dimension 2. (0.051 s) Computing T_19 on space of dimension 2. (0.05 s) Computing T_23 on space of dimension 2. (0.049 s) Computing T_29 on space of dimension 2. (0.05 s) Computing T_31 on space of dimension 2. (0.05 s) Computing T_37 on space of dimension 2. (0.05 s) Computing T_7 on space of dimension 3. (0.059 s) Computing T_11 on space of dimension 3. (0.061 s) Computing T_13 on space of dimension 3. (0.069 s) Computing T_17 on space of dimension 3. (0.07 s) Computing T_19 on space of dimension 3. (0.08 s) Computing T_23 on space of dimension 3. (0.07 s) Computing T_29 on space of dimension 3. (0.079 s) Computing T_31 on space of dimension 3. (0.069 s) Computing T_37 on space of dimension 3. (0.069 s) Computing T_7 on space of dimension 8. (0.231 s) Computing T_11 on space of dimension 8. (0.259 s) Computing T_13 on space of dimension 8. (0.27 s) Computing T_17 on space of dimension 8. (0.289 s) Computing T_19 on space of dimension 8. (0.301 s) Computing T_23 on space of dimension 8. (0.3 s) Computing T_29 on space of dimension 8. (0.309 s) Computing T_31 on space of dimension 8. (0.311 s) Computing T_37 on space of dimension 8. (0.319 s) Computing T_7 on space of dimension 9. (0.181 s) Computing T_11 on space of dimension 9. (0.199 s) Computing T_13 on space of dimension 9. (0.21 s) Computing T_17 on space of dimension 9. (0.22 s) Computing T_19 on space of dimension 9. (0.229 s) Computing T_23 on space of dimension 9. (0.231 s) Computing T_29 on space of dimension 9. (0.239 s) Computing T_31 on space of dimension 9. (0.239 s) Computing T_37 on space of dimension 9. (0.251 s) Computing T_7 on space of dimension 10. (0.291 s) Computing T_11 on space of dimension 10. (0.319 s) Computing T_13 on space of dimension 10. (0.34 s) Computing T_17 on space of dimension 10. (0.369 s) Computing T_19 on space of dimension 10. (0.38 s) Computing T_23 on space of dimension 10. (0.379 s) Computing T_29 on space of dimension 10. (0.391 s) Computing T_31 on space of dimension 10. (0.389 s) Computing T_37 on space of dimension 10. (0.399 s) Computing T_7 on space of dimension 13. (0.26 s) Computing T_11 on space of dimension 13. (0.291 s) Computing T_13 on space of dimension 13. (0.3 s) Computing T_17 on space of dimension 13. (0.319 s) Computing T_19 on space of dimension 13. (0.329 s) Computing T_23 on space of dimension 13. (0.331 s) Computing T_29 on space of dimension 13. (0.34 s) Computing T_31 on space of dimension 13. (0.349 s) Computing T_37 on space of dimension 13. (0.36 s) Computing T_7 on space of dimension 14. (0.349 s) Computing T_11 on space of dimension 14. (0.399 s) Computing T_13 on space of dimension 14. (0.42 s) Computing T_17 on space of dimension 14. (0.461 s) Computing T_19 on space of dimension 14. (0.46 s) Computing T_23 on space of dimension 14. (0.481 s) Computing T_29 on space of dimension 14. (0.501 s) Computing T_31 on space of dimension 14. (0.5 s) Computing T_37 on space of dimension 14. (0.511 s) Computing T_7 on space of dimension 14. (0.29 s) Computing T_11 on space of dimension 14. (0.341 s) Computing T_13 on space of dimension 14. (0.349 s) Computing T_17 on space of dimension 14. (0.391 s) Computing T_19 on space of dimension 14. (0.389 s) Computing T_23 on space of dimension 14. (0.399 s) Computing T_29 on space of dimension 14. (0.411 s) Computing T_31 on space of dimension 14. (0.42 s) Computing T_37 on space of dimension 14. (0.42 s) Computing T_7 on space of dimension 18. (0.6 s) Computing T_11 on space of dimension 18. (0.67 s) Computing T_13 on space of dimension 18. (0.71 s) Computing T_17 on space of dimension 18. (0.739 s) Computing T_19 on space of dimension 18. (0.761 s) Computing T_23 on space of dimension 18. (0.769 s) Computing T_29 on space of dimension 18. (0.789 s) Computing T_31 on space of dimension 18. (0.809 s) Computing T_37 on space of dimension 18. (0.809 s) Computing T_7 on space of dimension 19. (0.359 s) Computing T_11 on space of dimension 19. (0.409 s) Computing T_13 on space of dimension 19. (0.431 s) Computing T_17 on space of dimension 19. (0.471 s) Computing T_19 on space of dimension 19. (0.471 s) Computing T_23 on space of dimension 19. (0.49 s) Computing T_29 on space of dimension 19. (0.489 s) Computing T_31 on space of dimension 19. (0.5 s) Computing T_37 on space of dimension 19. (0.511 s) Computing T_1 on space of dimension 340. (0.009 s) T_2 sparse... (0.011 s). T_3 sparse... (0.01 s). Computing T_4 on space of dimension 340. (0.109 s) T_5 sparse... (0.009 s). Computing T_6 on space of dimension 340. (0.07 s) T_7 sparse... (0.011 s). Computing T_8 on space of dimension 340. (0.13 s) Computing T_9 on space of dimension 340. (0.1 s) Computing T_10 on space of dimension 340. Computing T_5 on space of dimension 340. (0.239 s) (0.319 s) T_11 sparse... (0.01 s). Computing T_12 on space of dimension 340. (0.131 s) T_13 sparse... (0.009 s). Computing T_14 on space of dimension 340. (0.1 s) Computing T_15 on space of dimension 340. (0.09 s) Computing T_16 on space of dimension 340. (0.139 s) T_17 sparse... (0.01 s). Computing T_18 on space of dimension 340. (0.099 s) T_19 sparse... (0.01 s). Computing T_20 on space of dimension 340. (0.149 s) Computing T_21 on space of dimension 340. (0.1 s) Computing T_22 on space of dimension 340. (0.099 s) T_23 sparse... (0.01 s). Computing T_24 on space of dimension 340. (0.251 s) Computing T_25 on space of dimension 340. (0.139 s) Computing T_26 on space of dimension 340. (0.099 s) Computing T_27 on space of dimension 340. (0.119 s) Computing T_28 on space of dimension 340. (0.181 s) T_29 sparse... (0.02 s). Computing T_30 on space of dimension 340. (0.1 s) T_31 sparse... (0.011 s). Computing T_32 on space of dimension 340. (0.159 s) Computing T_33 on space of dimension 340. (0.1 s) Computing T_34 on space of dimension 340. (0.1 s) Computing T_35 on space of dimension 340. (0.13 s) Computing T_36 on space of dimension 340. (0.17 s) T_37 sparse... (0.011 s). Computing T_38 on space of dimension 340. (0.099 s) Computing T_39 on space of dimension 340. (0.109 s) Computing T_40 on space of dimension 340. (0.279 s) T_41 sparse... (0.019 s). Computing T_42 on space of dimension 340. (0.101 s) T_43 sparse... (0.02 s). Computing T_44 on space of dimension 340. (0.189 s) Computing T_45 on space of dimension 340. (0.149 s) Computing T_46 on space of dimension 340. (0.109 s) T_47 sparse... (0.019 s). Computing T_48 on space of dimension 340. (0.371 s) Computing T_49 on space of dimension 340. (0.269 s) Computing T_50 on space of dimension 340. (0.099 s) Computing T_51 on space of dimension 340. (0.099 s) Computing T_52 on space of dimension 340. (0.189 s) T_53 sparse... (0.019 s). Computing T_54 on space of dimension 340. (0.111 s) Computing T_55 on space of dimension 340. (0.099 s) Computing T_56 on space of dimension 340. (0.34 s) Computing T_57 on space of dimension 340. (0.1 s) Computing T_58 on space of dimension 340. (0.11 s) T_59 sparse... (0.02 s). Computing T_60 on space of dimension 340. (0.18 s) T_61 sparse... (0.019 s). Computing T_62 on space of dimension 340. (0.1 s) Computing T_63 on space of dimension 340. (0.17 s) Computing T_64 on space of dimension 340. (0.25 s) Computing T_65 on space of dimension 340. (0.121 s) Computing T_66 on space of dimension 340. (0.109 s) T_67 sparse... (0.02 s). Computing T_68 on space of dimension 340. (0.189 s) Computing T_69 on space of dimension 340. (0.09 s) Computing T_70 on space of dimension 340. (0.11 s) T_71 sparse... (0.019 s). Computing T_72 on space of dimension 340. (0.331 s) T_73 sparse... (0.019 s). Computing T_74 on space of dimension 340. (0.11 s) Computing T_75 on space of dimension 340. (0.1 s) Computing T_76 on space of dimension 340. (0.18 s) Computing T_77 on space of dimension 340. (0.24 s) Computing T_78 on space of dimension 340. (0.109 s) T_79 sparse... (0.021 s). Computing T_80 on space of dimension 340. (0.42 s) Computing T_81 on space of dimension 340. (0.13 s) Computing T_82 on space of dimension 340. Computing T_41 on space of dimension 340. (1.57 s) (1.68 s) T_83 sparse... (0.02 s). Computing T_84 on space of dimension 340. (0.189 s) Computing T_85 on space of dimension 340. (0.129 s) Computing T_86 on space of dimension 340. Computing T_43 on space of dimension 340. (1.64 s) (1.75 s) Computing T_87 on space of dimension 340. (0.101 s) Computing T_88 on space of dimension 340. (0.34 s) T_89 sparse... (0.02 s). Computing T_90 on space of dimension 340. (0.099 s) Computing T_91 on space of dimension 340. (0.25 s) Computing T_92 on space of dimension 340. (0.19 s) Computing T_93 on space of dimension 340. (0.11 s) Computing T_94 on space of dimension 340. Computing T_47 on space of dimension 340. (1.8 s) (1.909 s) Computing T_95 on space of dimension 340. (0.13 s) Computing T_96 on space of dimension 340. (1.21 s) T_97 sparse... (0.029 s). Computing T_98 on space of dimension 340. (0.201 s) Computing T_99 on space of dimension 340. (0.179 s) Computing T_100 on space of dimension 340. (0.179 s) T_101 sparse... (0.029 s). Computing T_102 on space of dimension 340. (0.21 s) T_103 sparse... (0.029 s). Computing T_104 on space of dimension 340. (0.319 s) Computing T_105 on space of dimension 340. (0.11 s) Computing T_106 on space of dimension 340. Computing T_53 on space of dimension 340. (2.03 s) (2.24 s) T_107 sparse... (0.03 s). Computing T_108 on space of dimension 340. (0.18 s) T_109 sparse... (0.03 s). Computing T_110 on space of dimension 340. (0.199 s) Computing T_111 on space of dimension 340. (0.11 s) Computing T_112 on space of dimension 340. (0.529 s) T_113 sparse... (0.029 s). Computing T_114 on space of dimension 340. (0.199 s) Computing T_115 on space of dimension 340. (0.131 s) Computing T_116 on space of dimension 340. (0.199 s) Computing T_117 on space of dimension 340. (0.18 s) Computing T_118 on space of dimension 340. Computing T_59 on space of dimension 340. (2.279 s) (2.5 s) Computing T_119 on space of dimension 340. (0.251 s) Computing T_120 on space of dimension 340. (0.339 s) Computing T_121 on space of dimension 340. (0.369 s) Computing T_122 on space of dimension 340. Computing T_61 on space of dimension 340. (2.33 s) (2.54 s) Computing T_123 on space of dimension 340. (0.109 s) Computing T_124 on space of dimension 340. (0.189 s) Computing T_125 on space of dimension 340. (0.159 s) Computing T_126 on space of dimension 340. (0.21 s) T_127 sparse... (0.03 s). Computing T_128 on space of dimension 340. (0.25 s) Computing T_129 on space of dimension 340. (0.109 s) Computing T_130 on space of dimension 340. (0.21 s) T_131 sparse... (0.041 s). Computing T_132 on space of dimension 340. (0.191 s) Computing T_133 on space of dimension 340. (0.24 s) Computing T_134 on space of dimension 340. Computing T_67 on space of dimension 340. (2.579 s) (2.779 s) Computing T_135 on space of dimension 340. (0.3 s) Computing T_136 on space of dimension 340. (0.359 s) T_137 sparse... (0.04 s). Computing T_138 on space of dimension 340. (0.201 s) T_139 sparse... (0.039 s). Computing T_140 on space of dimension 340. (0.189 s) Computing T_141 on space of dimension 340. (0.109 s) Computing T_142 on space of dimension 340. Computing T_71 on space of dimension 340. (2.75 s) (2.97 s) Computing T_143 on space of dimension 340. (0.341 s) Computing T_144 on space of dimension 340. (0.47 s) Computing T_145 on space of dimension 340. (0.139 s) Computing T_146 on space of dimension 340. Computing T_73 on space of dimension 340. (2.789 s) (3 s) Computing T_147 on space of dimension 340. (0.189 s) Computing T_148 on space of dimension 340. (0.189 s) T_149 sparse... (0.04 s). Computing T_150 on space of dimension 340. (0.201 s) T_151 sparse... (0.039 s). Computing T_152 on space of dimension 340. (0.349 s) Computing T_153 on space of dimension 340. (0.189 s) Computing T_154 on space of dimension 340. (0.21 s) Computing T_155 on space of dimension 340. (0.131 s) Computing T_156 on space of dimension 340. (0.189 s) T_157 sparse... (0.04 s). Computing T_158 on space of dimension 340. Computing T_79 on space of dimension 340. (3.03 s) (3.23 s) Computing T_159 on space of dimension 340. (0.201 s) Computing T_160 on space of dimension 340. (1.46 s) Computing T_161 on space of dimension 340. (0.24 s) Computing T_162 on space of dimension 340. (0.211 s) T_163 sparse... (0.04 s). Computing T_164 on space of dimension 340. (0.19 s) Computing T_165 on space of dimension 340. (0.19 s) Computing T_166 on space of dimension 340. Computing T_83 on space of dimension 340. (3.189 s) (3.389 s) T_167 sparse... (0.039 s). Computing T_168 on space of dimension 340. (0.36 s) Computing T_169 on space of dimension 340. (0.441 s) Computing T_170 on space of dimension 340. (0.211 s) Computing T_171 on space of dimension 340. (0.201 s) Computing T_172 on space of dimension 340. (0.199 s) T_173 sparse... (0.049 s). Computing T_174 on space of dimension 340. (0.21 s) Computing T_175 on space of dimension 340. (0.479 s) Computing T_176 on space of dimension 340. (0.54 s) Computing T_177 on space of dimension 340. (0.199 s) Computing T_178 on space of dimension 340. Computing T_89 on space of dimension 340. (3.37 s) (3.57 s) T_179 sparse... (0.05 s). Computing T_180 on space of dimension 340. (0.189 s) T_181 sparse... (0.05 s). Computing T_182 on space of dimension 340. (0.219 s) Computing T_183 on space of dimension 340. (0.199 s) Computing T_184 on space of dimension 340. (0.359 s) Computing T_185 on space of dimension 340. (0.139 s) Computing T_186 on space of dimension 340. (0.199 s) Computing T_187 on space of dimension 340. (0.331 s) Computing T_188 on space of dimension 340. (0.189 s) Computing T_189 on space of dimension 340. (0.359 s) Computing T_190 on space of dimension 340. (0.21 s) T_191 sparse... (0.049 s). Computing T_192 on space of dimension 340. (1.34 s) T_193 sparse... (0.049 s). Computing T_194 on space of dimension 340. Computing T_97 on space of dimension 340. (3.68 s) (3.89 s) Computing T_195 on space of dimension 340. (0.199 s) Computing T_196 on space of dimension 340. (0.501 s) T_197 sparse... (0.059 s). Computing T_198 on space of dimension 340. (0.201 s) T_199 sparse... (0.049 s). Computing T_200 on space of dimension 340. (0.36 s) Computing T_201 on space of dimension 340. (0.2 s) Computing T_202 on space of dimension 340. Computing T_101 on space of dimension 340. (3.819 s) (4.029 s) Computing T_203 on space of dimension 340. (0.24 s) Computing T_204 on space of dimension 340. (0.501 s) Computing T_205 on space of dimension 340. (0.139 s) Computing T_206 on space of dimension 340. Computing T_103 on space of dimension 340. (3.869 s) (4.079 s) Computing T_207 on space of dimension 340. (0.191 s) Computing T_208 on space of dimension 340. (0.541 s) Computing T_209 on space of dimension 340. (0.359 s) Computing T_210 on space of dimension 340. (0.209 s) T_211 sparse... (0.06 s). Computing T_212 on space of dimension 340. (0.5 s) Computing T_213 on space of dimension 340. (0.199 s) Computing T_214 on space of dimension 340. Computing T_107 on space of dimension 340. (3.989 s) (4.189 s) Computing T_215 on space of dimension 340. (0.14 s) Computing T_216 on space of dimension 340. (0.36 s) Computing T_217 on space of dimension 340. (0.26 s) Computing T_218 on space of dimension 340. Computing T_109 on space of dimension 340. (4.029 s) (4.229 s) Computing T_219 on space of dimension 340. (0.19 s) Computing T_220 on space of dimension 340. (0.49 s) Computing T_221 on space of dimension 340. (0.399 s) Computing T_222 on space of dimension 340. (0.21 s) T_223 sparse... (0.059 s). Computing T_224 on space of dimension 340. (1.881 s) Computing T_225 on space of dimension 340. (0.18 s) Computing T_226 on space of dimension 340. Computing T_113 on space of dimension 340. (4.229 s) (4.439 s) T_227 sparse... (0.059 s). Computing T_228 on space of dimension 340. (0.501 s) T_229 sparse... (0.059 s). Computing T_230 on space of dimension 340. (0.21 s) Computing T_231 on space of dimension 340. (0.199 s) Computing T_232 on space of dimension 340. (0.361 s) T_233 sparse... (0.061 s). Computing T_234 on space of dimension 340. (0.201 s) Computing T_235 on space of dimension 340. (0.14 s) Computing T_236 on space of dimension 340. (0.5 s) Computing T_237 on space of dimension 340. (0.201 s) Computing T_238 on space of dimension 340. (0.21 s) T_239 sparse... (0.07 s). Computing T_240 on space of dimension 340. (0.539 s) T_241 sparse... (0.071 s). Computing T_242 on space of dimension 340. (0.209 s) Computing T_243 on space of dimension 340. (0.229 s) Computing T_244 on space of dimension 340. (0.5 s) Computing T_245 on space of dimension 340. (0.291 s) Computing T_246 on space of dimension 340. (0.201 s) Computing T_247 on space of dimension 340. (0.399 s) Computing T_248 on space of dimension 340. (0.359 s) Computing T_249 on space of dimension 340. (0.199 s) Computing T_250 on space of dimension 340. (0.21 s) T_251 sparse... (0.059 s). Computing T_252 on space of dimension 340. (0.489 s) Computing T_253 on space of dimension 340. (0.35 s) Computing T_254 on space of dimension 340. Computing T_127 on space of dimension 340. (4.659 s) (4.869 s) Computing T_255 on space of dimension 340. (0.211 s) Computing T_256 on space of dimension 340. (0.259 s) T_257 sparse... (0.069 s). Computing T_258 on space of dimension 340. (0.22 s) Computing T_259 on space of dimension 340. (0.25 s) Computing T_260 on space of dimension 340. (0.481 s) Computing T_261 on space of dimension 340. (0.179 s) Computing T_262 on space of dimension 340. Computing T_131 on space of dimension 340. (4.719 s) (4.929 s) T_263 sparse... (0.069 s). Computing T_264 on space of dimension 340. (0.36 s) Computing T_265 on space of dimension 340. (0.3 s) Computing T_266 on space of dimension 340. (0.199 s) Computing T_267 on space of dimension 340. (0.201 s) Computing T_268 on space of dimension 340. (0.489 s) T_269 sparse... (0.07 s). Computing T_270 on space of dimension 340. (0.199 s) T_271 sparse... (0.07 s). Computing T_272 on space of dimension 340. (0.529 s) Computing T_273 on space of dimension 340. (0.201 s) Computing T_274 on space of dimension 340. Computing T_137 on space of dimension 340. (5.01 s) (5.22 s) Computing T_275 on space of dimension 340. (0.371 s) Computing T_276 on space of dimension 340. (0.5 s) T_277 sparse... (0.081 s). Computing T_278 on space of dimension 340. Computing T_139 on space of dimension 340. (4.971 s) (5.181 s) Computing T_279 on space of dimension 340. (0.191 s) Computing T_280 on space of dimension 340. (0.36 s) T_281 sparse... (0.079 s). Computing T_282 on space of dimension 340. (0.199 s) T_283 sparse... (0.07 s). Computing T_284 on space of dimension 340. (0.5 s) Computing T_285 on space of dimension 340. (0.201 s) Computing T_286 on space of dimension 340. (0.199 s) Computing T_287 on space of dimension 340. (0.25 s) Computing T_288 on space of dimension 340. (1.729 s) Computing T_289 on space of dimension 340. (0.529 s) Computing T_290 on space of dimension 340. (0.22 s) Computing T_291 on space of dimension 340. (0.199 s) Computing T_292 on space of dimension 340. (0.49 s) T_293 sparse... (0.079 s). Computing T_294 on space of dimension 340. (0.21 s) Computing T_295 on space of dimension 340. (0.289 s) Computing T_296 on space of dimension 340. (0.361 s) Computing T_297 on space of dimension 340. (0.371 s) Computing T_298 on space of dimension 340. Computing T_149 on space of dimension 340. (5.349 s) (5.549 s) Computing T_299 on space of dimension 340. (0.409 s) Computing T_300 on space of dimension 340. (0.5 s) Computing T_301 on space of dimension 340. (0.25 s) Computing T_302 on space of dimension 340. Computing T_151 on space of dimension 340. (5.41 s) (5.62 s) Computing T_303 on space of dimension 340. (0.199 s) Computing T_304 on space of dimension 340. (0.541 s) Computing T_305 on space of dimension 340. (0.309 s) Computing T_306 on space of dimension 340. (0.21 s) T_307 sparse... (0.09 s). Computing T_308 on space of dimension 340. (0.49 s) Computing T_309 on space of dimension 340. (0.199 s) Computing T_310 on space of dimension 340. (0.201 s) T_311 sparse... (0.079 s). Computing T_312 on space of dimension 340. (0.349 s) T_313 sparse... (0.079 s). Computing T_314 on space of dimension 340. Computing T_157 on space of dimension 340. (5.569 s) (5.789 s) Computing T_315 on space of dimension 340. (0.181 s) Computing T_316 on space of dimension 340. (0.501 s) T_317 sparse... (0.081 s). Computing T_318 on space of dimension 340. (0.219 s) Computing T_319 on space of dimension 340. (0.34 s) Computing T_320 on space of dimension 340. (1.579 s) Computing T_321 on space of dimension 340. (0.2 s) Computing T_322 on space of dimension 340. (0.21 s) Computing T_323 on space of dimension 340. (0.501 s) Computing T_324 on space of dimension 340. (0.5 s) Computing T_325 on space of dimension 340. (0.371 s) Computing T_326 on space of dimension 340. Computing T_163 on space of dimension 340. (5.69 s) (5.89 s) Computing T_327 on space of dimension 340. (0.201 s) Computing T_328 on space of dimension 340. (0.349 s) Computing T_329 on space of dimension 340. (0.25 s) Computing T_330 on space of dimension 340. (0.201 s) T_331 sparse... (0.09 s). Computing T_332 on space of dimension 340. (0.489 s) Computing T_333 on space of dimension 340. (0.191 s) Computing T_334 on space of dimension 340. Computing T_167 on space of dimension 340. (11.569 s) (11.769 s) Computing T_335 on space of dimension 340. (0.299 s) Computing T_336 on space of dimension 340. (0.509 s) T_337 sparse... (0.09 s). Computing T_338 on space of dimension 340. (0.21 s) Computing T_339 on space of dimension 340. (0.199 s) Computing T_340 on space of dimension 340. (0.5 s) Computing T_341 on space of dimension 340. (0.349 s) Computing T_342 on space of dimension 340. (0.199 s) Computing T_343 on space of dimension 340. (0.721 s) Computing T_344 on space of dimension 340. (0.351 s) Computing T_345 on space of dimension 340. (0.21 s) Computing T_346 on space of dimension 340. Computing T_173 on space of dimension 340. (6.029 s) (6.239 s) T_347 sparse... (0.089 s). Computing T_348 on space of dimension 340. (0.501 s) T_349 sparse... (0.089 s). Computing T_350 on space of dimension 340. (0.211 s) Computing T_351 on space of dimension 340. (0.38 s) Computing T_352 on space of dimension 340. (2.099 s) T_353 sparse... (0.099 s). Computing T_354 on space of dimension 340. (0.21 s) Computing T_355 on space of dimension 340. (0.3 s) Computing T_356 on space of dimension 340. (0.5 s) Computing T_357 on space of dimension 340. (0.21 s) Computing T_358 on space of dimension 340. Computing T_179 on space of dimension 340. (6.17 s) (6.38 s) T_359 sparse... (0.101 s). Computing T_360 on space of dimension 340. (0.349 s) Computing T_361 on space of dimension 340. (0.55 s) Computing T_362 on space of dimension 340. Computing T_181 on space of dimension 340. (6.189 s) (6.399 s) Computing T_363 on space of dimension 340. (0.199 s) Computing T_364 on space of dimension 340. (0.5 s) Computing T_365 on space of dimension 340. (0.299 s) Computing T_366 on space of dimension 340. (0.21 s) T_367 sparse... (0.101 s). Computing T_368 on space of dimension 340. (0.55 s) Computing T_369 on space of dimension 340. (0.181 s) Computing T_370 on space of dimension 340. (0.21 s) Computing T_371 on space of dimension 340. (0.681 s) Computing T_372 on space of dimension 340. (0.501 s) T_373 sparse... (0.09 s). Computing T_374 on space of dimension 340. (0.211 s) Computing T_375 on space of dimension 340. (0.19 s) Computing T_376 on space of dimension 340. (0.36 s) Computing T_377 on space of dimension 340. (0.399 s) Computing T_378 on space of dimension 340. (0.21 s) T_379 sparse... (0.099 s). Computing T_380 on space of dimension 340. (0.49 s) Computing T_381 on space of dimension 340. (0.199 s) Computing T_382 on space of dimension 340. Computing T_191 on space of dimension 340. (6.43 s) (6.63 s) T_383 sparse... (0.099 s). Computing T_384 on space of dimension 340. (1.381 s) Computing T_385 on space of dimension 340. (0.3 s) Computing T_386 on space of dimension 340. Computing T_193 on space of dimension 340. (6.51 s) (6.72 s) Computing T_387 on space of dimension 340. (0.179 s) Computing T_388 on space of dimension 340. (0.5 s) T_389 sparse... (0.111 s). Computing T_390 on space of dimension 340. (0.209 s) Computing T_391 on space of dimension 340. (0.51 s) Computing T_392 on space of dimension 340. (1.05 s) Computing T_393 on space of dimension 340. (0.199 s) Computing T_394 on space of dimension 340. Computing T_197 on space of dimension 340. (6.68 s) (6.89 s) Computing T_395 on space of dimension 340. (0.31 s) Computing T_396 on space of dimension 340. (0.5 s) T_397 sparse... (0.099 s). Computing T_398 on space of dimension 340. Computing T_199 on space of dimension 340. (6.699 s) (6.909 s) Computing T_399 on space of dimension 340. (0.201 s) Computing T_400 on space of dimension 340. (0.541 s) T_401 sparse... (0.1 s). Computing T_402 on space of dimension 340. (0.21 s) Computing T_403 on space of dimension 340. (0.41 s) Computing T_404 on space of dimension 340. (0.5 s) Computing T_405 on space of dimension 340. (1.35 s) Computing T_406 on space of dimension 340. (0.211 s) Computing T_407 on space of dimension 340. (0.34 s) Computing T_408 on space of dimension 340. (1.049 s) T_409 sparse... (0.109 s). Computing T_410 on space of dimension 340. (0.21 s) Computing T_411 on space of dimension 340. (0.201 s) Computing T_412 on space of dimension 340. (0.5 s) Computing T_413 on space of dimension 340. (0.68 s) Computing T_414 on space of dimension 340. (0.21 s) Computing T_415 on space of dimension 340. (0.301 s) Computing T_416 on space of dimension 340. (2.23 s) Computing T_417 on space of dimension 340. (0.201 s) Computing T_418 on space of dimension 340. (0.21 s) T_419 sparse... (0.111 s). Computing T_420 on space of dimension 340. (0.5 s) T_421 sparse... (0.109 s). Computing T_422 on space of dimension 340. Computing T_211 on space of dimension 340. (6.911 s) (7.121 s) Computing T_423 on space of dimension 340. (0.189 s) Computing T_424 on space of dimension 340. (1.059 s) Computing T_425 on space of dimension 340. (0.371 s) Computing T_426 on space of dimension 340. (0.199 s) Computing T_427 on space of dimension 340. (0.68 s) Computing T_428 on space of dimension 340. (0.501 s) Computing T_429 on space of dimension 340. (0.199 s) Computing T_430 on space of dimension 340. (0.219 s) T_431 sparse... (0.329 s). Computing T_432 on space of dimension 340. (0.53 s) T_433 sparse... (0.109 s). Computing T_434 on space of dimension 340. (0.22 s) Computing T_435 on space of dimension 340. (0.191 s) Computing T_436 on space of dimension 340. (0.5 s) Computing T_437 on space of dimension 340. (0.5 s) Computing T_438 on space of dimension 340. (0.22 s) T_439 sparse... (0.121 s). Computing T_440 on space of dimension 340. (1.04 s) Computing T_441 on space of dimension 340. (0.47 s) Computing T_442 on space of dimension 340. (0.211 s) T_443 sparse... (0.11 s). Computing T_444 on space of dimension 340. (0.5 s) Computing T_445 on space of dimension 340. (0.3 s) Computing T_446 on space of dimension 340. Computing T_223 on space of dimension 340. (7.231 s) (7.441 s) Computing T_447 on space of dimension 340. (0.211 s) Computing T_448 on space of dimension 340. (2.099 s) T_449 sparse... (0.121 s). Computing T_450 on space of dimension 340. (0.209 s) Computing T_451 on space of dimension 340. (0.349 s) Computing T_452 on space of dimension 340. (0.5 s) Computing T_453 on space of dimension 340. (0.21 s) Computing T_454 on space of dimension 340. Computing T_227 on space of dimension 340. (7.36 s) (7.57 s) Computing T_455 on space of dimension 340. (0.3 s) Computing T_456 on space of dimension 340. (1.061 s) T_457 sparse... (0.119 s). Computing T_458 on space of dimension 340. Computing T_229 on space of dimension 340. (7.431 s) (7.641 s) Computing T_459 on space of dimension 340. (0.391 s) Computing T_460 on space of dimension 340. (0.5 s) T_461 sparse... (0.119 s). Computing T_462 on space of dimension 340. (0.21 s) T_463 sparse... (0.121 s). Computing T_464 on space of dimension 340. (0.561 s) Computing T_465 on space of dimension 340. (0.199 s) Computing T_466 on space of dimension 340. Computing T_233 on space of dimension 340. (7.519 s) (7.719 s) T_467 sparse... (0.119 s). Computing T_468 on space of dimension 340. (0.5 s) Computing T_469 on space of dimension 340. (0.691 s) Computing T_470 on space of dimension 340. (0.211 s) Computing T_471 on space of dimension 340. (0.209 s) Computing T_472 on space of dimension 340. (1.079 s) Computing T_473 on space of dimension 340. (0.359 s) Computing T_474 on space of dimension 340. (0.201 s) Computing T_475 on space of dimension 340. (0.38 s) Computing T_476 on space of dimension 340. (0.511 s) Computing T_477 on space of dimension 340. (0.47 s) Computing T_478 on space of dimension 340. Computing T_239 on space of dimension 340. (7.63 s) (7.84 s) T_479 sparse... (0.13 s). Computing T_480 on space of dimension 340. (1.96 s) Computing T_481 on space of dimension 340. (0.42 s) Computing T_482 on space of dimension 340. Computing T_241 on space of dimension 340. (7.701 s) (7.9 s) Computing T_483 on space of dimension 340. (0.21 s) Computing T_484 on space of dimension 340. (0.511 s) Computing T_485 on space of dimension 340. (0.299 s) Computing T_486 on space of dimension 340. (0.21 s) T_487 sparse... (0.13 s). Computing T_488 on space of dimension 340. (1.069 s) Computing T_489 on space of dimension 340. (0.21 s) Computing T_490 on space of dimension 340. (0.199 s) T_491 sparse... (0.13 s). Computing T_492 on space of dimension 340. (0.501 s) Computing T_493 on space of dimension 340. (0.51 s) Computing T_494 on space of dimension 340. (0.21 s) Computing T_495 on space of dimension 340. (0.469 s) Computing T_496 on space of dimension 340. (0.559 s) Computing T_497 on space of dimension 340. (0.689 s) Computing T_498 on space of dimension 340. (0.21 s) T_499 sparse... (0.13 s). Computing T_500 on space of dimension 340. (0.51 s) Computing T_501 on space of dimension 340. (0.201 s) Computing T_502 on space of dimension 340. Computing T_251 on space of dimension 340. (7.829 s) (8.039 s) T_503 sparse... (0.131 s). Computing T_504 on space of dimension 340. (1.07 s) Computing T_505 on space of dimension 340. (0.309 s) Computing T_506 on space of dimension 340. (0.21 s) Computing T_507 on space of dimension 340. (0.211 s) Computing T_508 on space of dimension 340. (0.519 s) T_509 sparse... (0.129 s). Computing T_510 on space of dimension 340. (0.211 s) Computing T_511 on space of dimension 340. (0.68 s) Computing T_512 on space of dimension 340. (0.26 s) Computing T_513 on space of dimension 340. (0.39 s) Computing T_514 on space of dimension 340. Computing T_257 on space of dimension 340. (8.05 s) (8.27 s) Computing T_515 on space of dimension 340. (0.31 s) Computing T_516 on space of dimension 340. (0.501 s) Computing T_517 on space of dimension 340. (0.359 s) Computing T_518 on space of dimension 340. (0.22 s) Computing T_519 on space of dimension 340. (0.21 s) Computing T_520 on space of dimension 340. (1.069 s) T_521 sparse... (0.139 s). Computing T_522 on space of dimension 340. (0.21 s) T_523 sparse... (0.139 s). Computing T_524 on space of dimension 340. (0.51 s) Computing T_525 on space of dimension 340. (0.199 s) Computing T_526 on space of dimension 340. Computing T_263 on space of dimension 340. (8.199 s) (8.42 s) Computing T_527 on space of dimension 340. (0.53 s) Computing T_528 on space of dimension 340. (0.56 s) Computing T_529 on space of dimension 340. (0.591 s) Computing T_530 on space of dimension 340. (0.211 s) Computing T_531 on space of dimension 340. (0.47 s) Computing T_532 on space of dimension 340. (0.509 s) Computing T_533 on space of dimension 340. (0.42 s) Computing T_534 on space of dimension 340. (0.201 s) Computing T_535 on space of dimension 340. (0.299 s) Computing T_536 on space of dimension 340. (1.069 s) Computing T_537 on space of dimension 340. (0.201 s) Computing T_538 on space of dimension 340. Computing T_269 on space of dimension 340. (8.26 s) (8.471 s) Computing T_539 on space of dimension 340. (2.141 s) Computing T_540 on space of dimension 340. (0.501 s) T_541 sparse... (0.14 s). Computing T_542 on space of dimension 340. Computing T_271 on space of dimension 340. (8.229 s) (8.451 s) Computing T_543 on space of dimension 340. (0.21 s) Computing T_544 on space of dimension 340. (2.41 s) Computing T_545 on space of dimension 340. (0.31 s) Computing T_546 on space of dimension 340. (0.221 s) T_547 sparse... (0.14 s). Computing T_548 on space of dimension 340. (0.5 s) Computing T_549 on space of dimension 340. (0.47 s) Computing T_550 on space of dimension 340. (0.21 s) Computing T_551 on space of dimension 340. (0.531 s) Computing T_552 on space of dimension 340. (1.069 s) Computing T_553 on space of dimension 340. (0.689 s) Computing T_554 on space of dimension 340. Computing T_277 on space of dimension 340. (8.4 s) (8.6 s) Computing T_555 on space of dimension 340. (0.201 s) Computing T_556 on space of dimension 340. (0.51 s) T_557 sparse... (0.151 s). Computing T_558 on space of dimension 340. (0.21 s) Computing T_559 on space of dimension 340. (0.421 s) Computing T_560 on space of dimension 340. (0.56 s) Computing T_561 on space of dimension 340. (0.21 s) Computing T_562 on space of dimension 340. Computing T_281 on space of dimension 340. (8.599 s) (8.809 s) T_563 sparse... (0.14 s). Computing T_564 on space of dimension 340. (0.5 s) Computing T_565 on space of dimension 340. (0.301 s) Computing T_566 on space of dimension 340. Computing T_283 on space of dimension 340. (8.521 s) (8.731 s) Computing T_567 on space of dimension 340. (1.711 s) Computing T_568 on space of dimension 340. (1.07 s) T_569 sparse... (0.15 s). Computing T_570 on space of dimension 340. (0.21 s) T_571 sparse... (0.149 s). Computing T_572 on space of dimension 340. (0.511 s) Computing T_573 on space of dimension 340. (0.191 s) Computing T_574 on space of dimension 340. (0.21 s) Computing T_575 on space of dimension 340. (0.381 s) Computing T_576 on space of dimension 340. (1.92 s) T_577 sparse... (0.15 s). Computing T_578 on space of dimension 340. (0.21 s) Computing T_579 on space of dimension 340. (0.21 s) Computing T_580 on space of dimension 340. (0.5 s) Computing T_581 on space of dimension 340. (0.689 s) Computing T_582 on space of dimension 340. (0.22 s) Computing T_583 on space of dimension 340. (1.001 s) Computing T_584 on space of dimension 340. (1.07 s) Computing T_585 on space of dimension 340. (0.46 s) Computing T_586 on space of dimension 340. Computing T_293 on space of dimension 340. (8.881 s) (9.131 s) T_587 sparse... (0.159 s). Computing T_588 on space of dimension 340. (0.539 s) Computing T_589 on space of dimension 340. (0.699 s) Computing T_590 on space of dimension 340. (0.23 s) Computing T_591 on space of dimension 340. (0.23 s) Computing T_592 on space of dimension 340. (0.931 s) T_593 sparse... (0.171 s). Computing T_594 on space of dimension 340. (0.229 s) Computing T_595 on space of dimension 340. (0.359 s) Computing T_596 on space of dimension 340. (0.52 s) Computing T_597 on space of dimension 340. (0.24 s) Computing T_598 on space of dimension 340. (0.219 s) T_599 sparse... (0.149 s). Computing T_600 on space of dimension 340. (1.149 s) T_601 sparse... (0.169 s). Computing T_602 on space of dimension 340. (0.261 s) Computing T_603 on space of dimension 340. (0.489 s) Computing T_604 on space of dimension 340. (0.55 s) Computing T_605 on space of dimension 340. (0.319 s) Computing T_606 on space of dimension 340. (0.221 s) T_607 sparse... (0.161 s). Computing T_608 on space of dimension 340. (2.6 s) Computing T_609 on space of dimension 340. (0.211 s) Computing T_610 on space of dimension 340. (0.229 s) Computing T_611 on space of dimension 340. (0.469 s) Computing T_612 on space of dimension 340. (0.519 s) T_613 sparse... (0.159 s). Computing T_614 on space of dimension 340. Computing T_307 on space of dimension 340. (9.579 s) (9.809 s) Computing T_615 on space of dimension 340. (0.219 s) Computing T_616 on space of dimension 340. (1.17 s) T_617 sparse... (0.159 s). Computing T_618 on space of dimension 340. (0.229 s) T_619 sparse... (0.17 s). Computing T_620 on space of dimension 340. (0.579 s) Computing T_621 on space of dimension 340. (0.521 s) Computing T_622 on space of dimension 340. Computing T_311 on space of dimension 340. (9.59 s) (9.8 s) Computing T_623 on space of dimension 340. (0.721 s) Computing T_624 on space of dimension 340. (0.631 s) Computing T_625 on space of dimension 340. (0.35 s) Computing T_626 on space of dimension 340. Computing T_313 on space of dimension 340. (9.34 s) (9.54 s) Computing T_627 on space of dimension 340. (0.21 s) Computing T_628 on space of dimension 340. (0.5 s) Computing T_629 on space of dimension 340. (0.53 s) Computing T_630 on space of dimension 340. (0.21 s) T_631 sparse... (0.161 s). Computing T_632 on space of dimension 340. (1.091 s) Computing T_633 on space of dimension 340. (0.201 s) Computing T_634 on space of dimension 340. Computing T_317 on space of dimension 340. (9.369 s) (9.59 s) Computing T_635 on space of dimension 340. (0.31 s) Computing T_636 on space of dimension 340. (0.511 s) Computing T_637 on space of dimension 340. (2.301 s) Computing T_638 on space of dimension 340. (0.21 s) Computing T_639 on space of dimension 340. (0.469 s) Computing T_640 on space of dimension 340. (1.709 s) T_641 sparse... (0.159 s). Computing T_642 on space of dimension 340. (0.21 s) T_643 sparse... (0.17 s). Computing T_644 on space of dimension 340. (0.51 s) Computing T_645 on space of dimension 340. (0.21 s) Computing T_646 on space of dimension 340. (0.211 s) T_647 sparse... (0.17 s). Computing T_648 on space of dimension 340. (1.08 s) Computing T_649 on space of dimension 340. (1.009 s) Computing T_650 on space of dimension 340. (0.21 s) Computing T_651 on space of dimension 340. (0.211 s) Computing T_652 on space of dimension 340. (0.51 s) T_653 sparse... (0.489 s). Computing T_654 on space of dimension 340. (0.21 s) Computing T_655 on space of dimension 340. (0.311 s) Computing T_656 on space of dimension 340. (0.569 s) Computing T_657 on space of dimension 340. (0.479 s) Computing T_658 on space of dimension 340. (0.21 s) T_659 sparse... (0.171 s). Computing T_660 on space of dimension 340. (0.5 s) T_661 sparse... (0.171 s). Computing T_662 on space of dimension 340. Computing T_331 on space of dimension 340. (9.539 s) (9.739 s) Computing T_663 on space of dimension 340. (0.201 s) Computing T_664 on space of dimension 340. (1.079 s) Computing T_665 on space of dimension 340. (0.309 s) Computing T_666 on space of dimension 340. (0.21 s) Computing T_667 on space of dimension 340. (0.55 s) Computing T_668 on space of dimension 340. (0.5 s) Computing T_669 on space of dimension 340. (0.201 s) Computing T_670 on space of dimension 340. (0.21 s) Computing T_671 on space of dimension 340. (1 s) Computing T_672 on space of dimension 340. (2.26 s) Total time: 5153.019 seconds Magma V2.7-1 Mon Jan 29 2001 05:21:04 on modular [Seed = 508615078] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2506 and weight 2.... I. Manin symbols list. (0.07 s) II. 2-term relations. (1.35 s) III. 3-term relations. Computing quotient by 1440 relations. Form quot and then images (1.22 s) (total time to create space = 2.681 s) Computing cuspidal part of Full Modular symbols space of level 2506, weight 2, and dimension 364 Computing new part of Modular symbols space of level 2506, weight 2, and dimension 357. Computing 2-new part of Modular symbols space of level 2506, weight 2, and dimension 357. Computing space of modular symbols of level 1253 and weight 2.... I. Manin symbols list. (0.009 s) II. 2-term relations. (0.431 s) III. 3-term relations. Computing quotient by 480 relations. Form quot and then images (0.23 s) (total time to create space = 0.679 s) Computing index-1 degeneracy map from level 2506 to 1253. (2.601 s) Computing index-2 degeneracy map from level 2506 to 1253. (2.509 s) Computing index-1 degeneracy map from level 1253 to 2506. (1.06 s) Computing index-2 degeneracy map from level 1253 to 2506. (1.32 s) Computing DualVectorSpace of Modular symbols space of level 2506, weight 2, and dimension 357. Computing complement of Modular symbols space of level 2506, weight 2, and dimension 357 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 364. (0.261 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 66 Computing T_3 on space of dimension 364. (0.189 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 2506, weight 2, and dimension 7 Computing 7-new part of Modular symbols space of level 2506, weight 2, and dimension 357. Computing space of modular symbols of level 358 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.15 s) III. 3-term relations. Computing quotient by 180 relations. Form quot and then images (0.069 s) (total time to create space = 0.219 s) Computing index-1 degeneracy map from level 2506 to 358. (0.289 s) Computing index-7 degeneracy map from level 2506 to 358. (0.491 s) Computing index-1 degeneracy map from level 358 to 2506. (1.07 s) Computing index-7 degeneracy map from level 358 to 2506. (1.28 s) Computing 179-new part of Modular symbols space of level 2506, weight 2, and dimension 357. Computing space of modular symbols of level 14 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.01 s) III. 3-term relations. Computing quotient by 8 relations. Form quot and then images (0 s) (total time to create space = 0.01 s) Computing index-1 degeneracy map from level 2506 to 14. (0.081 s) Computing index-179 degeneracy map from level 2506 to 14. (17.32 s) Computing index-1 degeneracy map from level 14 to 2506. (3.35 s) Computing index-179 degeneracy map from level 14 to 2506. (3.429 s) Finding newform decomposition of Modular symbols space of level 2506, weight 2, and dimension 357. Computing cuspidal part of Modular symbols space of level 2506, weight 2, and dimension 357 Decomposing space of level 2506 and dimension 89 using T_3. (will stop at 720) Computing T_3 on dual space of dimension 89. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing characteristic polynomial of T_3. x^89 + 4*x^88 - 166*x^87 - 672*x^86 + 13201*x^85 + 54104*x^84 - 669886*x^83 - 2780388*x^82 + 24378304*x^81 + 102483724*x^80 - 677956298*x^79 - 2886614192*x^78 + 14992849105*x^77 + 64638808672*x^76 - 270926385690*x^75 - 1182045865276*x^74 + 4079766941905*x^73 + 17995709946336*x^72 - 51960176764012*x^71 - 231370405053168*x^70 + 566200989109700*x^69 + 2539699768811120*x^68 - 5327798689564736*x^67 - 24002462197225920*x^66 + 43620096545272422*x^65 + 196601892359607952*x^64 - 312698770897390020*x^63 - 1402851956748556456*x^62 + 1973249286804940584*x^61 + 8755040613421451776*x^60 - 11010891636939532108*x^59 - 47933348921867160768*x^58 + 54539300751977600912*x^57 + 230728965034682623184*x^56 - 240551334807289258120*x^55 - 977874537198905958560*x^54 + 947041578816268857730*x^53 + 3651897432539478176080*x^52 - 3333496697191766754828*x^51 - 12018904757610056246456*x^50 + 10498386167294343642428*x^49 + 34841671307144061495568*x^48 - 29575964860760788599652*x^47 - 88860443934211242414920*x^46 + 74440990230857006926164*x^45 + 199007587582327085506312*x^44 - 167018951272888725019380*x^43 - 390309940968404644576768*x^42 + 332967330342465268857153*x^41 + 667955839000557647752676*x^40 - 587391112632340539166394*x^39 - 992671285067118803586760*x^38 + 912393108921722175734635*x^37 + 1273108063866904189243176*x^36 - 1240647585653925671521018*x^35 - 1397461943854777690764164*x^34 + 1467047251700185409598541*x^33 + 1298276373862515639453472*x^32 - 1497212271868110853531964*x^31 - 1004670025540775926266672*x^30 + 1307397118141135187301468*x^29 + 631806624070924983646472*x^28 - 967111905815299602846064*x^27 - 308916833015173783329608*x^26 + 598983332731349208420412*x^25 + 105883146005907977292800*x^24 - 306327812332906007584320*x^23 - 15988166049630826303536*x^22 + 127194008243310208446704*x^21 - 7352147877198751956896*x^20 - 41986152566466522473664*x^19 + 6609440100548224977792*x^18 + 10719169573290452222976*x^17 - 2707303330777054068736*x^16 - 2036244343889294077952*x^15 + 720229889636602707968*x^14 + 270400320502106693632*x^13 - 131385326219762712576*x^12 - 21982102127528017920*x^11 + 16321950172810117120*x^10 + 604404267186913280*x^9 - 1327144726312779776*x^8 + 68872083052953600*x^7 + 65213684572487680*x^6 - 7818762704125952*x^5 - 1620454580158464*x^4 + 309286521536512*x^3 + 9081028870144*x^2 - 4362076160000*x + 211392921600 time = 7.331 Factoring characteristic polynomial. [ , , , , , , , , , , ] time = 0.22 Cutting out subspace using f(T_3), where f=x - 2. Cutting out subspace using f(T_3), where f=x^2 - 2. Cutting out subspace using f(T_3), where f=x^3 + 3*x^2 - x - 4. Cutting out subspace using f(T_3), where f=x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1. Cutting out subspace using f(T_3), where f=x^7 + 3*x^6 - 6*x^5 - 18*x^4 + 8*x^3 + 22*x^2 - 5*x - 4. Cutting out subspace using f(T_3), where f=x^9 + 4*x^8 - 6*x^7 - 33*x^6 + 6*x^5 + 80*x^4 + 7*x^3 - 51*x^2 - 5*x + 2. Cutting out subspace using f(T_3), where f=x^10 - 3*x^9 - 16*x^8 + 48*x^7 + 74*x^6 - 226*x^5 - 69*x^4 + 268*x^3 - 64*x^2 - 48*x + 16. Cutting out subspace using f(T_3), where f=x^11 - 3*x^10 - 22*x^9 + 64*x^8 + 160*x^7 - 438*x^6 - 465*x^5 + 1124*x^4 + 478*x^3 - 948*x^2 - 8*x + 80. Cutting out subspace using f(T_3), where f=x^11 + 3*x^10 - 16*x^9 - 48*x^8 + 78*x^7 + 238*x^6 - 133*x^5 - 428*x^4 + 34*x^3 + 208*x^2 + 18*x - 20. Cutting out subspace using f(T_3), where f=x^12 - 4*x^11 - 18*x^10 + 79*x^9 + 98*x^8 - 538*x^7 - 87*x^6 + 1477*x^5 - 611*x^4 - 1272*x^3 + 1112*x^2 - 272*x + 16. Cutting out subspace using f(T_3), where f=x^17 - 40*x^15 + 5*x^14 + 652*x^13 - 136*x^12 - 5573*x^11 + 1383*x^10 + 26835*x^9 - 6450*x^8 - 73188*x^7 + 13618*x^6 + 109326*x^5 - 11076*x^4 - 81840*x^3 - 1088*x^2 + 23648*x + 4032. Computing representation of Modular symbols space of level 2506, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x + 1 p = %o, dimension = %o. 2 44 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 45 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^2 - 2 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 44 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^3 + 3*x^2 - x - 4 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1 p = %o, dimension = %o. 2 45 Computing T_3 on dual space of dimension 6. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1 p = %o, dimension = %o. 3 6 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1 p = %o, dimension = %o. 2 44 Computing T_3 on dual space of dimension 7. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^7 + 3*x^6 - 6*x^5 - 18*x^4 + 8*x^3 + 22*x^2 - 5*x - 4 p = %o, dimension = %o. 3 7 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 9. Goal dimension = 9. Computing T_2 on dual space of dimension 9. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1 p = %o, dimension = %o. 2 45 Computing T_3 on dual space of dimension 9. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^9 + 4*x^8 - 6*x^7 - 33*x^6 + 6*x^5 + 80*x^4 + 7*x^3 - 51*x^2 - 5*x + 2 p = %o, dimension = %o. 3 9 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 10. Goal dimension = 10. Computing T_2 on dual space of dimension 10. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1 p = %o, dimension = %o. 2 44 Computing T_3 on dual space of dimension 10. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.019 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^10 - 3*x^9 - 16*x^8 + 48*x^7 + 74*x^6 - 226*x^5 - 69*x^4 + 268*x^3 - 64*x^2 - 48*x + 16 p = %o, dimension = %o. 3 10 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 11. Goal dimension = 11. Computing T_2 on dual space of dimension 11. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1 p = %o, dimension = %o. 2 45 Computing T_3 on dual space of dimension 11. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^11 - 3*x^10 - 22*x^9 + 64*x^8 + 160*x^7 - 438*x^6 - 465*x^5 + 1124*x^4 + 478*x^3 - 948*x^2 - 8*x + 80 p = %o, dimension = %o. 3 11 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 11. Goal dimension = 11. Computing T_2 on dual space of dimension 11. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1 p = %o, dimension = %o. 2 44 Computing T_3 on dual space of dimension 11. T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^11 + 3*x^10 - 16*x^9 - 48*x^8 + 78*x^7 + 238*x^6 - 133*x^5 - 428*x^4 + 34*x^3 + 208*x^2 + 18*x - 20 p = %o, dimension = %o. 3 11 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1 p = %o, dimension = %o. 2 44 Computing T_3 on dual space of dimension 12. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^12 - 4*x^11 - 18*x^10 + 79*x^9 + 98*x^8 - 538*x^7 - 87*x^6 + 1477*x^5 - 611*x^4 - 1272*x^3 + 1112*x^2 - 272*x + 16 p = %o, dimension = %o. 3 12 Computing representation of Modular symbols space of level 2506, weight 2, and dimension 17. Goal dimension = 17. Computing T_2 on dual space of dimension 17. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^17 - 17*x^16 + 136*x^15 - 680*x^14 + 2380*x^13 - 6188*x^12 + 12376*x^11 - 19448*x^10 + 24310*x^9 - 24310*x^8 + 19448*x^7 - 12376*x^6 + 6188*x^5 - 2380*x^4 + 680*x^3 - 136*x^2 + 17*x - 1 p = %o, dimension = %o. 2 45 Computing T_3 on dual space of dimension 17. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). %o x^17 - 40*x^15 + 5*x^14 + 652*x^13 - 136*x^12 - 5573*x^11 + 1383*x^10 + 26835*x^9 - 6450*x^8 - 73188*x^7 + 13618*x^6 + 109326*x^5 - 11076*x^4 - 81840*x^3 - 1088*x^2 + 23648*x + 4032 p = %o, dimension = %o. 3 17 Computing cuspidal part of Full Modular symbols space of level 1253, weight 2, and dimension 122 Computing cuspidal part of Modular symbols space of level 1253, weight 2, and dimension 119 Computing new part of Modular symbols space of level 1253, weight 2, and dimension 119. Computing 7-new part of Modular symbols space of level 1253, weight 2, and dimension 119. Computing space of modular symbols of level 179 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.05 s) III. 3-term relations. Computing quotient by 60 relations. Form quot and then images (0.02 s) (total time to create space = 0.07 s) Computing index-1 degeneracy map from level 1253 to 179. (0.051 s) Computing index-7 degeneracy map from level 1253 to 179. (0.099 s) Computing index-1 degeneracy map from level 179 to 1253. (0.371 s) Computing index-7 degeneracy map from level 179 to 1253. (0.369 s) Computing DualVectorSpace of Modular symbols space of level 1253, weight 2, and dimension 119. Computing complement of Modular symbols space of level 1253, weight 2, and dimension 119 Computing representation of Modular symbols space of level 1253, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 122. (0.02 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 1253, weight 2, and dimension 3 Computing 179-new part of Modular symbols space of level 1253, weight 2, and dimension 119. Computing space of modular symbols of level 7 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 4 relations. Form quot and then images (0.01 s) (total time to create space = 0.01 s) Computing index-1 degeneracy map from level 1253 to 7. (0.02 s) Computing index-179 degeneracy map from level 1253 to 7. (7.581 s) Computing index-1 degeneracy map from level 7 to 1253. (0.98 s) Computing index-179 degeneracy map from level 7 to 1253. (0.921 s) Decomposing space of level 1253 and dimension 89 using T_2. (will stop at 720) Computing T_2 on dual space of dimension 89. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^89 - x^88 - 131*x^87 + 127*x^86 + 8261*x^85 - 7761*x^84 - 334023*x^83 + 303979*x^82 + 9731663*x^81 - 8575823*x^80 - 217671825*x^79 + 185678797*x^78 + 3888969649*x^77 - 3210160401*x^76 - 57013244249*x^75 + 45527326629*x^74 + 699212428660*x^73 - 539999925272*x^72 - 7277321963582*x^71 + 5434260646202*x^70 + 64986337233838*x^69 - 46911997898566*x^68 - 502172525559322*x^67 + 350371921009270*x^66 + 3380309909508925*x^65 - 2279196860516521*x^64 - 19925279592813849*x^63 + 12981544128317981*x^62 + 103269586214901880*x^61 - 65005749428164328*x^60 - 472094702177880100*x^59 + 287104280738930504*x^58 + 1908094701485453276*x^57 - 1121058108085282120*x^56 - 6829891417182802650*x^55 + 3876662958885951522*x^54 + 21673908358762128235*x^53 - 11885204739744990651*x^52 - 61009666260169195127*x^51 + 32322971842235934031*x^50 + 152336990281388745110*x^49 - 77980355589706351190*x^48 - 337252007975109321520*x^47 + 166812020991313713100*x^46 + 661361603618943391657*x^45 - 316101181881937720433*x^44 - 1147224732744839706559*x^43 + 529856632939814347195*x^42 + 1756981482385574867412*x^41 - 784121389254500467152*x^40 - 2370099306421731952548*x^39 + 1021954290523649710408*x^38 + 2807984275915555199597*x^37 - 1169469150011233116625*x^36 - 2911796602117759983645*x^35 + 1170778754147890400565*x^34 + 2632185286449877769864*x^33 - 1020975897073183697808*x^32 - 2064560163039542796616*x^31 + 771628809536555633768*x^30 + 1397476055908338021244*x^29 - 502436313136698834860*x^28 - 811259252720065320058*x^27 + 279922902880784655814*x^26 + 401011093675944943921*x^25 - 132372960356940016029*x^24 - 167393656160979144475*x^23 + 52639680704155611727*x^22 + 58443961814827924715*x^21 - 17412082688696150635*x^20 - 16876594938384213557*x^19 + 4729826030056263837*x^18 + 3977378563897573696*x^17 - 1039085766179330932*x^16 - 752813239105324724*x^15 + 181196597379250848*x^14 + 112166796025524140*x^13 - 24494319054356812*x^12 - 12820883417636336*x^11 + 2487312061425184*x^10 + 1085665433225488*x^9 - 181423746232048*x^8 - 64777293883776*x^7 + 8861636905024*x^6 + 2517680329216*x^5 - 255126045184*x^4 - 55369643008*x^3 + 3150368768*x^2 + 494784512*x + 3182592 time = 1.509 Factoring characteristic polynomial. [ , , , , , ] time = 0.319 Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x^3 - 3*x + 1. Cutting out subspace using f(T_2), where f=x^11 + 4*x^10 - 4*x^9 - 31*x^8 - 11*x^7 + 71*x^6 + 52*x^5 - 53*x^4 - 49*x^3 + 7*x^2 + 12*x + 2. Cutting out subspace using f(T_2), where f=x^21 - 3*x^20 - 26*x^19 + 80*x^18 + 279*x^17 - 889*x^16 - 1593*x^15 + 5346*x^14 + 5175*x^13 - 18911*x^12 - 9308*x^11 + 40044*x^10 + 7592*x^9 - 49322*x^8 + 514*x^7 + 32573*x^6 - 4147*x^5 - 9949*x^4 + 1321*x^3 + 1393*x^2 - 112*x - 74. Cutting out subspace using f(T_2), where f=x^23 + 2*x^22 - 31*x^21 - 60*x^20 + 410*x^19 + 764*x^18 - 3027*x^17 - 5403*x^16 + 13695*x^15 + 23322*x^14 - 39180*x^13 - 63565*x^12 + 70495*x^11 + 109226*x^10 - 76850*x^9 - 114360*x^8 + 47335*x^7 + 67580*x^6 - 15068*x^5 - 19598*x^4 + 2404*x^3 + 2112*x^2 - 192*x - 32. Cutting out subspace using f(T_2), where f=x^30 - 3*x^29 - 48*x^28 + 144*x^27 + 1028*x^26 - 3076*x^25 - 12981*x^24 + 38582*x^23 + 107654*x^22 - 315806*x^21 - 618575*x^20 + 1773776*x^19 + 2533439*x^18 - 7000369*x^17 - 7497228*x^16 + 19556167*x^15 + 16072745*x^14 - 38464655*x^13 - 24753033*x^12 + 52329798*x^11 + 26778023*x^10 - 47668249*x^9 - 19493037*x^8 + 27568457*x^7 + 8850566*x^6 - 9281986*x^5 - 2185706*x^4 + 1562484*x^3 + 215328*x^2 - 98080*x - 672. Computing representation of Modular symbols space of level 1253, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1253, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 3*x + 1 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 1253, weight 2, and dimension 11. Goal dimension = 11. Computing T_2 on dual space of dimension 11. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^11 + 4*x^10 - 4*x^9 - 31*x^8 - 11*x^7 + 71*x^6 + 52*x^5 - 53*x^4 - 49*x^3 + 7*x^2 + 12*x + 2 p = %o, dimension = %o. 2 11 Computing representation of Modular symbols space of level 1253, weight 2, and dimension 21. Goal dimension = 21. Computing T_2 on dual space of dimension 21. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^21 - 3*x^20 - 26*x^19 + 80*x^18 + 279*x^17 - 889*x^16 - 1593*x^15 + 5346*x^14 + 5175*x^13 - 18911*x^12 - 9308*x^11 + 40044*x^10 + 7592*x^9 - 49322*x^8 + 514*x^7 + 32573*x^6 - 4147*x^5 - 9949*x^4 + 1321*x^3 + 1393*x^2 - 112*x - 74 p = %o, dimension = %o. 2 21 Computing representation of Modular symbols space of level 1253, weight 2, and dimension 23. Goal dimension = 23. Computing T_2 on dual space of dimension 23. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^23 + 2*x^22 - 31*x^21 - 60*x^20 + 410*x^19 + 764*x^18 - 3027*x^17 - 5403*x^16 + 13695*x^15 + 23322*x^14 - 39180*x^13 - 63565*x^12 + 70495*x^11 + 109226*x^10 - 76850*x^9 - 114360*x^8 + 47335*x^7 + 67580*x^6 - 15068*x^5 - 19598*x^4 + 2404*x^3 + 2112*x^2 - 192*x - 32 p = %o, dimension = %o. 2 23 Computing representation of Modular symbols space of level 1253, weight 2, and dimension 30. Goal dimension = 30. Computing T_2 on dual space of dimension 30. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^30 - 3*x^29 - 48*x^28 + 144*x^27 + 1028*x^26 - 3076*x^25 - 12981*x^24 + 38582*x^23 + 107654*x^22 - 315806*x^21 - 618575*x^20 + 1773776*x^19 + 2533439*x^18 - 7000369*x^17 - 7497228*x^16 + 19556167*x^15 + 16072745*x^14 - 38464655*x^13 - 24753033*x^12 + 52329798*x^11 + 26778023*x^10 - 47668249*x^9 - 19493037*x^8 + 27568457*x^7 + 8850566*x^6 - 9281986*x^5 - 2185706*x^4 + 1562484*x^3 + 215328*x^2 - 98080*x - 672 p = %o, dimension = %o. 2 30 Computing cuspidal part of Full Modular symbols space of level 358, weight 2, and dimension 47 Computing cuspidal part of Modular symbols space of level 358, weight 2, and dimension 44 Computing new part of Modular symbols space of level 358, weight 2, and dimension 44. Computing 2-new part of Modular symbols space of level 358, weight 2, and dimension 44. Computing index-1 degeneracy map from level 358 to 179. (0.01 s) Computing index-2 degeneracy map from level 358 to 179. (0.02 s) Computing index-1 degeneracy map from level 179 to 358. (0.159 s) Computing index-2 degeneracy map from level 179 to 358. (0.181 s) Computing DualVectorSpace of Modular symbols space of level 358, weight 2, and dimension 44. Computing complement of Modular symbols space of level 358, weight 2, and dimension 44 Computing representation of Modular symbols space of level 358, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 47. (0.009 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 4*x^2 + 5*x - 2 p = %o, dimension = %o. 2 10 Computing T_3 on space of dimension 47. (0.01 s) Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - 12*x^2 + 48*x - 64 p = %o, dimension = %o. 3 3 Computing complement of Modular symbols space of level 358, weight 2, and dimension 3 Computing 179-new part of Modular symbols space of level 358, weight 2, and dimension 44. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 358 to 2. (0 s) Computing index-179 degeneracy map from level 358 to 2. (4.541 s) Computing index-1 degeneracy map from level 2 to 358. (0.97 s) Computing index-179 degeneracy map from level 2 to 358. (0.879 s) Decomposing space of level 358 and dimension 14 using T_3. (will stop at 720) Computing T_3 on dual space of dimension 14. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^14 - 2*x^13 - 27*x^12 + 54*x^11 + 266*x^10 - 506*x^9 - 1215*x^8 + 2018*x^7 + 2674*x^6 - 3198*x^5 - 2503*x^4 + 1138*x^3 + 449*x^2 - 104*x - 20 time = 0 Factoring characteristic polynomial. [ , , , , , ] time = 0 Cutting out subspace using f(T_3), where f=x - 2. Cutting out subspace using f(T_3), where f=x + 2. Cutting out subspace using f(T_3), where f=x^2 - 3*x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^4 + 6*x^3 + 11*x^2 + 6*x + 1. Decomposing space of level 358 and dimension 4 using T_3. (will stop at 720) Computing characteristic polynomial of T_3. x^4 - 6*x^3 + 11*x^2 - 6*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x^2 - 3*x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^4 + 6*x^3 + 11*x^2 + 6*x + 1. Decomposing space of level 358 and dimension 4 using T_5. (will stop at 720) Computing T_5 on dual space of dimension 4. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^4 - 3*x^3 - 8*x^2 + 21*x - 11 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Charpoly = x^2 - 6*x + 4. Cutting out subspace using f(T_5), where f=x^2 - x - 11. Cutting out subspace using f(T_3), where f=x^2 - x - 5. Cutting out subspace using f(T_3), where f=x^2 + 3*x + 1. Cutting out subspace using f(T_3), where f=x^4 + 2*x^3 - 7*x^2 - 8*x - 1. Computing representation of Modular symbols space of level 358, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 7 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 358, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 7 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 358, weight 2, and dimension 2. Goal dimension = 2. %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 7 %o x^2 - 3*x + 1 p = %o, dimension = %o. 3 4 Computing T_5 on space of dimension 47. (0.01 s) %o x^2 - 2*x + 1 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 358, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 7 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^2 - 3*x + 1 p = %o, dimension = %o. 3 4 Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). %o x^2 - x - 11 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 358, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 7 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^2 - x - 5 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 358, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 7 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^2 + 3*x + 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 358, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 7 Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). %o x^4 + 2*x^3 - 7*x^2 - 8*x - 1 p = %o, dimension = %o. 3 4 Computing cuspidal part of Full Modular symbols space of level 179, weight 2, and dimension 16 Computing cuspidal part of Modular symbols space of level 179, weight 2, and dimension 15 Computing new part of Modular symbols space of level 179, weight 2, and dimension 15. Computing 179-new part of Modular symbols space of level 179, weight 2, and dimension 15. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 179 and dimension 15 using T_2. (will stop at 720) Computing T_2 on dual space of dimension 15. Computing DualVectorSpace of Modular symbols space of level 179, weight 2, and dimension 15. Computing complement of Modular symbols space of level 179, weight 2, and dimension 15 Computing representation of Modular symbols space of level 179, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 16. (0.009 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 179, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^15 + 2*x^14 - 21*x^13 - 40*x^12 + 171*x^11 + 310*x^10 - 682*x^9 - 1182*x^8 + 1376*x^7 + 2300*x^6 - 1277*x^5 - 2114*x^4 + 360*x^3 + 712*x^2 + 64*x - 32 time = 0.009 Factoring characteristic polynomial. [ , , ] time = 0.009 Cutting out subspace using f(T_2), where f=x - 2. Cutting out subspace using f(T_2), where f=x^3 + x^2 - 2*x - 1. Cutting out subspace using f(T_2), where f=x^11 + 3*x^10 - 14*x^9 - 45*x^8 + 59*x^7 + 225*x^6 - 58*x^5 - 427*x^4 - 76*x^3 + 240*x^2 + 56*x - 16. Computing representation of Modular symbols space of level 179, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 179 to 2506. (1.19 s) Computing index-2 degeneracy map from level 179 to 2506. (1.099 s) Computing index-7 degeneracy map from level 179 to 2506. (1.411 s) Computing index-14 degeneracy map from level 179 to 2506. (1.44 s) Computing representation of Modular symbols space of level 179, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 + x^2 - 2*x - 1 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 179, weight 2, and dimension 11. Computing complement of Modular symbols space of level 179, weight 2, and dimension 11 Computing DualVectorSpace of Modular symbols space of level 179, weight 2, and dimension 5. Goal dimension = 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 5. (0 s) %o x^5 - 4*x^4 - x^3 + 15*x^2 - 7*x - 6 p = 2, dimension = 5. Computing complement of Modular symbols space of level 179, weight 2, and dimension 5 Computing cuspidal part of Full Modular symbols space of level 14, weight 2, and dimension 4 Computing cuspidal part of Modular symbols space of level 14, weight 2, and dimension 1 Computing new part of Modular symbols space of level 14, weight 2, and dimension 1. Computing 2-new part of Modular symbols space of level 14, weight 2, and dimension 1. Computing index-1 degeneracy map from level 14 to 7. (0 s) Computing index-2 degeneracy map from level 14 to 7. (0.009 s) Computing index-1 degeneracy map from level 7 to 14. (0.009 s) Computing index-2 degeneracy map from level 7 to 14. (0.009 s) Computing DualVectorSpace of Modular symbols space of level 14, weight 2, and dimension 1. Goal dimension = 1. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 1. Computing T_2 on space of dimension 4. (0 s) (0 s) %o x + 1 p = 2, dimension = 1. Computing 7-new part of Modular symbols space of level 14, weight 2, and dimension 1. Computing index-1 degeneracy map from level 14 to 2. (0.009 s) Computing index-7 degeneracy map from level 14 to 2. (0 s) Computing index-1 degeneracy map from level 2 to 14. (0.029 s) Computing index-7 degeneracy map from level 2 to 14. (0.019 s) Decomposing space of level 14 and dimension 1 using T_3. (will stop at 720) Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x + 2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 2. Sorting ... 2.671 seconds. J0( N: 2506 ) IntersectionGroup( M1: Modular symbols space of level 2506, weight 2, and dimension..., M2: Modular symbols space of level 2506, weight 2, and dimension... ) IntersectionGroup( S: [ Modular symbols space of level 2506, weight 2, and dimensi... ) In file "/home/was/modsym/calc.m", line 429, column 39: >> ZS := [Basis(IntegralRepresentation(S[i])) : i in [1..n]]; ^ Runtime error in 'IntegralRepresentation': The base field of M must be RationalField(). >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2506, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 1835.640 seconds Magma V2.7-1 Mon Jan 29 2001 05:51:44 on modular [Seed = 72039052] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2507 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.83 s) III. 3-term relations. Computing quotient by 880 relations. Form quot and then images (0.62 s) (total time to create space = 1.5 s) Computing cuspidal part of Full Modular symbols space of level 2507, weight 2, and dimension 222 Computing new part of Modular symbols space of level 2507, weight 2, and dimension 219. Computing 23-new part of Modular symbols space of level 2507, weight 2, and dimension 219. Computing space of modular symbols of level 109 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.029 s) III. 3-term relations. Computing quotient by 38 relations. Form quot and then images (0.011 s) (total time to create space = 0.04 s) Computing index-1 degeneracy map from level 2507 to 109. (0.079 s) Computing index-23 degeneracy map from level 2507 to 109. (0.671 s) Computing index-1 degeneracy map from level 109 to 2507. (0.649 s) Computing index-23 degeneracy map from level 109 to 2507. (0.85 s) Computing DualVectorSpace of Modular symbols space of level 2507, weight 2, and dimension 219. Computing complement of Modular symbols space of level 2507, weight 2, and dimension 219 Computing representation of Modular symbols space of level 2507, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 222. (0.22 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2507, weight 2, and dimension 3 Computing 109-new part of Modular symbols space of level 2507, weight 2, and dimension 219. Computing space of modular symbols of level 23 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.011 s) III. 3-term relations. Computing quotient by 8 relations. Form quot and then images (0 s) (total time to create space = 0.011 s) Computing index-1 degeneracy map from level 2507 to 23. (0.049 s) Computing index-109 degeneracy map from level 2507 to 23. (5.301 s) Computing index-1 degeneracy map from level 23 to 2507. (1.309 s) Computing index-109 degeneracy map from level 23 to 2507. (1.359 s) Finding newform decomposition of Modular symbols space of level 2507, weight 2, and dimension 219. Computing cuspidal part of Modular symbols space of level 2507, weight 2, and dimension 219 Decomposing space of level 2507 and dimension 199 using T_2. (will stop at 440) Computing T_2 on dual space of dimension 199. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^199 - x^198 - 301*x^197 + 299*x^196 + 44548*x^195 - 43944*x^194 - 4321555*x^193 + 4231897*x^192 + 309078578*x^191 - 300358110*x^190 - 17380252091*x^189 + 16755144929*x^188 + 800278170704*x^187 - 765059531392*x^186 - 31028927622989*x^185 + 29404757458239*x^184 + 1033939164785062*x^183 - 970891018054142*x^182 - 30072508135023351*x^181 + 27969920448908389*x^180 + 772837570403496955*x^179 - 711656319903162247*x^178 - 17722121735378090674*x^177 + 16149733762612182678*x^176 + 365556173930884531827*x^175 - 329511572535510140871*x^174 - 6828501140978011256539*x^173 + 6085552655979128677465*x^172 + 116171587377436355607106*x^171 - 102309339479077420073966*x^170 - 1808796101745362888308967*x^169 + 1573328103578682595965245*x^168 + 25883124411616071621981053*x^167 - 22224132820158234754020981*x^166 - 341637816780308678185821950*x^165 + 289405369775753050226831434*x^164 + 4172773113377020181475371619*x^163 - 3485310320413037468446059227*x^162 - 47294951529409503657814545749*x^161 + 38926005679503070540798435087*x^160 + 498673930476748153167232300503*x^159 - 404176106109412692394757544607*x^158 - 4902191349842119699684711397846*x^157 + 3910039929319884607201329583134*x^156 + 45018484164675434645551606073095*x^155 - 35311290258190935503443856718763*x^154 - 386885634979527563395248221337949*x^153 + 298207054538142575110040167596039*x^152 + 3116373165037711481969186507648548*x^151 - 2358648783509348362773383590416300*x^150 - 23561584578579705698967327311682151*x^149 + 17496329063716646858488692428807485*x^148 + 167416253441655902830330754300619977*x^147 - 121871447576147254219138525027234333*x^146 - 1119237074539567909431213599321964504*x^145 + 798001484609579144040666397460317612*x^144 + 7047256360617070275442850520911749440*x^143 - 4916716382427068319471472090643222852*x^142 - 41829953315651487278628639867838661110*x^141 + 28529337841316633450509339283553520894*x^140 + 234248883085248692075079076357159053981*x^139 - 156021659902952508019255204931027509933*x^138 - 1238526241502644963802727633234608019187*x^137 + 804722095989544159582371927294174576953*x^136 + 6186561180414295749375858549697343963445*x^135 - 3916772541375967555460683981750015845345*x^134 - 29211609267628572800020836402919944496784*x^133 + 17999088850773673391327430854033699790448*x^132 + 130448291007961221116577055773935022092662*x^131 - 78126357721025472609895416257129385809862*x^130 - 551167573697774461550972051938320516682536*x^129 + 320422584434680529104502848206968955131952*x^128 + 2204192431408759412184841897782882869835557*x^127 - 1242082785225505113768708029470099504449197*x^126 - 8345804606799725372079380547885476204473203*x^125 + 4551705020064917964829093060000089583277861*x^124 + 29925907680487557058144612666667951093376341*x^123 - 15771017990846640123637032001979129969240029*x^122 - 101641425051841885169718907157741036735716196*x^121 + 51670834144702229279119353700474194987926984*x^120 + 327038999406760354717901595530805731612335067*x^119 - 160081756222941008699508257548338669980706615*x^118 - 996948606809016246395866138884477080137351271*x^117 + 468955588992157382627563422155977550142561581*x^116 + 2879439840458155263571030815201427863079915378*x^115 - 1298883058740767624853993486373851733309339638*x^114 - 7879558328074418510779918342368731291948302683*x^113 + 3400816581009696505195399225787260404895356069*x^112 + 20428212582049868897757729621723852350111029042*x^111 - 8415267356786131781957282165495661208167419950*x^110 - 50170581410607455553484520691893795053785934517*x^109 + 19673869712501502590065008805528045470809256119*x^108 + 116706113098649898898322435434714392325063849710*x^107 - 43439146194712897188720292823084964948009225318*x^106 - 257086373781965429736106440104205337756281730529*x^105 + 90539678609609988013032561577415761299876645179*x^104 + 536167600623189068847940558795693265381041914617*x^103 - 178040925439260485806789257338814392192566477713*x^102 - 1058358636091064897646182411573378119729954329390*x^101 + 330093292398371135293727789085935986367159523262*x^100 + 1976651365328459013262002431209593298427181130059*x^99 - 576569348415495710093798238172394163876338299991*x^98 - 3491607787523267045894388237103106837989074951309*x^97 + 947910059200349698641650744906683184071774724419*x^96 + 5830836584918457650820171757132899681457482590062*x^95 - 1465261533514487398462515034127570019368384786570*x^94 - 9201027426928147587851644105290585549514812937775*x^93 + 2126865173547875037723369826127675597962840980617*x^92 + 13712267940657693724951419343013788033032005237931*x^91 - 2894512066612994407654945125427485270614839704707*x^90 - 19288300027858265647368735997586641618013839449032*x^89 + 3686469453405096063911162065551408698640888846348*x^88 + 25592359559821111098287481896548909855503547678305*x^87 - 4383683652589389837481906179132459831633774744761*x^86 - 32007610271627917429924370248875130053343326549411*x^85 + 4852637916119103582431480351849026076903523556161*x^84 + 37704327469093498044728251329538157345645955575845*x^83 - 4981196722046997870635280697772648743628065577301*x^82 - 41798911759056224488088111108476201937483259702052*x^81 + 4715965073671597168552045726432356418911621749828*x^80 + 43569862529852699479563904486902897739133368502805*x^79 - 4085725159846755575009928776135981810190869339509*x^78 - 42661443421424166171553854653614297408951698421667*x^77 + 3198959476347476777646144712500198110487052539989*x^76 + 39197727391310890037245380884088932266384216318585*x^75 - 2213962863072212275388908745955141785188935752053*x^74 - 33757866630968103350874279204857311139311186752144*x^73 + 1292567934030535441537605487217188828981015169020*x^72 + 27217801773316692548027873994512977972235473551493*x^71 - 556060870264770468924060359815769233412585488685*x^70 - 20517752218323329770164916993802810636726189180931*x^69 + 60026830430316434169208539701195885357800599065*x^68 + 14440964457068389690519296737886781890312130336460*x^67 + 205111626501262529136674551913776815153723849956*x^66 - 9475362539002814093073011638332544912836563493077*x^65 - 293148482405391706398457384882998014823009443797*x^64 + 5786559999076579059090838098408466651895324916532*x^63 + 273473393823256864233723754343981066345688230444*x^62 - 3283258976860318944062105282722751435455320105867*x^61 - 207348801367485801238421495123841895688419213103*x^60 + 1727517814696801172444496458429852101939787642093*x^59 + 135787276441043051133252329604273897185032088679*x^58 - 841155500217796276517934718961950653855301116654*x^57 - 78726829770510493047482141212756719432967347858*x^56 + 378175466544341173756760404610974231016823323211*x^55 + 40885998133110808976060972021128907374565769377*x^54 - 156608380664530970803197461026292754345638981109*x^53 - 19129854707837172961855881662677075355546630529*x^52 + 59578054548537695877148975789973142966328553949*x^51 + 8084338810292336100591521071531366564023423279*x^50 - 20760786776338494056086958778465625997779995914*x^49 - 3087734434580581589289360023650097589780885874*x^48 + 6605424255332849123617244636398900544283305044*x^47 + 1065100509782315040864265507433249307324779828*x^46 - 1912183614249168790463025879172097515412458406*x^45 - 331249147412277604272779006333844433469263346*x^44 + 501696914118103622194058612501456616548682892*x^43 + 92646256567166640127017082169890475123760928*x^42 - 118784729184687619091865988839253255554653404*x^41 - 23225950495735512811603161368178612493243964*x^40 + 25257748752708584602180492081747355506248957*x^39 + 5197896890661366704485656966315242129513299*x^38 - 4797305494397058253289931846701239161239561*x^37 - 1033433499197965763649753270924974203922381*x^36 + 808954721176917974817776684653527541985573*x^35 + 181489547811789715855434554058323736288227*x^34 - 120275493794903413600649666586003075302796*x^33 - 27965057022561119145325304646274219921996*x^32 + 15643620924825858391624749603646447643942*x^31 + 3750994710561985666747533821169168474546*x^30 - 1763931783700732859547757400020361522934*x^29 - 433911840388634369717481588546553627238*x^28 + 170640365751829877643980398320261510102*x^27 + 42813594905242974247815488633918035870*x^26 - 13991914472760735709752851854990486072*x^25 - 3555782539818945057975053992133308872*x^24 + 958790132236305480509050880483609301*x^23 + 244616034771935707748581356857065915*x^22 - 54001279106404609100752637468119387*x^21 - 13665999515384581955310369881136103*x^20 + 2451238299093799702842906245937775*x^19 + 604837144766238672311685397287585*x^18 - 87589736105460393602709632451596*x^17 - 20544092816707132803154325635028*x^16 + 2393275672054104103069361087740*x^15 + 513658691272583799997554927908*x^14 - 48105951164819095812405730448*x^13 - 8936871220762453720903848944*x^12 + 670252201930678464984329984*x^11 + 100225355117341121351336000*x^10 - 5805478693471155578201600*x^9 - 658549038813385337321472*x^8 + 25116255928119027244032*x^7 + 2380591101393364101120*x^6 - 42927892864558682112*x^5 - 3829534395362979840*x^4 + 27994076873588736*x^3 + 2049239767891968*x^2 - 11388495200256*x time = 75.87 Factoring characteristic polynomial. [ , , , , ] time = 1.45 Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x^41 + 2*x^40 - 58*x^39 - 114*x^38 + 1545*x^37 + 2985*x^36 - 25065*x^35 - 47636*x^34 + 276862*x^33 + 518302*x^32 - 2204778*x^31 - 4074881*x^30 + 13072690*x^29 + 23934855*x^28 - 58755168*x^27 - 107104840*x^26 + 201817725*x^25 + 368970645*x^24 - 529929761*x^23 - 982135321*x^22 + 1055699044*x^21 + 2015652851*x^20 - 1568418347*x^19 - 3164712491*x^18 + 1682474909*x^17 + 3748318674*x^16 - 1222029799*x^15 - 3277440962*x^14 + 507366642*x^13 + 2049237051*x^12 - 27213172*x^11 - 873938219*x^10 - 89400887*x^9 + 236155953*x^8 + 46073008*x^7 - 35611456*x^6 - 9541326*x^5 + 2305488*x^4 + 747224*x^3 - 31764*x^2 - 11655*x + 513. Cutting out subspace using f(T_2), where f=x^44 + 5*x^43 - 49*x^42 - 276*x^41 + 1059*x^40 + 7006*x^39 - 13019*x^38 - 108518*x^37 + 95083*x^36 + 1147752*x^35 - 336698*x^34 - 8789783*x^33 - 783905*x^32 + 50439716*x^31 + 17975261*x^30 - 221455819*x^29 - 121853899*x^28 + 753221662*x^27 + 522337639*x^26 - 1997792041*x^25 - 1595535562*x^24 + 4141470890*x^23 + 3612269154*x^22 - 6702826185*x^21 - 6140607057*x^20 + 8438294194*x^19 + 7833519508*x^18 - 8217005651*x^17 - 7420733947*x^16 + 6145285667*x^15 + 5114092787*x^14 - 3495497698*x^13 - 2479205782*x^12 + 1485765297*x^11 + 799618310*x^10 - 454068035*x^9 - 154672384*x^8 + 91878918*x^7 + 13959416*x^6 - 10383872*x^5 - 88423*x^4 + 442504*x^3 - 16200*x^2 - 4583*x - 136. Cutting out subspace using f(T_2), where f=x^55 - 4*x^54 - 79*x^53 + 330*x^52 + 2904*x^51 - 12765*x^50 - 65893*x^49 + 307763*x^48 + 1031844*x^47 - 5186063*x^46 - 11801288*x^45 + 64919030*x^44 + 101606593*x^43 - 626417696*x^42 - 667035470*x^41 + 4772034520*x^40 + 3323913023*x^39 - 29162067655*x^38 - 12157318010*x^37 + 144481503789*x^36 + 28894771562*x^35 - 584260622661*x^34 - 17225560729*x^33 + 1935610882854*x^32 - 204025474919*x^31 - 5259993373909*x^30 + 1115033709345*x^29 + 11713851532268*x^28 - 3459042458531*x^27 - 21314310313616*x^26 + 7648481972054*x^25 + 31531222911174*x^24 - 12771310776218*x^23 - 37657010037001*x^22 + 16399510617033*x^21 + 35969252057803*x^20 - 16232026391909*x^19 - 27150970544758*x^18 + 12301175597621*x^17 + 15949698215019*x^16 - 7040859938331*x^15 - 7148926940523*x^14 + 2982228660713*x^13 + 2381548358891*x^12 - 908654762543*x^11 - 568684662503*x^10 + 191607307711*x^9 + 92308811891*x^8 - 26504936496*x^7 - 9358004354*x^6 + 2227148396*x^5 + 505688056*x^4 - 101198656*x^3 - 9537856*x^2 + 2003520*x - 47232. Cutting out subspace using f(T_2), where f=x^58 - 4*x^57 - 85*x^56 + 351*x^55 + 3390*x^54 - 14510*x^53 - 84315*x^52 + 375851*x^51 + 1466053*x^50 - 6844754*x^49 - 18933353*x^48 + 93214410*x^47 + 188313746*x^46 - 985771172*x^45 - 1475835932*x^44 + 8298683627*x^43 + 9244939459*x^42 - 56564039339*x^41 - 46661218624*x^40 + 315833836934*x^39 + 190239515529*x^38 - 1456235986793*x^37 - 624471663204*x^36 + 5573050737634*x^35 + 1631896624852*x^34 - 17753216283484*x^33 - 3308699792359*x^32 + 47115265898515*x^31 + 4893216004908*x^30 - 104074563186419*x^29 - 4286577478862*x^28 + 190840716416097*x^27 - 890522744940*x^26 - 289212348209965*x^25 + 10412282492399*x^24 + 359936684186371*x^23 - 19649704623990*x^22 - 364747619732685*x^21 + 22549471082442*x^20 + 297618434476682*x^19 - 17494671372739*x^18 - 192705640247108*x^17 + 8927258419312*x^16 + 97124337669072*x^15 - 2440124924888*x^14 - 37115692372380*x^13 - 157849113618*x^12 + 10356053225300*x^11 + 426402387021*x^10 - 1988851809655*x^9 - 168422746377*x^8 + 236483080948*x^7 + 31473007182*x^6 - 13629126508*x^5 - 2494631048*x^4 + 101698208*x^3 + 21270528*x^2 + 513216*x - 3456. Computing representation of Modular symbols space of level 2507, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2507, weight 2, and dimension 41. Goal dimension = 41. Computing T_2 on dual space of dimension 41. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^41 + 2*x^40 - 58*x^39 - 114*x^38 + 1545*x^37 + 2985*x^36 - 25065*x^35 - 47636*x^34 + 276862*x^33 + 518302*x^32 - 2204778*x^31 - 4074881*x^30 + 13072690*x^29 + 23934855*x^28 - 58755168*x^27 - 107104840*x^26 + 201817725*x^25 + 368970645*x^24 - 529929761*x^23 - 982135321*x^22 + 1055699044*x^21 + 2015652851*x^20 - 1568418347*x^19 - 3164712491*x^18 + 1682474909*x^17 + 3748318674*x^16 - 1222029799*x^15 - 3277440962*x^14 + 507366642*x^13 + 2049237051*x^12 - 27213172*x^11 - 873938219*x^10 - 89400887*x^9 + 236155953*x^8 + 46073008*x^7 - 35611456*x^6 - 9541326*x^5 + 2305488*x^4 + 747224*x^3 - 31764*x^2 - 11655*x + 513 p = %o, dimension = %o. 2 40 Computing representation of Modular symbols space of level 2507, weight 2, and dimension 44. Goal dimension = 44. Computing T_2 on dual space of dimension 44. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^44 + 5*x^43 - 49*x^42 - 276*x^41 + 1059*x^40 + 7006*x^39 - 13019*x^38 - 108518*x^37 + 95083*x^36 + 1147752*x^35 - 336698*x^34 - 8789783*x^33 - 783905*x^32 + 50439716*x^31 + 17975261*x^30 - 221455819*x^29 - 121853899*x^28 + 753221662*x^27 + 522337639*x^26 - 1997792041*x^25 - 1595535562*x^24 + 4141470890*x^23 + 3612269154*x^22 - 6702826185*x^21 - 6140607057*x^20 + 8438294194*x^19 + 7833519508*x^18 - 8217005651*x^17 - 7420733947*x^16 + 6145285667*x^15 + 5114092787*x^14 - 3495497698*x^13 - 2479205782*x^12 + 1485765297*x^11 + 799618310*x^10 - 454068035*x^9 - 154672384*x^8 + 91878918*x^7 + 13959416*x^6 - 10383872*x^5 - 88423*x^4 + 442504*x^3 - 16200*x^2 - 4583*x - 136 p = %o, dimension = %o. 2 44 Computing representation of Modular symbols space of level 2507, weight 2, and dimension 55. Goal dimension = 55. Computing T_2 on dual space of dimension 55. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^55 - 4*x^54 - 79*x^53 + 330*x^52 + 2904*x^51 - 12765*x^50 - 65893*x^49 + 307763*x^48 + 1031844*x^47 - 5186063*x^46 - 11801288*x^45 + 64919030*x^44 + 101606593*x^43 - 626417696*x^42 - 667035470*x^41 + 4772034520*x^40 + 3323913023*x^39 - 29162067655*x^38 - 12157318010*x^37 + 144481503789*x^36 + 28894771562*x^35 - 584260622661*x^34 - 17225560729*x^33 + 1935610882854*x^32 - 204025474919*x^31 - 5259993373909*x^30 + 1115033709345*x^29 + 11713851532268*x^28 - 3459042458531*x^27 - 21314310313616*x^26 + 7648481972054*x^25 + 31531222911174*x^24 - 12771310776218*x^23 - 37657010037001*x^22 + 16399510617033*x^21 + 35969252057803*x^20 - 16232026391909*x^19 - 27150970544758*x^18 + 12301175597621*x^17 + 15949698215019*x^16 - 7040859938331*x^15 - 7148926940523*x^14 + 2982228660713*x^13 + 2381548358891*x^12 - 908654762543*x^11 - 568684662503*x^10 + 191607307711*x^9 + 92308811891*x^8 - 26504936496*x^7 - 9358004354*x^6 + 2227148396*x^5 + 505688056*x^4 - 101198656*x^3 - 9537856*x^2 + 2003520*x - 47232 p = %o, dimension = %o. 2 55 Computing representation of Modular symbols space of level 2507, weight 2, and dimension 58. Goal dimension = 58. Computing T_2 on dual space of dimension 58. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^58 - 4*x^57 - 85*x^56 + 351*x^55 + 3390*x^54 - 14510*x^53 - 84315*x^52 + 375851*x^51 + 1466053*x^50 - 6844754*x^49 - 18933353*x^48 + 93214410*x^47 + 188313746*x^46 - 985771172*x^45 - 1475835932*x^44 + 8298683627*x^43 + 9244939459*x^42 - 56564039339*x^41 - 46661218624*x^40 + 315833836934*x^39 + 190239515529*x^38 - 1456235986793*x^37 - 624471663204*x^36 + 5573050737634*x^35 + 1631896624852*x^34 - 17753216283484*x^33 - 3308699792359*x^32 + 47115265898515*x^31 + 4893216004908*x^30 - 104074563186419*x^29 - 4286577478862*x^28 + 190840716416097*x^27 - 890522744940*x^26 - 289212348209965*x^25 + 10412282492399*x^24 + 359936684186371*x^23 - 19649704623990*x^22 - 364747619732685*x^21 + 22549471082442*x^20 + 297618434476682*x^19 - 17494671372739*x^18 - 192705640247108*x^17 + 8927258419312*x^16 + 97124337669072*x^15 - 2440124924888*x^14 - 37115692372380*x^13 - 157849113618*x^12 + 10356053225300*x^11 + 426402387021*x^10 - 1988851809655*x^9 - 168422746377*x^8 + 236483080948*x^7 + 31473007182*x^6 - 13629126508*x^5 - 2494631048*x^4 + 101698208*x^3 + 21270528*x^2 + 513216*x - 3456 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 72039052 Time to this point: 943.9 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2507, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 944.250 seconds Magma V2.7-1 Mon Jan 29 2001 06:07:34 on modular [Seed = 2969535086] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2509 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.84 s) III. 3-term relations. Computing quotient by 908 relations. Form quot and then images (0.58 s) (total time to create space = 1.46 s) Computing cuspidal part of Full Modular symbols space of level 2509, weight 2, and dimension 226 Computing new part of Modular symbols space of level 2509, weight 2, and dimension 223. Computing 13-new part of Modular symbols space of level 2509, weight 2, and dimension 223. Computing space of modular symbols of level 193 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.049 s) III. 3-term relations. Computing quotient by 66 relations. Form quot and then images (0.02 s) (total time to create space = 0.069 s) Computing index-1 degeneracy map from level 2509 to 193. (0.1 s) Computing index-13 degeneracy map from level 2509 to 193. (0.35 s) Computing index-1 degeneracy map from level 193 to 2509. (0.719 s) Computing index-13 degeneracy map from level 193 to 2509. (0.74 s) Computing DualVectorSpace of Modular symbols space of level 2509, weight 2, and dimension 223. Computing complement of Modular symbols space of level 2509, weight 2, and dimension 223 Computing representation of Modular symbols space of level 2509, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 226. (0.231 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2509, weight 2, and dimension 3 Computing 193-new part of Modular symbols space of level 2509, weight 2, and dimension 223. Computing space of modular symbols of level 13 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 6 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 2509 to 13. (0.049 s) Computing index-193 degeneracy map from level 2509 to 13. (13.27 s) Computing index-1 degeneracy map from level 13 to 2509. (1.101 s) Computing index-193 degeneracy map from level 13 to 2509. (1.209 s) Finding newform decomposition of Modular symbols space of level 2509, weight 2, and dimension 223. Computing cuspidal part of Modular symbols space of level 2509, weight 2, and dimension 223 Decomposing space of level 2509 and dimension 193 using T_2. (will stop at 453) Computing T_2 on dual space of dimension 193. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). Computing characteristic polynomial of T_2. x^193 - 3*x^192 - 284*x^191 + 852*x^190 + 39628*x^189 - 118872*x^188 - 3621620*x^187 + 10861488*x^186 + 243828198*x^185 - 731019250*x^184 - 12896832086*x^183 + 38648454186*x^182 + 558130920384*x^181 - 1671595890740*x^180 - 20322755211732*x^179 + 60822159803900*x^178 + 635448583690883*x^177 - 1900104147874645*x^176 - 17328855221652180*x^175 + 51762338693054264*x^174 + 417200331110472885*x^173 - 1244687616957482071*x^172 - 8955006091904926284*x^171 + 26679223822893220948*x^170 + 172755419421541544176*x^169 - 513860730637423591476*x^168 - 3015504336622555580336*x^167 + 8953437550836857082112*x^166 + 47897961476478760905868*x^165 - 141927723126837543626504*x^164 - 695681670606615929220628*x^163 + 2056741801818507253786572*x^162 + 9278087202412967773959833*x^161 - 27361477338270043966134859*x^160 - 114035734335932650554222418*x^159 + 335367398065404359716870602*x^158 + 1295808698950570095046590089*x^157 - 3799271481471019994192181475*x^156 - 13651330252149872261113458386*x^155 + 39892242699025510644875655922*x^154 + 133665349317455605300697590864*x^153 - 389183494265880232327475195320*x^152 - 1219065461798078245517780253368*x^151 + 3535462195586332407192177667128*x^150 + 10376460989408263748224039579652*x^149 - 29964488391042251605927195778240*x^148 - 82574080159370148512213520405030*x^147 + 237349271706911973339405005141878*x^146 + 615301843071405680969627332673947*x^145 - 1759787603519324235383870103076517*x^144 - 4299214209722491763935471340132304*x^143 + 12229917690539323682369795869121804*x^142 + 28202599097273737253358635458244886*x^141 - 79765253684549824565555841723813322*x^140 - 173889756201940109993777543020401776*x^139 + 488775943897023103098374507793077312*x^138 + 1008736305636147687263176647177260597*x^137 - 2816690418000228282269217844274695895*x^136 - 5510450091657433301562009953033926922*x^135 + 15278550699219760343599111354105210050*x^134 + 28369143907520040997372625966427655664*x^133 - 78068652444112334014522519406522433800*x^132 - 137739811131232723597324774072452409470*x^131 + 376028777748272726371947785774641508038*x^130 + 631094652227449565672555850892936720005*x^129 - 1708352173943292644799483250469018388151*x^128 - 2730138972034976564905174252020739528086*x^127 + 7324431294101207430616654455028162482918*x^126 + 11156594830185338087234795402994370664923*x^125 - 29648811595889678235921733439980045527449*x^124 - 43083045992673012513336282878326929219672*x^123 + 113356017136132596894930030024516585993104*x^122 + 157272020878604142088827850692495526170545*x^121 - 409472539418310888638039464294920302665379*x^120 - 542852671669814895931812590687769444491724*x^119 + 1397849104205815405344885624202629559098748*x^118 + 1772094065266361030643273211902544901816210*x^117 - 4510639092903437005302379074433698387233150*x^116 - 5471788359821859721498569212687847253899298*x^115 + 13760071821071207787264656955316415128123954*x^114 + 15982633037339519903872311892845317256177222*x^113 - 39686896981397026944998043648727617185652702*x^112 - 44163000446187097035539022168880381706203220*x^111 + 108226475621858799107702003570802780908361980*x^110 + 115438593352788962015171864294762163640927047*x^109 - 279044580089713881140690663924657062512025005*x^108 - 285425834830501008559522211019049802965638862*x^107 + 680204076366937790264888408037584520281216046*x^106 + 667466760469690154054717736589120941511404865*x^105 - 1567402988673455040865237429944332549307595075*x^104 - 1475982300235183529367247250684039427537038218*x^103 + 3413710646117136490077760671534159406532846210*x^102 + 3085641265115308999653670410252045062434728399*x^101 - 7025621538302407265580935504064795003507886345*x^100 - 6096723134435813802404344190174463459495391636*x^99 + 13659688252187685495900206018470652475002673824*x^98 + 11381098931573514121760913202232491514858221498*x^97 - 25081829535478747763130679152504663720432413638*x^96 - 20064759801068009158537806548954262982220279222*x^95 + 43479301826227751091422172333279024882592685906*x^94 + 33392264808722639785596051719665336287400879479*x^93 - 71126450391348442621162984073979253914278021773*x^92 - 52431700685621455936746544267321537059769690246*x^91 + 109749485231589512028647640217044553692480107370*x^90 + 77629195656416181893934096843639931167592577222*x^89 - 159650700355153178622880567485486320505185529930*x^88 - 108307344632398907545331477376619625362287695028*x^87 + 218819604036609327721741788529107441375038629284*x^86 + 142292263032086437637874396515946360315882879675*x^85 - 282405903774911550028141631100616900523711750369*x^84 - 175894671857687405937951503478421425701034858360*x^83 + 342951332913608807027885997319828982466956947720*x^82 + 204407195462849678802973244996916879215228601794*x^81 - 391592337909822471130167654447152907582828562086*x^80 - 223100295747326879278541246225444099956132875550*x^79 + 420070317699298930656835809276997152535944737574*x^78 + 228462285828027327573520605756176302236164850044*x^77 - 422969308341196969753607634927406886256029738136*x^76 - 219254015118626680787926482520933409161559627714*x^75 + 399370206727138191830616525767100725971051333122*x^74 + 196952724817458211312939437626373781246827802131*x^73 - 353239465272729994055697505148768880157949595393*x^72 - 165375215358737242243111907361060536172591717044*x^71 + 292347826152246838662659438994798209138110717752*x^70 + 129607368106749845787283450256489614007687851209*x^69 - 226119921265272991167796004841682549280542755615*x^68 - 94652928134940325219408558533236804854009653044*x^67 + 163235684487531237042612869292821312633551549256*x^66 + 64299360459595617490956443282957156362996308507*x^65 - 109827735203295769282763874613156106493247048757*x^64 - 40549806134179521139475588898674722193439391234*x^63 + 68764330218616313838057907031720825039300266510*x^62 + 23687872655302675780331302471348679820764726580*x^61 - 39998895082403349718734435099433161076390114864*x^60 - 12786458186175776985768941763749550902972141988*x^59 + 21576752765896625855925631571251817458883932052*x^58 + 6359966272000841464547171793598833313975073543*x^57 - 10772871845631589762409468180516601739846645809*x^56 - 2905766365223259126416077641282957203683387434*x^55 + 4967814799222007014737733595936220501236171086*x^54 + 1214975086387348637527108601102986340171186250*x^53 - 2110998194935540603905246586123411482534451178*x^52 - 462891454360314015315196674625453701802872428*x^51 + 824533178356045951162037798554798033047932784*x^50 + 159841351347817886752581329921030055886346200*x^49 - 295211454460215793499619158658082905456787084*x^48 - 49691841613058179539201324739846752771144300*x^47 + 96594903909906604391866235084225165771190632*x^46 + 13784801740342795638694743644280679850396264*x^45 - 28789242664831761316984343358235022767887064*x^44 - 3369195078512580816590854419128063227924816*x^43 + 7786973433121992552926756317266897382546400*x^42 + 711167868752296731220255439087879537483447*x^41 - 1903712825194730119990469462114332101140133*x^40 - 124957687949266669296246985189429847964526*x^39 + 418750446447030483230872827808450492502030*x^38 + 16748999944531335537890996128957128154087*x^37 - 82454622931149913375756937800734152742745*x^36 - 1189827202919766114953790184050086814690*x^35 + 14450274735892220448521848404298010307826*x^34 - 159749951313964726778812864273694721793*x^33 - 2239149273452794306056777192748866940493*x^32 + 81688492157981763800924463145175379766*x^31 + 304471355351737599247140815981773645230*x^30 - 18855388806091235648681629445130170352*x^29 - 36010396158046248153814697259885235232*x^28 + 3153149347912468147855443518069011882*x^27 + 3665838201240783194904541980431042558*x^26 - 416816677230225375399319090322832335*x^25 - 317145136404053494152952106164046083*x^24 + 44696633932205054124056327067822612*x^23 + 22949380188114797883619244259992768*x^22 - 3909012073609799530915966065029224*x^21 - 1360412636807016394776454706851120*x^20 + 277488080267093331948502389048180*x^19 + 64163304471107363676927301300640*x^18 - 15800633718482633720297032092780*x^17 - 2299976169054758673104861476744*x^16 + 708544193587298797424054789152*x^15 + 57347898019157264321349527628*x^14 - 24375216302663093660242071709*x^13 - 758190474536336926189122673*x^12 + 619857748049001166917618402*x^11 - 5038148266211902565283990*x^10 - 11028458272927205158565415*x^9 + 441046297514323037531161*x^8 + 125474374271069002960722*x^7 - 8533243972295961776854*x^6 - 760578497294675795402*x^5 + 76319127640032476342*x^4 + 1210371024964026944*x^3 - 267418229844778580*x^2 + 5095265356078245*x + 66647224644525 time = 60.459 Factoring characteristic polynomial. [ , , , ] time = 1.091 Cutting out subspace using f(T_2), where f=x^44 + 8*x^43 - 30*x^42 - 394*x^41 + 92*x^40 + 8725*x^39 + 9324*x^38 - 114474*x^37 - 215321*x^36 + 984190*x^35 + 2557052*x^34 - 5753608*x^33 - 19905426*x^32 + 22576010*x^31 + 110119023*x^30 - 52722598*x^29 - 449477125*x^28 + 20976271*x^27 + 1379207874*x^26 + 361282056*x^25 - 3206654829*x^24 - 1594187924*x^23 + 5650148625*x^22 + 3886819981*x^21 - 7497091063*x^20 - 6400424553*x^19 + 7395534509*x^18 + 7472298948*x^17 - 5316281279*x^16 - 6241094865*x^15 + 2708274554*x^14 + 3694411475*x^13 - 944758188*x^12 - 1515682037*x^11 + 219696949*x^10 + 416420009*x^9 - 35364348*x^8 - 72939485*x^7 + 4705524*x^6 + 7521252*x^5 - 540475*x^4 - 385729*x^3 + 34249*x^2 + 5860*x - 405. Cutting out subspace using f(T_2), where f=x^46 + 8*x^45 - 35*x^44 - 432*x^43 + 258*x^42 + 10643*x^41 + 8138*x^40 - 158123*x^39 - 247207*x^38 + 1575528*x^37 + 3458081*x^36 - 11047352*x^35 - 31341556*x^34 + 55320678*x^33 + 202823983*x^32 - 193669804*x^31 - 978850876*x^30 + 425357723*x^29 + 3602242165*x^28 - 262368773*x^27 - 10219746959*x^26 - 1973274948*x^25 + 22431941410*x^24 + 8910590709*x^23 - 38013833130*x^22 - 21282118350*x^21 + 49383805816*x^20 + 34274642485*x^19 - 48592430188*x^18 - 39309348527*x^17 + 35589864895*x^16 + 32441188666*x^15 - 18945949152*x^14 - 19087711168*x^13 + 7099377799*x^12 + 7824870624*x^11 - 1792098611*x^10 - 2155105998*x^9 + 285763756*x^8 + 378560787*x^7 - 25823499*x^6 - 39416847*x^5 + 1045960*x^4 + 2154513*x^3 - 5348*x^2 - 46962*x - 415. Cutting out subspace using f(T_2), where f=x^51 - 11*x^50 - 19*x^49 + 627*x^48 - 961*x^47 - 15848*x^46 + 49248*x^45 + 228696*x^44 - 1072524*x^43 - 1952290*x^42 + 14579386*x^41 + 7564072*x^40 - 138454350*x^39 + 36749589*x^38 + 967164926*x^37 - 801904028*x^36 - 5101430066*x^35 + 6640447099*x^34 + 20544115237*x^33 - 36280151979*x^32 - 63042987778*x^31 + 145626072496*x^30 + 144567203674*x^29 - 447061382019*x^28 - 233797095053*x^27 + 1068620227235*x^26 + 216209934076*x^25 - 2003659986866*x^24 + 53983509732*x^23 + 2950442830625*x^22 - 574071883080*x^21 - 3401208488916*x^20 + 1077044825011*x^19 + 3049042895793*x^18 - 1224505344781*x^17 - 2104871302448*x^16 + 952798148413*x^15 + 1104534133885*x^14 - 518527395539*x^13 - 433078951438*x^12 + 194668915201*x^11 + 123803407025*x^10 - 48444541023*x^9 - 24796797890*x^8 + 7424086741*x^7 + 3239923500*x^6 - 613222124*x^5 - 241746572*x^4 + 21278225*x^3 + 8123270*x^2 - 226741*x - 90927. Cutting out subspace using f(T_2), where f=x^52 - 8*x^51 - 48*x^50 + 536*x^49 + 756*x^48 - 16597*x^47 + 3222*x^46 + 314914*x^45 - 338940*x^44 - 4091068*x^43 + 6953068*x^42 + 38478636*x^41 - 86011640*x^40 - 269766039*x^39 + 751498487*x^38 + 1425360412*x^37 - 4929713974*x^36 - 5631107607*x^35 + 25043242440*x^34 + 15944210360*x^33 - 100236647267*x^32 - 27572729474*x^31 + 319073237776*x^30 + 1154672347*x^29 - 810908078658*x^28 + 169245267154*x^27 + 1644433982275*x^26 - 627653799030*x^25 - 2647762432084*x^24 + 1402105186115*x^23 + 3351386331895*x^22 - 2227187921868*x^21 - 3278813217681*x^20 + 2624737480522*x^19 + 2410532066556*x^18 - 2312026904873*x^17 - 1265462477167*x^16 + 1505525521736*x^15 + 422948922494*x^14 - 704929650579*x^13 - 55943137057*x^12 + 225551873262*x^11 - 18368446266*x^10 - 44790776231*x^9 + 9954132733*x^8 + 4397658893*x^7 - 1713721878*x^6 - 47336988*x^5 + 94042083*x^4 - 12042905*x^3 - 185869*x^2 + 107868*x - 4361. Computing representation of Modular symbols space of level 2509, weight 2, and dimension 44. Goal dimension = 44. Computing T_2 on dual space of dimension 44. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). %o x^44 + 8*x^43 - 30*x^42 - 394*x^41 + 92*x^40 + 8725*x^39 + 9324*x^38 - 114474*x^37 - 215321*x^36 + 984190*x^35 + 2557052*x^34 - 5753608*x^33 - 19905426*x^32 + 22576010*x^31 + 110119023*x^30 - 52722598*x^29 - 449477125*x^28 + 20976271*x^27 + 1379207874*x^26 + 361282056*x^25 - 3206654829*x^24 - 1594187924*x^23 + 5650148625*x^22 + 3886819981*x^21 - 7497091063*x^20 - 6400424553*x^19 + 7395534509*x^18 + 7472298948*x^17 - 5316281279*x^16 - 6241094865*x^15 + 2708274554*x^14 + 3694411475*x^13 - 944758188*x^12 - 1515682037*x^11 + 219696949*x^10 + 416420009*x^9 - 35364348*x^8 - 72939485*x^7 + 4705524*x^6 + 7521252*x^5 - 540475*x^4 - 385729*x^3 + 34249*x^2 + 5860*x - 405 p = %o, dimension = %o. 2 42 Computing representation of Modular symbols space of level 2509, weight 2, and dimension 46. Goal dimension = 46. Computing T_2 on dual space of dimension 46. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^46 + 8*x^45 - 35*x^44 - 432*x^43 + 258*x^42 + 10643*x^41 + 8138*x^40 - 158123*x^39 - 247207*x^38 + 1575528*x^37 + 3458081*x^36 - 11047352*x^35 - 31341556*x^34 + 55320678*x^33 + 202823983*x^32 - 193669804*x^31 - 978850876*x^30 + 425357723*x^29 + 3602242165*x^28 - 262368773*x^27 - 10219746959*x^26 - 1973274948*x^25 + 22431941410*x^24 + 8910590709*x^23 - 38013833130*x^22 - 21282118350*x^21 + 49383805816*x^20 + 34274642485*x^19 - 48592430188*x^18 - 39309348527*x^17 + 35589864895*x^16 + 32441188666*x^15 - 18945949152*x^14 - 19087711168*x^13 + 7099377799*x^12 + 7824870624*x^11 - 1792098611*x^10 - 2155105998*x^9 + 285763756*x^8 + 378560787*x^7 - 25823499*x^6 - 39416847*x^5 + 1045960*x^4 + 2154513*x^3 - 5348*x^2 - 46962*x - 415 p = %o, dimension = %o. 2 46 Computing representation of Modular symbols space of level 2509, weight 2, and dimension 51. Goal dimension = 51. Computing T_2 on dual space of dimension 51. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^51 - 11*x^50 - 19*x^49 + 627*x^48 - 961*x^47 - 15848*x^46 + 49248*x^45 + 228696*x^44 - 1072524*x^43 - 1952290*x^42 + 14579386*x^41 + 7564072*x^40 - 138454350*x^39 + 36749589*x^38 + 967164926*x^37 - 801904028*x^36 - 5101430066*x^35 + 6640447099*x^34 + 20544115237*x^33 - 36280151979*x^32 - 63042987778*x^31 + 145626072496*x^30 + 144567203674*x^29 - 447061382019*x^28 - 233797095053*x^27 + 1068620227235*x^26 + 216209934076*x^25 - 2003659986866*x^24 + 53983509732*x^23 + 2950442830625*x^22 - 574071883080*x^21 - 3401208488916*x^20 + 1077044825011*x^19 + 3049042895793*x^18 - 1224505344781*x^17 - 2104871302448*x^16 + 952798148413*x^15 + 1104534133885*x^14 - 518527395539*x^13 - 433078951438*x^12 + 194668915201*x^11 + 123803407025*x^10 - 48444541023*x^9 - 24796797890*x^8 + 7424086741*x^7 + 3239923500*x^6 - 613222124*x^5 - 241746572*x^4 + 21278225*x^3 + 8123270*x^2 - 226741*x - 90927 p = %o, dimension = %o. 2 51 Computing representation of Modular symbols space of level 2509, weight 2, and dimension 52. Goal dimension = 52. Computing T_2 on dual space of dimension 52. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^52 - 8*x^51 - 48*x^50 + 536*x^49 + 756*x^48 - 16597*x^47 + 3222*x^46 + 314914*x^45 - 338940*x^44 - 4091068*x^43 + 6953068*x^42 + 38478636*x^41 - 86011640*x^40 - 269766039*x^39 + 751498487*x^38 + 1425360412*x^37 - 4929713974*x^36 - 5631107607*x^35 + 25043242440*x^34 + 15944210360*x^33 - 100236647267*x^32 - 27572729474*x^31 + 319073237776*x^30 + 1154672347*x^29 - 810908078658*x^28 + 169245267154*x^27 + 1644433982275*x^26 - 627653799030*x^25 - 2647762432084*x^24 + 1402105186115*x^23 + 3351386331895*x^22 - 2227187921868*x^21 - 3278813217681*x^20 + 2624737480522*x^19 + 2410532066556*x^18 - 2312026904873*x^17 - 1265462477167*x^16 + 1505525521736*x^15 + 422948922494*x^14 - 704929650579*x^13 - 55943137057*x^12 + 225551873262*x^11 - 18368446266*x^10 - 44790776231*x^9 + 9954132733*x^8 + 4397658893*x^7 - 1713721878*x^6 - 47336988*x^5 + 94042083*x^4 - 12042905*x^3 - 185869*x^2 + 107868*x - 4361 p = %o, dimension = %o. 2 52 Computing cuspidal part of Full Modular symbols space of level 193, weight 2, and dimension 16 Computing cuspidal part of Modular symbols space of level 193, weight 2, and dimension 15 Computing new part of Modular symbols space of level 193, weight 2, and dimension 15. Computing 193-new part of Modular symbols space of level 193, weight 2, and dimension 15. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 193 and dimension 15 using T_2. (will stop at 453) Computing T_2 on dual space of dimension 15. Computing DualVectorSpace of Modular symbols space of level 193, weight 2, and dimension 15. Computing complement of Modular symbols space of level 193, weight 2, and dimension 15 Computing representation of Modular symbols space of level 193, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 16. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 193, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^15 + 3*x^14 - 17*x^13 - 51*x^12 + 114*x^11 + 330*x^10 - 398*x^9 - 1032*x^8 + 773*x^7 + 1601*x^6 - 761*x^5 - 1117*x^4 + 232*x^3 + 274*x^2 + 37*x + 1 time = 0 Factoring characteristic polynomial. [ , , ] time = 0.009 Cutting out subspace using f(T_2), where f=x^2 + 3*x + 1. Cutting out subspace using f(T_2), where f=x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1. Cutting out subspace using f(T_2), where f=x^8 - 2*x^7 - 9*x^6 + 18*x^5 + 21*x^4 - 44*x^3 - 11*x^2 + 27*x + 1. Computing representation of Modular symbols space of level 193, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 + 3*x + 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 193, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 193, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^8 - 2*x^7 - 9*x^6 + 18*x^5 + 21*x^4 - 44*x^3 - 11*x^2 + 27*x + 1 p = %o, dimension = %o. 2 8 Sorting ... 0.02 seconds. Computing T_3 on dual space of dimension 44. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 44. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 44. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 44. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 44. T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 44. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 44. T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 44. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 44. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 44. T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). Computing T_37 on dual space of dimension 44. T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 46. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 46. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 46. T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 46. T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 46. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 46. T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 46. T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 46. T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 46. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 46. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.011 s). Computing T_37 on dual space of dimension 46. T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0 s). Computing T_3 on dual space of dimension 51. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 51. T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 51. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 51. T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 51. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 51. T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). Computing T_19 on dual space of dimension 51. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 51. T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 51. T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). Computing T_31 on dual space of dimension 51. T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). Computing T_37 on dual space of dimension 51. T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 52. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 52. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 52. T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 52. T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 52. T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 52. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 52. T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 52. T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 52. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 52. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 52. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). Computing q-expansion. T_2 sparse... (0 s). T_3 sparse... (0.01 s). T_5 sparse... (0.01 s). T_7 sparse... (0 s). T_11 sparse... (0.01 s). T_13 sparse... (0.01 s). T_17 sparse... (0 s). T_19 sparse... (0 s). T_23 sparse... (0.01 s). T_29 sparse... (0.01 s). T_31 sparse... (0.01 s). T_37 sparse... (0.011 s). (1.25 s) Computing q-expansion. (1.341 s) Computing q-expansion. (2.379 s) Computing q-expansion. (3.131 s) Computing character group of torus of J_0(13*193)/F_13. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 2969535086 Time to this point: 1913.59 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2509, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 1914.029 seconds Magma V2.7-1 Mon Jan 29 2001 06:39:44 on modular [Seed = 1578202135] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2510 and weight 2.... I. Manin symbols list. (0.07 s) II. 2-term relations. (1.4 s) III. 3-term relations. Computing quotient by 1512 relations. Form quot and then images (1.301 s) (total time to create space = 2.811 s) Computing cuspidal part of Full Modular symbols space of level 2510, weight 2, and dimension 382 Computing new part of Modular symbols space of level 2510, weight 2, and dimension 375. Computing 2-new part of Modular symbols space of level 2510, weight 2, and dimension 375. Computing space of modular symbols of level 1255 and weight 2.... I. Manin symbols list. (0.011 s) II. 2-term relations. (0.471 s) III. 3-term relations. Computing quotient by 504 relations. Form quot and then images (0.259 s) (total time to create space = 0.751 s) Computing index-1 degeneracy map from level 2510 to 1255. (3.66 s) Computing index-2 degeneracy map from level 2510 to 1255. (3.631 s) Computing index-1 degeneracy map from level 1255 to 2510. (1.359 s) Computing index-2 degeneracy map from level 1255 to 2510. (1.06 s) Computing DualVectorSpace of Modular symbols space of level 2510, weight 2, and dimension 375. Computing complement of Modular symbols space of level 2510, weight 2, and dimension 375 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 382. (0.269 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 69 Computing T_3 on space of dimension 382. (0.209 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 2510, weight 2, and dimension 7 Computing 5-new part of Modular symbols space of level 2510, weight 2, and dimension 375. Computing space of modular symbols of level 502 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.21 s) III. 3-term relations. Computing quotient by 252 relations. Form quot and then images (0.1 s) (total time to create space = 0.32 s) Computing index-1 degeneracy map from level 2510 to 502. (0.591 s) Computing index-5 degeneracy map from level 2510 to 502. (0.711 s) Computing index-1 degeneracy map from level 502 to 2510. (1.19 s) Computing index-5 degeneracy map from level 502 to 2510. (1.48 s) Computing 251-new part of Modular symbols space of level 2510, weight 2, and dimension 375. Computing space of modular symbols of level 10 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.01 s) III. 3-term relations. Computing quotient by 6 relations. Form quot and then images (0 s) (total time to create space = 0.01 s) Computing index-1 degeneracy map from level 2510 to 10. (0.081 s) Computing index-251 degeneracy map from level 2510 to 10. (29.769 s) Computing index-1 degeneracy map from level 10 to 2510. (3.899 s) Computing index-251 degeneracy map from level 10 to 2510. (4.221 s) Finding newform decomposition of Modular symbols space of level 2510, weight 2, and dimension 375. Computing cuspidal part of Modular symbols space of level 2510, weight 2, and dimension 375 Decomposing space of level 2510 and dimension 85 using T_3. (will stop at 756) Computing T_3 on dual space of dimension 85. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^85 - 174*x^83 + 14523*x^81 - 774474*x^79 + 32*x^78 + 29653545*x^77 - 4832*x^76 - 868544474*x^75 + 348208*x^74 + 20246574326*x^73 - 15945248*x^72 - 385858844900*x^71 + 521220656*x^70 + 6128904922682*x^69 - 12952540696*x^68 - 82304306273132*x^67 + 254461426936*x^66 + 944648391075953*x^65 - 4057481993344*x^64 - 9344874580085142*x^63 + 53498509958384*x^62 + 80199191367690336*x^61 - 591237090270648*x^60 - 600157001778548058*x^59 + 5531713067325472*x^58 + 3931456637928969449*x^57 - 44140136104857592*x^56 - 22610364594124841002*x^55 + 301983466337420848*x^54 + 114402716841253905610*x^53 - 1777710523084124064*x^52 - 509952454941335763320*x^51 + 9023182358733074936*x^50 + 2003954625756418299433*x^49 - 39513302417183144040*x^48 - 6942899879488956356402*x^47 + 149150728518808702848*x^46 + 21196256549104026022117*x^45 - 484035518154699875616*x^44 - 56958283138469726120706*x^43 + 1344082522510189760952*x^42 + 134489559211699298894141*x^41 - 3168424006707435146296*x^40 - 278380470900123293440786*x^39 + 6258560456380878505464*x^38 + 503622103269686748402561*x^37 - 10124332546062363673240*x^36 - 793362064512266397414776*x^35 + 12801903765554017797024*x^34 + 1083368758990068055610571*x^33 - 11141565363704261961976*x^32 - 1275449228733032581297254*x^31 + 2873846993576393284832*x^30 + 1286232701642026038073793*x^29 + 10575103807049976926504*x^28 - 1102535184549013428856280*x^27 - 23530330556311079583392*x^26 + 795926550345389194404808*x^25 + 29606566567290101820128*x^24 - 478558354737860059483840*x^23 - 26659752144588168839552*x^22 + 236431080625945756278608*x^21 + 18100843563026907380736*x^20 - 94390178943459441061376*x^19 - 9357104391328588717056*x^18 + 29817389086584819882752*x^17 + 3651408640109177346048*x^16 - 7253860844785767661568*x^15 - 1053018576047511633920*x^14 + 1311068346098438696960*x^13 + 216839260494565736448*x^12 - 167548254695126269952*x^11 - 30241770105669943296*x^10 + 14088856446085496832*x^9 + 2622369022996381696*x^8 - 696797152967393280*x^7 - 120593601976598528*x^6 + 16811699077120000*x^5 + 1955531728093184*x^4 - 156972875776000*x^3 + 2215095828480*x^2 time = 5.809 Factoring characteristic polynomial. [ , , , , , , , , , , , ] time = 0.25 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). Charpoly = x^2 + 2*x + 1. Decomposing space of level 2510 and dimension 2 using T_3. (will stop at 756) Computing characteristic polynomial of T_3. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Charpoly = x^2 + 2*x + 1. Decomposing space of level 2510 and dimension 2 using T_7. (will stop at 756) Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Computing characteristic polynomial of T_7. x^2 - x - 20 time = 0.011 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_7), where f=x - 5. Cutting out subspace using f(T_7), where f=x + 4. Cutting out subspace using f(T_3), where f=x + 2. Cutting out subspace using f(T_3), where f=x^2 - 2. Cutting out subspace using f(T_3), where f=x^2 + 4*x + 2. Cutting out subspace using f(T_3), where f=x^4 - 4*x^2 - x + 1. Cutting out subspace using f(T_3), where f=x^5 + 4*x^4 - 9*x^2 + x + 2. Cutting out subspace using f(T_3), where f=x^7 + 2*x^6 - 10*x^5 - 15*x^4 + 33*x^3 + 28*x^2 - 36*x - 8. Cutting out subspace using f(T_3), where f=x^9 + 4*x^8 - 10*x^7 - 47*x^6 + 27*x^5 + 172*x^4 - 12*x^3 - 200*x^2 + 64. Cutting out subspace using f(T_3), where f=x^12 - 5*x^11 - 11*x^10 + 81*x^9 + 12*x^8 - 459*x^7 + 208*x^6 + 1068*x^5 - 751*x^4 - 804*x^3 + 707*x^2 - 120*x + 4. Cutting out subspace using f(T_3), where f=x^12 - 3*x^11 - 19*x^10 + 57*x^9 + 116*x^8 - 347*x^7 - 288*x^6 + 824*x^5 + 289*x^4 - 686*x^3 - 73*x^2 + 104*x - 2. Cutting out subspace using f(T_3), where f=x^14 - x^13 - 39*x^12 + 35*x^11 + 606*x^10 - 485*x^9 - 4786*x^8 + 3420*x^7 + 20263*x^6 - 13000*x^5 - 44417*x^4 + 25280*x^3 + 44172*x^2 - 19400*x - 12960. Cutting out subspace using f(T_3), where f=x^15 - 7*x^14 - 11*x^13 + 171*x^12 - 130*x^11 - 1473*x^10 + 2314*x^9 + 5656*x^8 - 11909*x^7 - 9710*x^6 + 26139*x^5 + 7172*x^4 - 23874*x^3 - 4968*x^2 + 8184*x + 2608. Computing representation of Modular symbols space of level 2510, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 43 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x p = %o, dimension = %o. 3 2 Computing T_5 on space of dimension 382. (0.289 s) Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 5 2 Computing T_7 on space of dimension 382. (0.351 s) Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x - 5 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 43 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 5 2 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). %o x + 4 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 42 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x + 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 43 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^2 - 2 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 42 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^2 + 4*x + 2 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 43 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^4 - 4*x^2 - x + 1 p = %o, dimension = %o. 3 4 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 2 42 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^5 + 4*x^4 - 9*x^2 + x + 2 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on dual space of dimension 7. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1 p = %o, dimension = %o. 2 42 Computing T_3 on dual space of dimension 7. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^7 + 2*x^6 - 10*x^5 - 15*x^4 + 33*x^3 + 28*x^2 - 36*x - 8 p = %o, dimension = %o. 3 7 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 9. Goal dimension = 9. Computing T_2 on dual space of dimension 9. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1 p = %o, dimension = %o. 2 43 Computing T_3 on dual space of dimension 9. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^9 + 4*x^8 - 10*x^7 - 47*x^6 + 27*x^5 + 172*x^4 - 12*x^3 - 200*x^2 + 64 p = %o, dimension = %o. 3 9 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1 p = %o, dimension = %o. 2 42 Computing T_3 on dual space of dimension 12. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^12 - 5*x^11 - 11*x^10 + 81*x^9 + 12*x^8 - 459*x^7 + 208*x^6 + 1068*x^5 - 751*x^4 - 804*x^3 + 707*x^2 - 120*x + 4 p = %o, dimension = %o. 3 12 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1 p = %o, dimension = %o. 2 43 Computing T_3 on dual space of dimension 12. T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^12 - 3*x^11 - 19*x^10 + 57*x^9 + 116*x^8 - 347*x^7 - 288*x^6 + 824*x^5 + 289*x^4 - 686*x^3 - 73*x^2 + 104*x - 2 p = %o, dimension = %o. 3 12 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 14. Goal dimension = 14. Computing T_2 on dual space of dimension 14. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^14 + 14*x^13 + 91*x^12 + 364*x^11 + 1001*x^10 + 2002*x^9 + 3003*x^8 + 3432*x^7 + 3003*x^6 + 2002*x^5 + 1001*x^4 + 364*x^3 + 91*x^2 + 14*x + 1 p = %o, dimension = %o. 2 43 Computing T_3 on dual space of dimension 14. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^14 - x^13 - 39*x^12 + 35*x^11 + 606*x^10 - 485*x^9 - 4786*x^8 + 3420*x^7 + 20263*x^6 - 13000*x^5 - 44417*x^4 + 25280*x^3 + 44172*x^2 - 19400*x - 12960 p = %o, dimension = %o. 3 14 Computing representation of Modular symbols space of level 2510, weight 2, and dimension 15. Goal dimension = 15. Computing T_2 on dual space of dimension 15. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^15 - 15*x^14 + 105*x^13 - 455*x^12 + 1365*x^11 - 3003*x^10 + 5005*x^9 - 6435*x^8 + 6435*x^7 - 5005*x^6 + 3003*x^5 - 1365*x^4 + 455*x^3 - 105*x^2 + 15*x - 1 p = %o, dimension = %o. 2 42 Computing T_3 on dual space of dimension 15. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^15 - 7*x^14 - 11*x^13 + 171*x^12 - 130*x^11 - 1473*x^10 + 2314*x^9 + 5656*x^8 - 11909*x^7 - 9710*x^6 + 26139*x^5 + 7172*x^4 - 23874*x^3 - 4968*x^2 + 8184*x + 2608 p = %o, dimension = %o. 3 15 Computing cuspidal part of Full Modular symbols space of level 1255, weight 2, and dimension 128 Computing cuspidal part of Modular symbols space of level 1255, weight 2, and dimension 125 Computing new part of Modular symbols space of level 1255, weight 2, and dimension 125. Computing 5-new part of Modular symbols space of level 1255, weight 2, and dimension 125. Computing space of modular symbols of level 251 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.081 s) III. 3-term relations. Computing quotient by 84 relations. Form quot and then images (0.019 s) (total time to create space = 0.111 s) Computing index-1 degeneracy map from level 1255 to 251. (0.059 s) Computing index-5 degeneracy map from level 1255 to 251. (0.08 s) Computing index-1 degeneracy map from level 251 to 1255. (0.45 s) Computing index-5 degeneracy map from level 251 to 1255. (0.359 s) Computing DualVectorSpace of Modular symbols space of level 1255, weight 2, and dimension 125. Computing complement of Modular symbols space of level 1255, weight 2, and dimension 125 Computing representation of Modular symbols space of level 1255, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 128. (0.03 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 1255, weight 2, and dimension 3 Computing 251-new part of Modular symbols space of level 1255, weight 2, and dimension 125. Computing space of modular symbols of level 5 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 1255 to 5. (0.019 s) Computing index-251 degeneracy map from level 1255 to 5. (14.349 s) Computing index-1 degeneracy map from level 5 to 1255. (1.941 s) Computing index-251 degeneracy map from level 5 to 1255. (1.39 s) Decomposing space of level 1255 and dimension 83 using T_2. (will stop at 756) Computing T_2 on dual space of dimension 83. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^83 + x^82 - 121*x^81 - 117*x^80 + 7028*x^79 + 6560*x^78 - 260960*x^77 - 234708*x^76 + 6960382*x^75 + 6020218*x^74 - 142061606*x^73 - 117909990*x^72 + 2308023099*x^71 + 1833989427*x^70 - 30656960431*x^69 - 23263038363*x^68 + 339336962945*x^67 + 245215013165*x^66 - 3174507978277*x^65 - 2177998814381*x^64 + 25369050090752*x^63 + 16470769545408*x^62 - 174611416834684*x^61 - 106889758450688*x^60 + 1041652360411960*x^59 + 598840967538708*x^58 - 5411973769645264*x^57 - 2909171233416052*x^56 + 24578412454177265*x^55 + 12294197128687809*x^54 - 97828739710134879*x^53 - 45293889385303619*x^52 + 341876563796311582*x^51 + 145655232579277602*x^50 - 1050041499848367236*x^49 - 409017882614505168*x^48 + 2835426007547878722*x^47 + 1002639609247198598*x^46 - 6729136913166993150*x^45 - 2143322404299312686*x^44 + 14021902969852413939*x^43 + 3988808071472821127*x^42 - 25613131621621012835*x^41 - 6448108080024907059*x^40 + 40921049086929252954*x^39 + 9029626734449214110*x^38 - 57014541323634387698*x^37 - 10920657785880243478*x^36 + 69022757391913925530*x^35 + 11373495817085690078*x^34 - 72283354225948597972*x^33 - 10177226698675064592*x^32 + 65135110122298923567*x^31 + 7820088687960231643*x^30 - 50185878346097344015*x^29 - 5172770674183455191*x^28 + 32816258189536791092*x^27 + 2965532558938577600*x^26 - 18049894128332728816*x^25 - 1489016226456914572*x^24 + 8262231027077864453*x^23 + 660921183972847185*x^22 - 3106558504298144945*x^21 - 258987645872972341*x^20 + 943796776345966359*x^19 + 87830723851249523*x^18 - 226746642205866189*x^17 - 24818631585303945*x^16 + 41814305478207276*x^15 + 5560819571303628*x^14 - 5661146260575912*x^13 - 931916637789044*x^12 + 522319319655536*x^11 + 108433358559652*x^10 - 28190342164968*x^9 - 7800656168364*x^8 + 521855418966*x^7 + 271742536558*x^6 + 14674869872*x^5 - 1547097868*x^4 - 142084449*x^3 + 315739*x^2 + 197965*x + 825 time = 0.759 Factoring characteristic polynomial. [ , , , , , ] time = 0.22 Cutting out subspace using f(T_2), where f=x^2 - 3*x + 1. Cutting out subspace using f(T_2), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Charpoly = x^4 + 4*x^3 - 4*x^2 - 16*x + 16. Decomposing space of level 1255 and dimension 4 using T_2. (will stop at 756) Computing characteristic polynomial of T_2. x^4 + 2*x^3 - x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Charpoly = x^4 - 4*x^3 - 4*x^2 + 16*x + 16. Decomposing space of level 1255 and dimension 4 using T_3. (will stop at 756) Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^4 - 2*x^3 - 5*x^2 + 6*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0.01 Cutting out subspace using f(T_3), where f=x^4 - 2*x^3 - 5*x^2 + 6*x + 4. Cutting out subspace using f(T_2), where f=x^14 + x^13 - 21*x^12 - 17*x^11 + 173*x^10 + 109*x^9 - 702*x^8 - 334*x^7 + 1431*x^6 + 539*x^5 - 1308*x^4 - 502*x^3 + 395*x^2 + 177*x + 11. Cutting out subspace using f(T_2), where f=x^18 + 9*x^17 + 14*x^16 - 96*x^15 - 327*x^14 + 211*x^13 + 1976*x^12 + 988*x^11 - 5190*x^10 - 5498*x^9 + 5931*x^8 + 9517*x^7 - 1688*x^6 - 6362*x^5 - 1202*x^4 + 1017*x^3 + 328*x^2 + 13*x - 1. Cutting out subspace using f(T_2), where f=x^21 - 5*x^20 - 18*x^19 + 121*x^18 + 92*x^17 - 1209*x^16 + 200*x^15 + 6465*x^14 - 3931*x^13 - 20104*x^12 + 17139*x^11 + 37163*x^10 - 36918*x^9 - 40327*x^8 + 43231*x^7 + 24531*x^6 - 27148*x^5 - 7717*x^4 + 8336*x^3 + 1146*x^2 - 965*x - 75. Cutting out subspace using f(T_2), where f=x^24 - 3*x^23 - 32*x^22 + 98*x^21 + 435*x^20 - 1371*x^19 - 3275*x^18 + 10759*x^17 + 14906*x^16 - 52128*x^15 - 41860*x^14 + 161706*x^13 + 70230*x^12 - 322002*x^11 - 62370*x^10 + 400807*x^9 + 17741*x^8 - 293054*x^7 + 7121*x^6 + 111980*x^5 - 416*x^4 - 17941*x^3 - 1576*x^2 + 229*x + 1. Computing representation of Modular symbols space of level 1255, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 - 3*x + 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 1255, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^4 + 2*x^3 - x^2 - 2*x + 1 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1255, weight 2, and dimension 14. Goal dimension = 14. Computing T_2 on dual space of dimension 14. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^14 + x^13 - 21*x^12 - 17*x^11 + 173*x^10 + 109*x^9 - 702*x^8 - 334*x^7 + 1431*x^6 + 539*x^5 - 1308*x^4 - 502*x^3 + 395*x^2 + 177*x + 11 p = %o, dimension = %o. 2 14 Computing representation of Modular symbols space of level 1255, weight 2, and dimension 18. Goal dimension = 18. Computing T_2 on dual space of dimension 18. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^18 + 9*x^17 + 14*x^16 - 96*x^15 - 327*x^14 + 211*x^13 + 1976*x^12 + 988*x^11 - 5190*x^10 - 5498*x^9 + 5931*x^8 + 9517*x^7 - 1688*x^6 - 6362*x^5 - 1202*x^4 + 1017*x^3 + 328*x^2 + 13*x - 1 p = %o, dimension = %o. 2 18 Computing representation of Modular symbols space of level 1255, weight 2, and dimension 21. Goal dimension = 21. Computing T_2 on dual space of dimension 21. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^21 - 5*x^20 - 18*x^19 + 121*x^18 + 92*x^17 - 1209*x^16 + 200*x^15 + 6465*x^14 - 3931*x^13 - 20104*x^12 + 17139*x^11 + 37163*x^10 - 36918*x^9 - 40327*x^8 + 43231*x^7 + 24531*x^6 - 27148*x^5 - 7717*x^4 + 8336*x^3 + 1146*x^2 - 965*x - 75 p = %o, dimension = %o. 2 21 Computing representation of Modular symbols space of level 1255, weight 2, and dimension 24. Goal dimension = 24. Computing T_2 on dual space of dimension 24. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^24 - 3*x^23 - 32*x^22 + 98*x^21 + 435*x^20 - 1371*x^19 - 3275*x^18 + 10759*x^17 + 14906*x^16 - 52128*x^15 - 41860*x^14 + 161706*x^13 + 70230*x^12 - 322002*x^11 - 62370*x^10 + 400807*x^9 + 17741*x^8 - 293054*x^7 + 7121*x^6 + 111980*x^5 - 416*x^4 - 17941*x^3 - 1576*x^2 + 229*x + 1 p = %o, dimension = %o. 2 24 Computing cuspidal part of Full Modular symbols space of level 502, weight 2, and dimension 65 Computing cuspidal part of Modular symbols space of level 502, weight 2, and dimension 62 Computing new part of Modular symbols space of level 502, weight 2, and dimension 62. Computing 2-new part of Modular symbols space of level 502, weight 2, and dimension 62. Computing index-1 degeneracy map from level 502 to 251. (0.03 s) Computing index-2 degeneracy map from level 502 to 251. (0.031 s) Computing index-1 degeneracy map from level 251 to 502. (0.2 s) Computing index-2 degeneracy map from level 251 to 502. (0.189 s) Computing DualVectorSpace of Modular symbols space of level 502, weight 2, and dimension 62. Computing complement of Modular symbols space of level 502, weight 2, and dimension 62 Computing representation of Modular symbols space of level 502, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 65. (0.009 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 4*x^2 + 5*x - 2 p = %o, dimension = %o. 2 13 Computing T_3 on space of dimension 65. (0.009 s) Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - 12*x^2 + 48*x - 64 p = %o, dimension = %o. 3 3 Computing complement of Modular symbols space of level 502, weight 2, and dimension 3 Computing 251-new part of Modular symbols space of level 502, weight 2, and dimension 62. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 502 to 2. (0.01 s) Computing index-251 degeneracy map from level 502 to 2. (10.401 s) Computing index-1 degeneracy map from level 2 to 502. (1.99 s) Computing index-251 degeneracy map from level 2 to 502. (1.47 s) Decomposing space of level 502 and dimension 20 using T_3. (will stop at 756) Computing T_3 on dual space of dimension 20. T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^20 - 2*x^19 - 35*x^18 + 62*x^17 + 512*x^16 - 776*x^15 - 4073*x^14 + 5064*x^13 + 19201*x^12 - 18762*x^11 - 54801*x^10 + 41190*x^9 + 93050*x^8 - 55884*x^7 - 89899*x^6 + 47732*x^5 + 44268*x^4 - 24192*x^3 - 7520*x^2 + 5568*x - 704 time = 0.01 Factoring characteristic polynomial. [ , , , , ] time = 0.01 Cutting out subspace using f(T_3), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 2*x + 1. Decomposing space of level 502 and dimension 2 using T_3. (will stop at 756) Computing characteristic polynomial of T_3. x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 8*x + 16. Decomposing space of level 502 and dimension 2 using T_5. (will stop at 756) Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 - 5*x + 3 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x^2 - 5*x + 3. Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). Charpoly = x^2 + 8*x + 16. Decomposing space of level 502 and dimension 2 using T_3. (will stop at 756) Computing characteristic polynomial of T_3. x^2 + 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0 s). Charpoly = x^2 - 10*x + 25. Decomposing space of level 502 and dimension 2 using T_5. (will stop at 756) Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 + 3*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x^2 + 3*x + 1. Cutting out subspace using f(T_3), where f=x^5 - 2*x^4 - 9*x^3 + 14*x^2 + 16*x - 8. Cutting out subspace using f(T_3), where f=x^5 + x^4 - 7*x^3 - 4*x^2 + 6*x - 1. Cutting out subspace using f(T_3), where f=x^6 - x^5 - 16*x^4 + 9*x^3 + 74*x^2 - 8*x - 88. Computing representation of Modular symbols space of level 502, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 502, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 502, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 5. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^5 - 2*x^4 - 9*x^3 + 14*x^2 + 16*x - 8 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 502, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 5. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^5 + x^4 - 7*x^3 - 4*x^2 + 6*x - 1 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 502, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 6. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^6 - x^5 - 16*x^4 + 9*x^3 + 74*x^2 - 8*x - 88 p = %o, dimension = %o. 3 6 Computing cuspidal part of Full Modular symbols space of level 251, weight 2, and dimension 22 Computing cuspidal part of Modular symbols space of level 251, weight 2, and dimension 21 Computing new part of Modular symbols space of level 251, weight 2, and dimension 21. Computing 251-new part of Modular symbols space of level 251, weight 2, and dimension 21. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 251 and dimension 21 using T_2. (will stop at 756) Computing T_2 on dual space of dimension 21. Computing DualVectorSpace of Modular symbols space of level 251, weight 2, and dimension 21. Computing complement of Modular symbols space of level 251, weight 2, and dimension 21 Computing representation of Modular symbols space of level 251, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 22. (0.009 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 251, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^21 - 33*x^19 - 2*x^18 + 458*x^17 + 52*x^16 - 3484*x^15 - 554*x^14 + 15890*x^13 + 3130*x^12 - 44762*x^11 - 10140*x^10 + 77651*x^9 + 19050*x^8 - 80633*x^7 - 20104*x^6 + 47432*x^5 + 11016*x^4 - 14368*x^3 - 2816*x^2 + 1728*x + 256 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_2), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Charpoly = x^4 - 4*x^3 - 4*x^2 + 16*x + 16. Decomposing space of level 251 and dimension 4 using T_2. (will stop at 756) Computing characteristic polynomial of T_2. x^4 + 2*x^3 - x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Charpoly = x^4 + 2*x^3 - x^2 - 2*x + 1. Decomposing space of level 251 and dimension 4 using T_3. (will stop at 756) Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^4 + 2*x^3 - 2*x^2 - 3*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0.009 Cutting out subspace using f(T_3), where f=x^4 + 2*x^3 - 2*x^2 - 3*x + 1. Cutting out subspace using f(T_2), where f=x^17 - 2*x^16 - 28*x^15 + 54*x^14 + 317*x^13 - 582*x^12 - 1867*x^11 + 3178*x^10 + 6186*x^9 - 9216*x^8 - 11921*x^7 + 13680*x^6 + 13752*x^5 - 9400*x^4 - 8800*x^3 + 1920*x^2 + 2240*x + 256. Computing representation of Modular symbols space of level 251, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 + 2*x^3 - x^2 - 2*x + 1 p = %o, dimension = %o. 2 4 Computing index-1 degeneracy map from level 251 to 2510. (1.289 s) Computing index-2 degeneracy map from level 251 to 2510. (1.161 s) Computing index-5 degeneracy map from level 251 to 2510. (1.389 s) Computing index-10 degeneracy map from level 251 to 2510. (1.341 s) Computing representation of Modular symbols space of level 251, weight 2, and dimension 17. Computing complement of Modular symbols space of level 251, weight 2, and dimension 17 Computing DualVectorSpace of Modular symbols space of level 251, weight 2, and dimension 5. Goal dimension = 5. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 5. (0 s) %o x^5 - x^4 - 7*x^3 + x^2 + 7*x - 3 p = 2, dimension = 5. Computing complement of Modular symbols space of level 251, weight 2, and dimension 5 Sorting ... 6.47 seconds. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 1578202135 Time to this point: 1978.66 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2510, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 1979.470 seconds Magma V2.7-1 Mon Jan 29 2001 07:12:51 on modular [Seed = 778109860] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2513 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.89 s) III. 3-term relations. Computing quotient by 960 relations. Form quot and then images (0.631 s) (total time to create space = 1.57 s) Computing cuspidal part of Full Modular symbols space of level 2513, weight 2, and dimension 242 Computing new part of Modular symbols space of level 2513, weight 2, and dimension 239. Computing 7-new part of Modular symbols space of level 2513, weight 2, and dimension 239. Computing space of modular symbols of level 359 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.1 s) III. 3-term relations. Computing quotient by 120 relations. Form quot and then images (0.04 s) (total time to create space = 0.141 s) Computing index-1 degeneracy map from level 2513 to 359. (0.149 s) Computing index-7 degeneracy map from level 2513 to 359. (0.229 s) Computing index-1 degeneracy map from level 359 to 2513. (0.589 s) Computing index-7 degeneracy map from level 359 to 2513. (0.761 s) Computing DualVectorSpace of Modular symbols space of level 2513, weight 2, and dimension 239. Computing complement of Modular symbols space of level 2513, weight 2, and dimension 239 Computing representation of Modular symbols space of level 2513, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 242. (0.25 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2513, weight 2, and dimension 3 Computing 359-new part of Modular symbols space of level 2513, weight 2, and dimension 239. Computing space of modular symbols of level 7 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 4 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 2513 to 7. (0.049 s) Computing index-359 degeneracy map from level 2513 to 7. (39.26 s) Computing index-1 degeneracy map from level 7 to 2513. (3.591 s) Computing index-359 degeneracy map from level 7 to 2513. (2.56 s) Finding newform decomposition of Modular symbols space of level 2513, weight 2, and dimension 239. Computing cuspidal part of Modular symbols space of level 2513, weight 2, and dimension 239 Decomposing space of level 2513 and dimension 179 using T_2. (will stop at 480) Computing T_2 on dual space of dimension 179. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing characteristic polynomial of T_2. x^179 + x^178 - 266*x^177 - 262*x^176 + 34717*x^175 + 33673*x^174 - 2963558*x^173 - 2829902*x^172 + 186096548*x^171 + 174908520*x^170 - 9167128278*x^169 - 8478418006*x^168 + 368902942137*x^167 + 335655995329*x^166 - 12470712299164*x^165 - 11159990189960*x^164 + 361413719167343*x^163 + 318019955416971*x^162 - 9119428423261566*x^161 - 7888214943139764*x^160 + 202790673666374268*x^159 + 172385908528728614*x^158 - 4013099297218795528*x^157 - 3351618268460545830*x^156 + 71241564212804426850*x^155 + 58439142989922408464*x^154 - 1142082223617910285518*x^153 - 919887839547525422266*x^152 + 16626761952497089572369*x^151 + 13145584497956760485677*x^150 - 220871922808400487398852*x^149 - 171360623460074688555170*x^148 + 2688320287705799637064710*x^147 + 2046016450804353591470232*x^146 - 30086757606630856048063758*x^145 - 22455141458249921180581804*x^144 + 310578258482609869394157159*x^143 + 227234132237746949045311157*x^142 - 2965158930027897140662740229*x^141 - 2125970270223157580966489057*x^140 + 26244820215291824645791517855*x^139 + 18433106149999255688808331607*x^138 - 215810616772348009118872682895*x^137 - 148424815522543030481042069151*x^136 + 1651749238241635680493119881902*x^135 + 1111945176395087912053668656246*x^134 - 11786177632360259957913400725336*x^133 - 7763147326820077441897870667258*x^132 + 78522251915653688306789594480069*x^131 + 50582009719196591740888574010703*x^130 - 489061810368581109968432046482179*x^129 - 307971773641109091839063457930727*x^128 + 2850893397951733271684307482081150*x^127 + 1754160426693572925158079075502774*x^126 - 15569707990664252529402651435536103*x^125 - 9356186322500400240533854975699473*x^124 + 79734219384745915269056454942085379*x^123 + 46770629057452002643366606482539817*x^122 - 383184062023087481251620898673609490*x^121 - 219288899682591063716145336936055708*x^120 + 1729247546092579007861466251698159026*x^119 + 964957190511537719404632158162102800*x^118 - 7332311632121475693413171775693644432*x^117 - 3987348705997204205981758434806161928*x^116 + 29225828915307284669412299043406658130*x^115 + 15478995991044560648687136740542382546*x^114 - 109548567134480922884677058178125584551*x^113 - 56473494729620291340758011069155180841*x^112 + 386276178318900624243236084351181347641*x^111 + 193693992865349284830861153041067301479*x^110 - 1281578807965171026631148785150824409900*x^109 - 624670183276608998898750691386606893328*x^108 + 4001497198912518317129174805706906627432*x^107 + 1894570832403101795027785025952815064404*x^106 - 11759076095233285088023552021433436402019*x^105 - 5404167505465786116557164549360042634641*x^104 + 32524606343887216071572872199872145071557*x^103 + 14498009240288539845052731971103336765455*x^102 - 84669211307161493460364645861568545479659*x^101 - 36578474083015569769463153061691913532663*x^100 + 207430397317262167565431227976644285374922*x^99 + 86781995622774493781651930930922289241582*x^98 - 478172124260615613422002955432523882608160*x^97 - 193572495015679109435416125495338688978852*x^96 + 1036968619830714031106121161544606053905297*x^95 + 405849841169290211032914749995921630797589*x^94 - 2114920591979353674102509496784125813607369*x^93 - 799590874711629024178827414433770839731607*x^92 + 4055273669744210956284704707979568277500433*x^91 + 1479789131736976796473839466150737258896483*x^90 - 7307472860143712357833909085711539495432632*x^89 - 2571500749915765815952890402123293816670664*x^88 + 12368892759153126972397375275118629900527559*x^87 + 4194020783793995194017690331095429398085835*x^86 - 19655243206579730798864998888071426755412999*x^85 - 6416697187101055111837158737521119280597001*x^84 + 29305456466429426776433499065034839980164804*x^83 + 9204238409123208470254774276586915961789738*x^82 - 40968465610607679470056007533131907839312328*x^81 - 12370776973024531395240733164233560811911456*x^80 + 53661131945232798603560037291897288368666182*x^79 + 15568845039590069288047566444063314795396046*x^78 - 65799790746545474282698247767599372512921314*x^77 - 18334313390742794808107305469639457109967848*x^76 + 75466766139443126854338240268980872231845360*x^75 + 20188423174246865788258362797606174363930958*x^74 - 80877952323595713826082716003305696666096175*x^73 - 20769859310746630788818427462613150657345373*x^72 + 80907171536261662728990211566407270714175735*x^71 + 19948321576879469137902288409012084387359025*x^70 - 75461597574630007893344093549365222562536966*x^69 - 17871222569056900690905128656420908005168656*x^68 + 65539696198693500538259342726582037812593466*x^67 + 14920944665416524649638647969888205618651668*x^66 - 52933949630717620177639613861746063126840709*x^65 - 11599433311384852301491854604361369287150329*x^64 + 39698922630909737992630259597663556431628601*x^63 + 8388093986155689713783935045852243987588353*x^62 - 27602458223569067471079293880482178530198290*x^61 - 5636937165190794227817953768385137283560806*x^60 + 17762072548432097565801615162850015374308226*x^59 + 3516551005856755265967056800401099446059482*x^58 - 10558568009079435299484742067102035184845567*x^57 - 2034172544986489875648676363790872225937479*x^56 + 5786290713656819479589230195547697679120569*x^55 + 1089700883646103229378975207465029481639301*x^54 - 2916884445024392842824955319782991402328281*x^53 - 539827970188251647424092510043405995599707*x^52 + 1349315720947941112191924309965289723990458*x^51 + 246896736357536665497094330045198314970512*x^50 - 571261126183280880588201028383850780972147*x^49 - 104050503271243410381585985364551293338579*x^48 + 220708333755653129727249500097594548297372*x^47 + 40312459332489460189672251544938245196476*x^46 - 77565453631749941768329435125852682135790*x^45 - 14318700019264370299433189938539857700060*x^44 + 24707510167820549615166419706048883487966*x^43 + 4647409787767269621678867829931386250196*x^42 - 7104919067598983334728338264036251548702*x^41 - 1373010084776544856527724560628832097758*x^40 + 1836079140889552869944256398498721468899*x^39 + 367546578295867680193575249992965744775*x^38 - 424210465775282434874675117336672606302*x^37 - 88680168323157962632609311883971697940*x^36 + 87104202702707432947815674088214240264*x^35 + 19167398673486090361602828994205083666*x^34 - 15784645729452603885501764077704928607*x^33 - 3685340296039165876402350689098096691*x^32 + 2503604575928576607183085672381523608*x^31 + 625285900266828069884525129674210116*x^30 - 344080191608503425964000377084525700*x^29 - 92757729470856500014899126678408816*x^28 + 40464185989940324375255619217033894*x^27 + 11902449840407401786279797918667486*x^26 - 4006570655734479497315766491594827*x^25 - 1304598834287424304234248905418775*x^24 + 326760356747612285102006223483432*x^23 + 120328736534121727109085951660704*x^22 - 21254048364515805692862549443346*x^21 - 9171224576980542205518080622392*x^20 + 1044567879605182555844633448930*x^19 + 564792314563276205000527879924*x^18 - 34505981018940144755352953209*x^17 - 27315180366243041536706957933*x^16 + 470543574127353858795869276*x^15 + 1000066097741289257298986248*x^14 + 18432333986835715003495510*x^13 - 26420447451487095690489758*x^12 - 1218145192423158314749268*x^11 + 473764331215715899736980*x^10 + 30817519365664466356194*x^9 - 5393935182359024848318*x^8 - 390905699437733398852*x^7 + 37870594714039921940*x^6 + 2396480829869998980*x^5 - 165472724892309924*x^4 - 5758583356751616*x^3 + 382329526332528*x^2 + 219827804337*x - 141811075539 time = 51.251 Factoring characteristic polynomial. [ , , , , ] time = 1.221 Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x^32 + 6*x^31 - 23*x^30 - 197*x^29 + 145*x^28 + 2849*x^27 + 919*x^26 - 23894*x^25 - 21134*x^24 + 128686*x^23 + 162881*x^22 - 464951*x^21 - 736719*x^20 + 1140155*x^19 + 2185640*x^18 - 1865486*x^17 - 4406689*x^16 + 1912364*x^15 + 6067275*x^14 - 994835*x^13 - 5620436*x^12 - 64401*x^11 + 3396429*x^10 + 400229*x^9 - 1283801*x^8 - 214639*x^7 + 291339*x^6 + 49764*x^5 - 37590*x^4 - 5168*x^3 + 2500*x^2 + 187*x - 67. Cutting out subspace using f(T_2), where f=x^39 - x^38 - 56*x^37 + 55*x^36 + 1430*x^35 - 1377*x^34 - 22068*x^33 + 20796*x^32 + 229973*x^31 - 211653*x^30 - 1713089*x^29 + 1536155*x^28 + 9419441*x^27 - 8206291*x^26 - 38935238*x^25 + 32835300*x^24 + 122113543*x^23 - 99194901*x^22 - 291391441*x^21 + 226406065*x^20 + 527682404*x^19 - 388145598*x^18 - 719944811*x^17 + 493540190*x^16 + 731318196*x^15 - 455838953*x^14 - 543830905*x^13 + 295977534*x^12 + 289280990*x^11 - 128103617*x^10 - 106556062*x^9 + 33532250*x^8 + 25837650*x^7 - 4190721*x^6 - 3729134*x^5 + 11772*x^4 + 238800*x^3 + 33012*x^2 + 360*x - 81. Cutting out subspace using f(T_2), where f=x^50 + 3*x^49 - 70*x^48 - 211*x^47 + 2280*x^46 + 6907*x^45 - 45908*x^44 - 139800*x^43 + 640324*x^42 + 1960414*x^41 - 6570845*x^40 - 20225900*x^39 + 51431111*x^38 + 159133516*x^37 - 314197226*x^36 - 976630422*x^35 + 1520765665*x^34 + 4742982485*x^33 - 5888510446*x^32 - 18386109148*x^31 + 18348484660*x^30 + 57139930094*x^29 - 46154585922*x^28 - 142480783266*x^27 + 93820466496*x^26 + 284393866018*x^25 - 154000650663*x^24 - 451948501143*x^23 + 203584943483*x^22 + 566970256444*x^21 - 215596167199*x^20 - 554832673635*x^19 + 181077782265*x^18 + 416949423283*x^17 - 118497501105*x^16 - 235875598066*x^15 + 58678050410*x^14 + 98026230141*x^13 - 21040008150*x^12 - 29065311218*x^11 + 5139613065*x^10 + 5934833726*x^9 - 788516977*x^8 - 794184770*x^7 + 67175079*x^6 + 64100534*x^5 - 2510386*x^4 - 2651040*x^3 + 25528*x^2 + 36696*x - 1169. Cutting out subspace using f(T_2), where f=x^57 - 8*x^56 - 62*x^55 + 651*x^54 + 1457*x^53 - 24694*x^52 - 8126*x^51 + 579388*x^50 - 405987*x^49 - 9404212*x^48 + 13217185*x^47 + 111804482*x^46 - 221817611*x^45 - 1004187252*x^44 + 2555532752*x^43 + 6909586138*x^42 - 22016270555*x^41 - 36344116256*x^40 + 147553302821*x^39 + 142182382281*x^38 - 786010438002*x^37 - 375443385854*x^36 + 3368605979750*x^35 + 380449884158*x^34 - 11687598313989*x^33 + 2042201725234*x^32 + 32890764670489*x^31 - 13569763821554*x^30 - 74936805603559*x^29 + 46420127937411*x^28 + 137459974963768*x^27 - 111449241643147*x^26 - 201023614680476*x^25 + 201470885186741*x^24 + 230749044808179*x^23 - 280329675165040*x^22 - 202817193627021*x^21 + 301388262612318*x^20 + 130787102736615*x^19 - 248839485571538*x^18 - 56519930080064*x^17 + 155613847575519*x^16 + 11945544533257*x^15 - 72129509089807*x^14 + 2299395793708*x^13 + 24012160222343*x^12 - 2560968501943*x^11 - 5484471263253*x^10 + 823105032298*x^9 + 802820919076*x^8 - 127464259466*x^7 - 67735785540*x^6 + 8276570055*x^5 + 2730889093*x^4 - 97829887*x^3 - 23980919*x^2 + 806413*x + 22353. Computing representation of Modular symbols space of level 2513, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2513, weight 2, and dimension 32. Goal dimension = 32. Computing T_2 on dual space of dimension 32. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^32 + 6*x^31 - 23*x^30 - 197*x^29 + 145*x^28 + 2849*x^27 + 919*x^26 - 23894*x^25 - 21134*x^24 + 128686*x^23 + 162881*x^22 - 464951*x^21 - 736719*x^20 + 1140155*x^19 + 2185640*x^18 - 1865486*x^17 - 4406689*x^16 + 1912364*x^15 + 6067275*x^14 - 994835*x^13 - 5620436*x^12 - 64401*x^11 + 3396429*x^10 + 400229*x^9 - 1283801*x^8 - 214639*x^7 + 291339*x^6 + 49764*x^5 - 37590*x^4 - 5168*x^3 + 2500*x^2 + 187*x - 67 p = %o, dimension = %o. 2 32 Computing representation of Modular symbols space of level 2513, weight 2, and dimension 39. Goal dimension = 39. Computing T_2 on dual space of dimension 39. T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^39 - x^38 - 56*x^37 + 55*x^36 + 1430*x^35 - 1377*x^34 - 22068*x^33 + 20796*x^32 + 229973*x^31 - 211653*x^30 - 1713089*x^29 + 1536155*x^28 + 9419441*x^27 - 8206291*x^26 - 38935238*x^25 + 32835300*x^24 + 122113543*x^23 - 99194901*x^22 - 291391441*x^21 + 226406065*x^20 + 527682404*x^19 - 388145598*x^18 - 719944811*x^17 + 493540190*x^16 + 731318196*x^15 - 455838953*x^14 - 543830905*x^13 + 295977534*x^12 + 289280990*x^11 - 128103617*x^10 - 106556062*x^9 + 33532250*x^8 + 25837650*x^7 - 4190721*x^6 - 3729134*x^5 + 11772*x^4 + 238800*x^3 + 33012*x^2 + 360*x - 81 p = %o, dimension = %o. 2 39 Computing representation of Modular symbols space of level 2513, weight 2, and dimension 50. Goal dimension = 50. Computing T_2 on dual space of dimension 50. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^50 + 3*x^49 - 70*x^48 - 211*x^47 + 2280*x^46 + 6907*x^45 - 45908*x^44 - 139800*x^43 + 640324*x^42 + 1960414*x^41 - 6570845*x^40 - 20225900*x^39 + 51431111*x^38 + 159133516*x^37 - 314197226*x^36 - 976630422*x^35 + 1520765665*x^34 + 4742982485*x^33 - 5888510446*x^32 - 18386109148*x^31 + 18348484660*x^30 + 57139930094*x^29 - 46154585922*x^28 - 142480783266*x^27 + 93820466496*x^26 + 284393866018*x^25 - 154000650663*x^24 - 451948501143*x^23 + 203584943483*x^22 + 566970256444*x^21 - 215596167199*x^20 - 554832673635*x^19 + 181077782265*x^18 + 416949423283*x^17 - 118497501105*x^16 - 235875598066*x^15 + 58678050410*x^14 + 98026230141*x^13 - 21040008150*x^12 - 29065311218*x^11 + 5139613065*x^10 + 5934833726*x^9 - 788516977*x^8 - 794184770*x^7 + 67175079*x^6 + 64100534*x^5 - 2510386*x^4 - 2651040*x^3 + 25528*x^2 + 36696*x - 1169 p = %o, dimension = %o. 2 49 Computing representation of Modular symbols space of level 2513, weight 2, and dimension 57. Goal dimension = 57. Computing T_2 on dual space of dimension 57. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^57 - 8*x^56 - 62*x^55 + 651*x^54 + 1457*x^53 - 24694*x^52 - 8126*x^51 + 579388*x^50 - 405987*x^49 - 9404212*x^48 + 13217185*x^47 + 111804482*x^46 - 221817611*x^45 - 1004187252*x^44 + 2555532752*x^43 + 6909586138*x^42 - 22016270555*x^41 - 36344116256*x^40 + 147553302821*x^39 + 142182382281*x^38 - 786010438002*x^37 - 375443385854*x^36 + 3368605979750*x^35 + 380449884158*x^34 - 11687598313989*x^33 + 2042201725234*x^32 + 32890764670489*x^31 - 13569763821554*x^30 - 74936805603559*x^29 + 46420127937411*x^28 + 137459974963768*x^27 - 111449241643147*x^26 - 201023614680476*x^25 + 201470885186741*x^24 + 230749044808179*x^23 - 280329675165040*x^22 - 202817193627021*x^21 + 301388262612318*x^20 + 130787102736615*x^19 - 248839485571538*x^18 - 56519930080064*x^17 + 155613847575519*x^16 + 11945544533257*x^15 - 72129509089807*x^14 + 2299395793708*x^13 + 24012160222343*x^12 - 2560968501943*x^11 - 5484471263253*x^10 + 823105032298*x^9 + 802820919076*x^8 - 127464259466*x^7 - 67735785540*x^6 + 8276570055*x^5 + 2730889093*x^4 - 97829887*x^3 - 23980919*x^2 + 806413*x + 22353 p = %o, dimension = %o. 2 57 Computing cuspidal part of Full Modular symbols space of level 359, weight 2, and dimension 31 Computing cuspidal part of Modular symbols space of level 359, weight 2, and dimension 30 Computing new part of Modular symbols space of level 359, weight 2, and dimension 30. Computing 359-new part of Modular symbols space of level 359, weight 2, and dimension 30. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 359 and dimension 30 using T_2. (will stop at 480) Computing T_2 on dual space of dimension 30. Computing DualVectorSpace of Modular symbols space of level 359, weight 2, and dimension 30. Computing complement of Modular symbols space of level 359, weight 2, and dimension 30 Computing representation of Modular symbols space of level 359, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 31. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 359, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^30 + x^29 - 45*x^28 - 43*x^27 + 901*x^26 + 819*x^25 - 10598*x^24 - 9118*x^23 + 81442*x^22 + 65960*x^21 - 430147*x^20 - 326117*x^19 + 1599266*x^18 + 1128770*x^17 - 4215524*x^16 - 2755032*x^15 + 7829072*x^14 + 4709968*x^13 - 10048484*x^12 - 5516195*x^11 + 8608653*x^10 + 4235917*x^9 - 4658781*x^8 - 1969433*x^7 + 1465341*x^6 + 478276*x^5 - 238112*x^4 - 44898*x^3 + 17396*x^2 + 1125*x - 381 time = 0.01 Factoring characteristic polynomial. [ , , , ] time = 0.031 Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x^4 + 2*x^3 - 3*x^2 - 5*x + 1. Cutting out subspace using f(T_2), where f=x^24 - x^23 - 39*x^22 + 38*x^21 + 658*x^20 - 619*x^19 - 6300*x^18 + 5654*x^17 + 37740*x^16 - 31780*x^15 - 147096*x^14 + 113400*x^13 + 376092*x^12 - 255412*x^11 - 621508*x^10 + 349080*x^9 + 638532*x^8 - 266744*x^7 - 378124*x^6 + 98609*x^5 + 110695*x^4 - 14509*x^3 - 11972*x^2 + 780*x + 381. Computing representation of Modular symbols space of level 359, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 359, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 359, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 + 2*x^3 - 3*x^2 - 5*x + 1 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 359, weight 2, and dimension 24. Computing complement of Modular symbols space of level 359, weight 2, and dimension 24 Computing DualVectorSpace of Modular symbols space of level 359, weight 2, and dimension 7. Goal dimension = 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). Computing T_2 on space of dimension 7. (0 s) %o x^7 - x^6 - 10*x^5 + 5*x^4 + 25*x^3 - 7*x^2 - 16*x + 3 p = 2, dimension = 7. Computing complement of Modular symbols space of level 359, weight 2, and dimension 7 Sorting ... 0.139 seconds. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 778109860 Time to this point: 973.14 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2513, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 973.330 seconds Magma V2.7-1 Mon Jan 29 2001 07:29:05 on modular [Seed = 577569690] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2514 and weight 2.... I. Manin symbols list. (0.08 s) II. 2-term relations. (1.58 s) III. 3-term relations. Computing quotient by 1680 relations. Form quot and then images (1.56 s) (total time to create space = 3.27 s) Computing cuspidal part of Full Modular symbols space of level 2514, weight 2, and dimension 424 Computing new part of Modular symbols space of level 2514, weight 2, and dimension 417. Computing 2-new part of Modular symbols space of level 2514, weight 2, and dimension 417. Computing space of modular symbols of level 1257 and weight 2.... I. Manin symbols list. (0.009 s) II. 2-term relations. (0.469 s) III. 3-term relations. Computing quotient by 560 relations. Form quot and then images (0.301 s) (total time to create space = 0.79 s) Computing index-1 degeneracy map from level 2514 to 1257. (4.44 s) Computing index-2 degeneracy map from level 2514 to 1257. (4.289 s) Computing index-1 degeneracy map from level 1257 to 2514. (1.251 s) Computing index-2 degeneracy map from level 1257 to 2514. (1.279 s) Computing DualVectorSpace of Modular symbols space of level 2514, weight 2, and dimension 417. Computing complement of Modular symbols space of level 2514, weight 2, and dimension 417 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 424. (0.319 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.019 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 77 Computing T_3 on space of dimension 424. (0.251 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.02 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). %o x^7 - 13*x^6 + 69*x^5 - 193*x^4 + 307*x^3 - 279*x^2 + 135*x - 27 p = %o, dimension = %o. 3 25 Computing T_5 on space of dimension 424. (0.34 s) Computing T_5 on dual space of dimension 7. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.019 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). %o x^7 - 42*x^6 + 756*x^5 - 7560*x^4 + 45360*x^3 - 163296*x^2 + 326592*x - 279936 p = %o, dimension = %o. 5 7 Computing complement of Modular symbols space of level 2514, weight 2, and dimension 7 Computing 3-new part of Modular symbols space of level 2514, weight 2, and dimension 417. Computing space of modular symbols of level 838 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.35 s) III. 3-term relations. Computing quotient by 420 relations. Form quot and then images (0.199 s) (total time to create space = 0.56 s) Computing index-1 degeneracy map from level 2514 to 838. (2.07 s) Computing index-3 degeneracy map from level 2514 to 838. (2.089 s) Computing index-1 degeneracy map from level 838 to 2514. (1.379 s) Computing index-3 degeneracy map from level 838 to 2514. (1.189 s) Computing 419-new part of Modular symbols space of level 2514, weight 2, and dimension 417. Computing space of modular symbols of level 6 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 4 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 2514 to 6. (0.08 s) Computing index-419 degeneracy map from level 2514 to 6. (72.44 s) Computing index-1 degeneracy map from level 6 to 2514. (8.409 s) Computing index-419 degeneracy map from level 6 to 2514. (7.819 s) Finding newform decomposition of Modular symbols space of level 2514, weight 2, and dimension 417. Computing cuspidal part of Modular symbols space of level 2514, weight 2, and dimension 417 Decomposing space of level 2514 and dimension 71 using T_5. (will stop at 840) Computing T_5 on dual space of dimension 71. T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing characteristic polynomial of T_5. x^71 + 2*x^70 - 216*x^69 - 416*x^68 + 22114*x^67 + 40972*x^66 - 1428200*x^65 - 2543248*x^64 + 65332867*x^63 + 111721734*x^62 - 2253360096*x^61 - 3697364600*x^60 + 60906281482*x^59 + 95817744940*x^58 - 1323864316912*x^57 - 1995375375368*x^56 + 23563550349209*x^55 + 34001026586786*x^54 - 347956128281216*x^53 - 480289688558712*x^52 + 4303596377937048*x^51 + 5677582393384232*x^50 - 44891851038732728*x^49 - 56549400146794576*x^48 + 396883404359077008*x^47 + 476821902897532224*x^46 - 2983595137707079984*x^45 - 3414096050323425760*x^44 + 19108251083424691888*x^43 + 20791703874532965984*x^42 - 104327344956452699712*x^41 - 107732460050318398528*x^40 + 485369460006532952256*x^39 + 474543384314524173312*x^38 - 1921183586247498158720*x^37 - 1773409277356877082368*x^36 + 6452535987229017908480*x^35 + 5604976224615577103104*x^34 - 18318532153178623163136*x^33 - 14916720889872820217856*x^32 + 43734385249234208562432*x^31 + 33238609075432737334784*x^30 - 87229473218267192518656*x^29 - 61571779756711655425024*x^28 + 144144550354309778567168*x^27 + 93984113250657308882944*x^26 - 195304123375134468136960*x^25 - 116935815143988044591104*x^24 + 214175525718262576132096*x^23 + 117020741707283825246208*x^22 - 187037776575156894842880*x^21 - 92642828981959008681984*x^20 + 127443841856606096588800*x^19 + 56825656980356683661312*x^18 - 66013271442905543213056*x^17 - 26289486524633900384256*x^16 + 25128042823653039013888*x^15 + 8848688003301291065344*x^14 - 6714897475843852861440*x^13 - 2059156141935343697920*x^12 + 1178592952117792604160*x^11 + 306340742157779861504*x^10 - 121422928375476912128*x^9 - 25386074217906176000*x^8 + 5694544443089092608*x^7 + 848277618875695104*x^6 - 27443810229288960*x^5 time = 2.569 Factoring characteristic polynomial. [ , , , , , , , , , ] time = 0.121 Cutting out subspace using f(T_5), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 5. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 5. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). Charpoly = x^5. Decomposing space of level 2514 and dimension 5 using T_5. (will stop at 840) Computing characteristic polynomial of T_5. x^5 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 5. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 5. T_5 sparse... (0.011 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Charpoly = x^5 - 20*x^4 + 160*x^3 - 640*x^2 + 1280*x - 1024. Decomposing space of level 2514 and dimension 5 using T_7. (will stop at 840) Computing T_7 on dual space of dimension 5. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Computing characteristic polynomial of T_7. x^5 + x^4 - 16*x^3 - 27*x^2 - 6*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x^5 + x^4 - 16*x^3 - 27*x^2 - 6*x + 4. Cutting out subspace using f(T_5), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Charpoly = x^2 + 14*x + 49. Decomposing space of level 2514 and dimension 2 using T_5. (will stop at 840) Computing characteristic polynomial of T_5. x^2 + 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Charpoly = x^2 + 8*x + 16. Decomposing space of level 2514 and dimension 2 using T_7. (will stop at 840) Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing characteristic polynomial of T_7. x^2 + 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.02 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.011 s). T_5 sparse... (0.019 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Charpoly = x^2 - 2*x + 1. Decomposing space of level 2514 and dimension 2 using T_11. (will stop at 840) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing characteristic polynomial of T_11. x^2 + 2*x - 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_11), where f=x^2 + 2*x - 4. Cutting out subspace using f(T_5), where f=x + 4. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.02 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Charpoly = x^2 + 12*x + 36. Decomposing space of level 2514 and dimension 2 using T_5. (will stop at 840) Computing characteristic polynomial of T_5. x^2 + 8*x + 16 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x + 4. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.019 s). T_5 sparse... (0.011 s). Charpoly = x^2 + 8*x + 16. Decomposing space of level 2514 and dimension 2 using T_7. (will stop at 840) Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing characteristic polynomial of T_7. x^2 - 2*x - 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x^2 - 2*x - 4. Cutting out subspace using f(T_5), where f=x^2 + 2*x - 4. Cutting out subspace using f(T_5), where f=x^6 + 4*x^5 - 4*x^4 - 14*x^3 + 8*x^2 + 8*x - 4. Cutting out subspace using f(T_5), where f=x^8 - 4*x^7 - 11*x^6 + 42*x^5 + 29*x^4 - 134*x^3 + 8*x^2 + 124*x - 52. Cutting out subspace using f(T_5), where f=x^9 + 2*x^8 - 28*x^7 - 50*x^6 + 232*x^5 + 384*x^4 - 532*x^3 - 784*x^2 + 256*x + 256. Cutting out subspace using f(T_5), where f=x^11 - 8*x^10 - 3*x^9 + 152*x^8 - 175*x^7 - 992*x^6 + 1500*x^5 + 2642*x^4 - 3520*x^3 - 2796*x^2 + 1516*x - 40. Cutting out subspace using f(T_5), where f=x^12 - 2*x^11 - 41*x^10 + 76*x^9 + 657*x^8 - 1112*x^7 - 5156*x^6 + 7800*x^5 + 19988*x^4 - 26096*x^3 - 31872*x^2 + 33024*x + 6144. Cutting out subspace using f(T_5), where f=x^14 - 4*x^13 - 45*x^12 + 204*x^11 + 625*x^10 - 3600*x^9 - 1892*x^8 + 25058*x^7 - 12996*x^6 - 56988*x^5 + 35172*x^4 + 61648*x^3 - 16256*x^2 - 32768*x - 8192. Computing representation of Modular symbols space of level 2514, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 2 36 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 5. T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). %o x^5 p = %o, dimension = %o. 5 5 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 36 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.019 s). T_3 sparse... (0.009 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). %o x^2 + 4*x + 4 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 36 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.019 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). %o x^2 + 8*x + 16 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 36 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 2. T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). %o x^2 + 2*x - 4 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^6 + 5*x^5 + 10*x^4 + 10*x^3 + 5*x^2 + x p = %o, dimension = %o. 2 35 Computing T_3 on dual space of dimension 6. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.019 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 6. T_5 sparse... (0.021 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). %o x^6 + 4*x^5 - 4*x^4 - 14*x^3 + 8*x^2 + 8*x - 4 p = %o, dimension = %o. 5 6 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.02 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1 p = %o, dimension = %o. 2 35 Computing T_3 on dual space of dimension 8. T_3 sparse... (0.02 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.02 s). T_3 sparse... (0.01 s). %o x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1 p = %o, dimension = %o. 3 17 Computing T_5 on dual space of dimension 8. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). %o x^8 - 4*x^7 - 11*x^6 + 42*x^5 + 29*x^4 - 134*x^3 + 8*x^2 + 124*x - 52 p = %o, dimension = %o. 5 8 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 9. Goal dimension = 9. Computing T_2 on dual space of dimension 9. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.02 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1 p = %o, dimension = %o. 2 35 Computing T_3 on dual space of dimension 9. T_3 sparse... (0.011 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1 p = %o, dimension = %o. 3 17 Computing T_5 on dual space of dimension 9. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). %o x^9 + 2*x^8 - 28*x^7 - 50*x^6 + 232*x^5 + 384*x^4 - 532*x^3 - 784*x^2 + 256*x + 256 p = %o, dimension = %o. 5 9 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 11. Goal dimension = 11. Computing T_2 on dual space of dimension 11. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1 p = %o, dimension = %o. 2 36 Computing T_3 on dual space of dimension 11. T_3 sparse... (0.01 s). T_3 sparse... (0.019 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 11. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). %o x^11 - 8*x^10 - 3*x^9 + 152*x^8 - 175*x^7 - 992*x^6 + 1500*x^5 + 2642*x^4 - 3520*x^3 - 2796*x^2 + 1516*x - 40 p = %o, dimension = %o. 5 11 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.02 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1 p = %o, dimension = %o. 2 35 Computing T_3 on dual space of dimension 12. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.019 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.019 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 12. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.02 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.02 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). %o x^12 - 56/17*x^11 - 1688/51*x^10 + 1991/17*x^9 + 18788/51*x^8 - 26177/17*x^7 - 66172/51*x^6 + 455462/51*x^5 - 41124/17*x^4 - 1027664/51*x^3 + 858368/51*x^2 + 297728/51*x p = %o, dimension = %o. 5 0 Computing representation of Modular symbols space of level 2514, weight 2, and dimension 14. Goal dimension = 14. Computing T_2 on dual space of dimension 14. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.019 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.019 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^14 - 14*x^13 + 91*x^12 - 364*x^11 + 1001*x^10 - 2002*x^9 + 3003*x^8 - 3432*x^7 + 3003*x^6 - 2002*x^5 + 1001*x^4 - 364*x^3 + 91*x^2 - 14*x + 1 p = %o, dimension = %o. 2 36 Computing T_3 on dual space of dimension 14. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^14 - 14*x^13 + 91*x^12 - 364*x^11 + 1001*x^10 - 2002*x^9 + 3003*x^8 - 3432*x^7 + 3003*x^6 - 2002*x^5 + 1001*x^4 - 364*x^3 + 91*x^2 - 14*x + 1 p = %o, dimension = %o. 3 18 Computing T_5 on dual space of dimension 14. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.021 s). %o x^14 - 4*x^13 - 45*x^12 + 204*x^11 + 625*x^10 - 3600*x^9 - 1892*x^8 + 25058*x^7 - 12996*x^6 - 56988*x^5 + 35172*x^4 + 61648*x^3 - 16256*x^2 - 32768*x - 8192 p = %o, dimension = %o. 5 14 Computing cuspidal part of Full Modular symbols space of level 1257, weight 2, and dimension 142 Computing cuspidal part of Modular symbols space of level 1257, weight 2, and dimension 139 Computing new part of Modular symbols space of level 1257, weight 2, and dimension 139. Computing 3-new part of Modular symbols space of level 1257, weight 2, and dimension 139. Computing space of modular symbols of level 419 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.129 s) III. 3-term relations. Computing quotient by 140 relations. Form quot and then images (0.05 s) (total time to create space = 0.179 s) Computing index-1 degeneracy map from level 1257 to 419. (0.11 s) Computing index-3 degeneracy map from level 1257 to 419. (0.099 s) Computing index-1 degeneracy map from level 419 to 1257. (0.44 s) Computing index-3 degeneracy map from level 419 to 1257. (0.36 s) Computing DualVectorSpace of Modular symbols space of level 1257, weight 2, and dimension 139. Computing complement of Modular symbols space of level 1257, weight 2, and dimension 139 Computing representation of Modular symbols space of level 1257, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 142. (0.03 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 1257, weight 2, and dimension 3 Computing 419-new part of Modular symbols space of level 1257, weight 2, and dimension 139. Computing space of modular symbols of level 3 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 1257 to 3. (0.029 s) Computing index-419 degeneracy map from level 1257 to 3. (39.681 s) Computing index-1 degeneracy map from level 3 to 1257. (4.269 s) Computing index-419 degeneracy map from level 3 to 1257. (3.11 s) Decomposing space of level 1257 and dimension 69 using T_2. (will stop at 840) Computing T_2 on dual space of dimension 69. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^69 + 3*x^68 - 96*x^67 - 292*x^66 + 4370*x^65 + 13498*x^64 - 125514*x^63 - 394410*x^62 + 2553339*x^61 + 8179953*x^60 - 39149868*x^59 - 128183888*x^58 + 470070013*x^57 + 1577582411*x^56 - 4533182852*x^55 - 15648142248*x^54 + 35730207877*x^53 + 127388063267*x^52 - 233003221144*x^51 - 862333946984*x^50 + 1267751554143*x^49 + 4900633066997*x^48 - 5786414251716*x^47 - 23543684948620*x^46 + 22219535536633*x^45 + 96090608729003*x^44 - 71812068513868*x^43 - 334273465618300*x^42 + 194909448238838*x^41 + 993049734912118*x^40 - 441800684460138*x^39 - 2521154937935842*x^38 + 827566568199764*x^37 + 5467941095430448*x^36 - 1256374959492576*x^35 - 10116554337784760*x^34 + 1486189766332416*x^33 + 15928632908774448*x^32 - 1237991075232046*x^31 - 21270378488701506*x^30 + 441249588601112*x^29 + 23981741283485520*x^28 + 603015642117016*x^27 - 22701972472766152*x^26 - 1380821074449729*x^25 + 17920381867639441*x^24 + 1559406438335918*x^23 - 11698268661054226*x^22 - 1221381519721950*x^21 + 6251809321145650*x^20 + 711028233574252*x^19 - 2701704048813500*x^18 - 313184051439381*x^17 + 929732196620201*x^16 + 104322595514268*x^15 - 249883230565196*x^14 - 26039800278048*x^13 + 51153219458608*x^12 + 4804308903992*x^11 - 7713831644520*x^10 - 644470318597*x^9 + 818044554041*x^8 + 61430319384*x^7 - 56863363296*x^6 - 3969493798*x^5 + 2284046722*x^4 + 154970820*x^3 - 38758156*x^2 - 2665395*x - 42993 time = 0.63 Factoring characteristic polynomial. [ , , , , , , ] time = 0.161 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). Charpoly = x^2 - 6*x + 9. Decomposing space of level 1257 and dimension 2 using T_2. (will stop at 840) Computing characteristic polynomial of T_2. x^2 + 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). Charpoly = x^2 + 2*x + 1. Decomposing space of level 1257 and dimension 2 using T_5. (will stop at 840) Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 + 2*x - 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x^2 + 2*x - 4. Cutting out subspace using f(T_2), where f=x^2 + 3*x + 1. Cutting out subspace using f(T_2), where f=x^5 + 2*x^4 - 4*x^3 - 4*x^2 + 3*x + 1. Cutting out subspace using f(T_2), where f=x^10 + 6*x^9 + 4*x^8 - 37*x^7 - 64*x^6 + 51*x^5 + 158*x^4 + 25*x^3 - 93*x^2 - 21*x + 17. Cutting out subspace using f(T_2), where f=x^13 - x^12 - 16*x^11 + 14*x^10 + 97*x^9 - 73*x^8 - 276*x^7 + 171*x^6 + 369*x^5 - 168*x^4 - 203*x^3 + 50*x^2 + 33*x + 1. Cutting out subspace using f(T_2), where f=x^18 - 3*x^17 - 27*x^16 + 86*x^15 + 284*x^14 - 1000*x^13 - 1418*x^12 + 6035*x^11 + 2952*x^10 - 20032*x^9 + 1196*x^8 + 35383*x^7 - 15293*x^6 - 28271*x^5 + 21571*x^4 + 4397*x^3 - 8453*x^2 + 2745*x - 281. Cutting out subspace using f(T_2), where f=x^19 - 6*x^18 - 10*x^17 + 119*x^16 - 48*x^15 - 924*x^14 + 1064*x^13 + 3547*x^12 - 5787*x^11 - 6914*x^10 + 14882*x^9 + 5973*x^8 - 19404*x^7 - 828*x^6 + 12142*x^5 - 1048*x^4 - 3248*x^3 + 208*x^2 + 288*x + 9. Computing representation of Modular symbols space of level 1257, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 1257, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^2 + 3*x + 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 1257, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). %o x^5 + 2*x^4 - 4*x^3 - 4*x^2 + 3*x + 1 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 1257, weight 2, and dimension 10. Goal dimension = 10. Computing T_2 on dual space of dimension 10. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^10 + 6*x^9 + 4*x^8 - 37*x^7 - 64*x^6 + 51*x^5 + 158*x^4 + 25*x^3 - 93*x^2 - 21*x + 17 p = %o, dimension = %o. 2 10 Computing representation of Modular symbols space of level 1257, weight 2, and dimension 13. Goal dimension = 13. Computing T_2 on dual space of dimension 13. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^13 - x^12 - 16*x^11 + 14*x^10 + 97*x^9 - 73*x^8 - 276*x^7 + 171*x^6 + 369*x^5 - 168*x^4 - 203*x^3 + 50*x^2 + 33*x + 1 p = %o, dimension = %o. 2 13 Computing representation of Modular symbols space of level 1257, weight 2, and dimension 18. Goal dimension = 18. Computing T_2 on dual space of dimension 18. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^18 - 3*x^17 - 27*x^16 + 86*x^15 + 284*x^14 - 1000*x^13 - 1418*x^12 + 6035*x^11 + 2952*x^10 - 20032*x^9 + 1196*x^8 + 35383*x^7 - 15293*x^6 - 28271*x^5 + 21571*x^4 + 4397*x^3 - 8453*x^2 + 2745*x - 281 p = %o, dimension = %o. 2 18 Computing representation of Modular symbols space of level 1257, weight 2, and dimension 19. Goal dimension = 19. Computing T_2 on dual space of dimension 19. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^19 - 6*x^18 - 10*x^17 + 119*x^16 - 48*x^15 - 924*x^14 + 1064*x^13 + 3547*x^12 - 5787*x^11 - 6914*x^10 + 14882*x^9 + 5973*x^8 - 19404*x^7 - 828*x^6 + 12142*x^5 - 1048*x^4 - 3248*x^3 + 208*x^2 + 288*x + 9 p = %o, dimension = %o. 2 19 Computing cuspidal part of Full Modular symbols space of level 838, weight 2, and dimension 107 Computing cuspidal part of Modular symbols space of level 838, weight 2, and dimension 104 Computing new part of Modular symbols space of level 838, weight 2, and dimension 104. Computing 2-new part of Modular symbols space of level 838, weight 2, and dimension 104. Computing index-1 degeneracy map from level 838 to 419. (0.06 s) Computing index-2 degeneracy map from level 838 to 419. (0.07 s) Computing index-1 degeneracy map from level 419 to 838. (0.33 s) Computing index-2 degeneracy map from level 419 to 838. (0.28 s) Computing DualVectorSpace of Modular symbols space of level 838, weight 2, and dimension 104. Computing complement of Modular symbols space of level 838, weight 2, and dimension 104 Computing representation of Modular symbols space of level 838, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 107. (0.019 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 4*x^2 + 5*x - 2 p = %o, dimension = %o. 2 20 Computing T_3 on space of dimension 107. (0.02 s) Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^3 - 12*x^2 + 48*x - 64 p = %o, dimension = %o. 3 3 Computing complement of Modular symbols space of level 838, weight 2, and dimension 3 Computing 419-new part of Modular symbols space of level 838, weight 2, and dimension 104. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 838 to 2. (0.02 s) Computing index-419 degeneracy map from level 838 to 2. (35.54 s) Computing index-1 degeneracy map from level 2 to 838. (4.789 s) Computing index-419 degeneracy map from level 2 to 838. (3.719 s) Decomposing space of level 838 and dimension 34 using T_3. (will stop at 840) Computing T_3 on dual space of dimension 34. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^34 - 2*x^33 - 63*x^32 + 122*x^31 + 1780*x^30 - 3340*x^29 - 29817*x^28 + 54306*x^27 + 329863*x^26 - 584988*x^25 - 2540941*x^24 + 4410778*x^23 + 13996612*x^22 - 23981274*x^21 - 55699814*x^20 + 95436488*x^19 + 159564430*x^18 - 279161978*x^17 - 322572437*x^16 + 596732394*x^15 + 438514162*x^14 - 915904236*x^13 - 353826251*x^12 + 974803958*x^11 + 91528880*x^10 - 673388498*x^9 + 105492120*x^8 + 262568436*x^7 - 102719799*x^6 - 37237464*x^5 + 28601532*x^4 - 3798576*x^3 - 806976*x^2 + 238464*x - 15552 time = 0.02 Factoring characteristic polynomial. [ , , , ] time = 0.03 Cutting out subspace using f(T_3), where f=x^5 + 5*x^4 + 5*x^3 - 4*x^2 - 3*x + 1. Cutting out subspace using f(T_3), where f=x^8 - 3*x^7 - 11*x^6 + 32*x^5 + 31*x^4 - 85*x^3 - 22*x^2 + 64*x - 8. Cutting out subspace using f(T_3), where f=x^9 + 2*x^8 - 13*x^7 - 22*x^6 + 53*x^5 + 67*x^4 - 87*x^3 - 53*x^2 + 57*x - 9. Cutting out subspace using f(T_3), where f=x^12 - 6*x^11 - 9*x^10 + 110*x^9 - 65*x^8 - 665*x^7 + 879*x^6 + 1455*x^5 - 2655*x^4 - 819*x^3 + 2538*x^2 - 432*x - 216. Computing representation of Modular symbols space of level 838, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 2 17 Computing T_3 on dual space of dimension 5. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^5 + 5*x^4 + 5*x^3 - 4*x^2 - 3*x + 1 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 838, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1 p = %o, dimension = %o. 2 17 Computing T_3 on dual space of dimension 8. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^8 - 3*x^7 - 11*x^6 + 32*x^5 + 31*x^4 - 85*x^3 - 22*x^2 + 64*x - 8 p = %o, dimension = %o. 3 8 Computing representation of Modular symbols space of level 838, weight 2, and dimension 9. Goal dimension = 9. Computing T_2 on dual space of dimension 9. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1 p = %o, dimension = %o. 2 17 Computing T_3 on dual space of dimension 9. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). %o x^9 + 2*x^8 - 13*x^7 - 22*x^6 + 53*x^5 + 67*x^4 - 87*x^3 - 53*x^2 + 57*x - 9 p = %o, dimension = %o. 3 9 Computing representation of Modular symbols space of level 838, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1 p = %o, dimension = %o. 2 17 Computing T_3 on dual space of dimension 12. T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^12 - 6*x^11 - 9*x^10 + 110*x^9 - 65*x^8 - 665*x^7 + 879*x^6 + 1455*x^5 - 2655*x^4 - 819*x^3 + 2538*x^2 - 432*x - 216 p = %o, dimension = %o. 3 12 Computing cuspidal part of Full Modular symbols space of level 419, weight 2, and dimension 36 Computing cuspidal part of Modular symbols space of level 419, weight 2, and dimension 35 Computing new part of Modular symbols space of level 419, weight 2, and dimension 35. Computing 419-new part of Modular symbols space of level 419, weight 2, and dimension 35. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 419 and dimension 35 using T_2. (will stop at 840) Computing T_2 on dual space of dimension 35. Computing DualVectorSpace of Modular symbols space of level 419, weight 2, and dimension 35. Computing complement of Modular symbols space of level 419, weight 2, and dimension 35 Computing representation of Modular symbols space of level 419, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 36. (0.009 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 419, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing characteristic polynomial of T_2. x^35 - 54*x^33 + 1319*x^31 + 2*x^30 - 19289*x^29 - 94*x^28 + 188404*x^27 + 1932*x^26 - 1298339*x^25 - 22946*x^24 + 6501130*x^23 + 175206*x^22 - 24003568*x^21 - 905072*x^20 + 65642072*x^19 + 3241320*x^18 - 132428736*x^17 - 8113628*x^16 + 194721349*x^15 + 14131782*x^14 - 204295679*x^13 - 16820976*x^12 + 148014973*x^11 + 13173382*x^10 - 70540279*x^9 - 6290484*x^8 + 20584488*x^7 + 1550008*x^6 - 3315760*x^5 - 118784*x^4 + 258048*x^3 - 5760*x^2 - 7168*x + 512 time = 0.009 Factoring characteristic polynomial. [ , ] time = 0.04 Cutting out subspace using f(T_2), where f=x^9 + 2*x^8 - 7*x^7 - 13*x^6 + 15*x^5 + 25*x^4 - 9*x^3 - 15*x^2 - x + 1. Cutting out subspace using f(T_2), where f=x^26 - 2*x^25 - 43*x^24 + 85*x^23 + 807*x^22 - 1571*x^21 - 8689*x^20 + 16575*x^19 + 59362*x^18 - 110217*x^17 - 268789*x^16 + 481513*x^15 + 817911*x^14 - 1398615*x^13 - 1658267*x^12 + 2674771*x^11 + 2166607*x^10 - 3262315*x^9 - 1701132*x^8 + 2384864*x^7 + 697992*x^6 - 932912*x^5 - 104448*x^4 + 158080*x^3 - 4736*x^2 - 6656*x + 512. Computing representation of Modular symbols space of level 419, weight 2, and dimension 9. Goal dimension = 9. Computing T_2 on dual space of dimension 9. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^9 + 2*x^8 - 7*x^7 - 13*x^6 + 15*x^5 + 25*x^4 - 9*x^3 - 15*x^2 - x + 1 p = %o, dimension = %o. 2 9 Computing index-1 degeneracy map from level 419 to 2514. (1.559 s) Computing index-2 degeneracy map from level 419 to 2514. (1.429 s) Computing index-3 degeneracy map from level 419 to 2514. (1.55 s) Computing index-6 degeneracy map from level 419 to 2514. (1.55 s) Computing representation of Modular symbols space of level 419, weight 2, and dimension 26. Computing complement of Modular symbols space of level 419, weight 2, and dimension 26 Computing DualVectorSpace of Modular symbols space of level 419, weight 2, and dimension 10. Goal dimension = 10. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_2 on space of dimension 10. (0 s) %o x^10 - x^9 - 13*x^8 + 8*x^7 + 54*x^6 - 20*x^5 - 84*x^4 + 12*x^3 + 44*x^2 + 4*x - 3 p = 2, dimension = 10. Computing complement of Modular symbols space of level 419, weight 2, and dimension 10 Sorting ... 8.09 seconds. J0( N: 2514 ) IntersectionGroup( M1: Modular symbols space of level 2514, weight 2, and dimension..., M2: Modular symbols space of level 2514, weight 2, and dimension... ) IntersectionGroup( S: [ Modular symbols space of level 2514, weight 2, and dimensi... ) IntegralRepresentation( M: Modular symbols space of level 2514, weight 2, and dimension... ) SaturateWithRespectToBasis( V: Vector space of degree 424, dimension 0 over Rational Field, B: [ (1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0... ) Saturate( B: [] ) In file "/home/was/modsym/linalg.m", line 166, column 13: >> if Type(B[1]) eq SeqEnum then ^ Runtime error in '[]': Sequence element 1 not defined >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2514, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 3036.929 seconds Magma V2.7-1 Mon Jan 29 2001 08:34:12 on modular [Seed = 308085615] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2515 and weight 2.... I. Manin symbols list. (0.03 s) II. 2-term relations. (0.931 s) III. 3-term relations. Computing quotient by 1008 relations. Form quot and then images (0.699 s) (total time to create space = 1.691 s) Computing cuspidal part of Full Modular symbols space of level 2515, weight 2, and dimension 254 Computing new part of Modular symbols space of level 2515, weight 2, and dimension 251. Computing 5-new part of Modular symbols space of level 2515, weight 2, and dimension 251. Computing space of modular symbols of level 503 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.139 s) III. 3-term relations. Computing quotient by 168 relations. Form quot and then images (0.06 s) (total time to create space = 0.199 s) Computing index-1 degeneracy map from level 2515 to 503. (0.221 s) Computing index-5 degeneracy map from level 2515 to 503. (0.229 s) Computing index-1 degeneracy map from level 503 to 2515. (0.621 s) Computing index-5 degeneracy map from level 503 to 2515. (0.729 s) Computing DualVectorSpace of Modular symbols space of level 2515, weight 2, and dimension 251. Computing complement of Modular symbols space of level 2515, weight 2, and dimension 251 Computing representation of Modular symbols space of level 2515, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 254. (0.26 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2515, weight 2, and dimension 3 Computing 503-new part of Modular symbols space of level 2515, weight 2, and dimension 251. Computing space of modular symbols of level 5 and weight 2.... I. Manin symbols list. (0.001 s) II. 2-term relations. (0.011 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0.011 s) Computing index-1 degeneracy map from level 2515 to 5. (0.049 s) Computing index-503 degeneracy map from level 2515 to 5. (73.12 s) Computing index-1 degeneracy map from level 5 to 2515. (6.201 s) Computing index-503 degeneracy map from level 5 to 2515. (3.92 s) Finding newform decomposition of Modular symbols space of level 2515, weight 2, and dimension 251. Computing cuspidal part of Modular symbols space of level 2515, weight 2, and dimension 251 Decomposing space of level 2515 and dimension 167 using T_2. (will stop at 504) Computing T_2 on dual space of dimension 167. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing characteristic polynomial of T_2. x^167 + 3*x^166 - 245*x^165 - 735*x^164 + 29412*x^163 + 88228*x^162 - 2306190*x^161 - 6916636*x^160 + 132833662*x^159 + 398271998*x^158 - 5993318210*x^157 - 17962254748*x^156 + 220583537689*x^155 + 660746109499*x^154 - 6809703968590*x^153 - 20384479440598*x^152 + 179950260148458*x^151 + 538233967391354*x^150 - 4133772420341009*x^149 - 12352218390705501*x^148 + 83553199471858165*x^147 + 249384053722731831*x^146 - 1500446537273310569*x^145 - 4472550874065780531*x^144 + 24130850871367058241*x^143 + 71821213418936323175*x^142 - 349857567893273803096*x^141 - 1039505312082034637304*x^140 + 4598274125139003398906*x^139 + 13636065214422772189362*x^138 - 55047963085171360354888*x^137 - 162888598339226868699728*x^136 + 602693572912481381338793*x^135 + 1779058527365543851938107*x^134 - 6056017852344248363496851*x^133 - 17828146167549193260255549*x^132 + 56019561536955464450960154*x^131 + 164420825770057397708408502*x^130 - 478313424325895741619276156*x^129 - 1399237853486505056698609562*x^128 + 3778509668120850404081981658*x^127 + 11013253372862574946312542702*x^126 - 27672906432382270454069229730*x^125 - 80335984428966593320051012204*x^124 + 188234378604005350275332756543*x^123 + 544061374101714106638717194689*x^122 - 1191084022669676563828555457478*x^121 - 3426153507743978563459143743654*x^120 + 7020871825943064864282537264613*x^119 + 20090028487674030511046968731095*x^118 - 38599027350100725908191905119110*x^117 - 109821537126041372804535218182656*x^116 + 198135787060728670713957534160828*x^115 + 560245460504930757537126419227196*x^114 - 950505669085548272574746614498988*x^113 - 2669574927108520719131900002052538*x^112 + 4264817023917988412661852403789488*x^111 + 11890813461735246165175568362532884*x^110 - 17910093501058455392135073004124079*x^109 - 49541309836359444380729965766858709*x^108 + 70436514732593790757598727674331444*x^107 + 193171193365049507421031971650894644*x^106 - 259541815079432309515405935641433851*x^105 - 705218116205079165269109011966096493*x^104 + 896379677115989840904551328223938872*x^103 + 2411322762271216361665708062014486472*x^102 - 2902542518560375421236260310228995716*x^101 - 7723994970539335576771701246902152898*x^100 + 8813668766305766118094032066781139971*x^99 + 23181867200071057522807967576057292961*x^98 - 25100387409415945955210855674127670555*x^97 - 65193169135925503690653467832491016235*x^96 + 67045451866676934518592057595668523101*x^95 + 171788421904996888491432691576498616447*x^94 - 167961446259999804807953973307113745976*x^93 - 424110276802555775893441638687053684234*x^92 + 394597843911845018709481883682872105490*x^91 + 980790736854629724730020549115192302614*x^90 - 869212093778729650644989170989585518433*x^89 - 2124079802951198007713969599531842561163*x^88 + 1794782460983471489773063897237926623613*x^87 + 4306367660009537921929229759804014612519*x^86 - 3472720720190379489632154903075802595498*x^85 - 8169779838615145862704033769372975156762*x^84 + 6293968575138182070406311761190237968594*x^83 + 14495908173788977553347744544734701994854*x^82 - 10679917356902039657599697804947086285722*x^81 - 24041193367970592593954023722411597396878*x^80 + 16957363241422032879620303716256388582683*x^79 + 37242903145738761577336193960431355073125*x^78 - 25177926873894113030707105669292047818403*x^77 - 53848008798078034213987736123014215015221*x^76 + 34933435046665921037923622847900307471463*x^75 + 72603019092121873498789457130431769296021*x^74 - 45255728757040257013931628184381247589987*x^73 - 91195934286287533796674592294115511418651*x^72 + 54692643865109860716707089763079401024613*x^71 + 106601433888521364852906613549282034605299*x^70 - 61599619415831529080231772079835030928099*x^69 - 115824316891830351245586075515519121938665*x^68 + 64587322576296626571341507515502244643708*x^67 + 116819683975064800615768705113120047514240*x^66 - 62967348643153021969893078840919510728183*x^65 - 109216093624046757692092649044979655678453*x^64 + 57004544300557933169942784470107937749760*x^63 + 94498794049076792249444404312995518580996*x^62 - 47852008772061824141974343055917855906032*x^61 - 75541299530727978371772643273650750124966*x^60 + 37187432699398176677727694834645116174338*x^59 + 55685191518602621827091345555158541708886*x^58 - 26707776529508584047781181188648351190768*x^57 - 37773978964647184069397206847102623551678*x^56 + 17692483747416112036331837851035673706159*x^55 + 23526555889591658684544447451731103946033*x^54 - 10787687942036431188258963135565992005002*x^53 - 13420116928751308806014470394560811181022*x^52 + 6040043059836991576142414873224881043354*x^51 + 6991980690173325700987412066619979071686*x^50 - 3097419912149048769301817157334258425567*x^49 - 3317300316147755169959222383477733105911*x^48 + 1450653842323816633607934933001205134928*x^47 + 1428467677948362470463285862345271368236*x^46 - 618514007539666047955253607128591185200*x^45 - 556243617655078409983783830164452726508*x^44 + 239232709691887005359948558289496533224*x^43 + 195075327823626598097250516323055215384*x^42 - 83611072457030495169519573697678198107*x^41 - 61336021025397928120851822431419448983*x^40 + 26288470196682373240574562742555626367*x^39 + 17203075259198596467620519212718810281*x^38 - 7399144748920102143263394922588936937*x^37 - 4279617624159760679867804078595763515*x^36 + 1853980324709748074767833087999730517*x^35 + 938268496996959255462500686277837519*x^34 - 410983552020219793730409652403076412*x^33 - 179976502553620263801831430250528392*x^32 + 80033973954135454767373340639994340*x^31 + 29955522164101317177810298459402736*x^30 - 13582402183253599301219973747973650*x^29 - 4285525689397026573065137536068406*x^28 + 1990517344707167884498661333630260*x^27 + 521315615948839351742856094993168*x^26 - 249287195885064184485953420927808*x^25 - 53261947562447912193549113807616*x^24 + 26360058412845723959145615276250*x^23 + 4507690755753033304037323472770*x^22 - 2320836428522684698192422061410*x^21 - 311359321642905807909860886478*x^20 + 167391689203673802680943923193*x^19 + 17303299984727290343968701747*x^18 - 9703713867138624444774245979*x^17 - 766231306181177316701905361*x^16 + 442051226696979749277074221*x^15 + 27121240410075509484223915*x^14 - 15401880481241073856682263*x^13 - 786211498375192504813955*x^12 + 396731554919892512587983*x^11 + 19268846956218275279245*x^10 - 7208531421188692646497*x^9 - 392113007207023572099*x^8 + 85374659284182682559*x^7 + 5931626704658866377*x^6 - 548134983666841604*x^5 - 55252246133490308*x^4 + 675469462163664*x^3 + 221486874306240*x^2 + 8414719898688*x + 101027905344 time = 35.931 Factoring characteristic polynomial. [ , , , , , , ] time = 1.09 Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). Charpoly = x^2 - 6*x + 9. Decomposing space of level 2515 and dimension 2 using T_2. (will stop at 504) Computing characteristic polynomial of T_2. x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). Charpoly = x^2 - 4*x + 4. Decomposing space of level 2515 and dimension 2 using T_3. (will stop at 504) Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^2 - x - 2 time = 0.001 Factoring characteristic polynomial. [ , ] time = 0.001 Cutting out subspace using f(T_3), where f=x - 2. Cutting out subspace using f(T_3), where f=x + 1. Cutting out subspace using f(T_2), where f=x^2 + x - 1. Cutting out subspace using f(T_2), where f=x^3 - 2*x^2 - x + 1. Cutting out subspace using f(T_2), where f=x^27 + 5*x^26 - 24*x^25 - 150*x^24 + 211*x^23 + 1950*x^22 - 572*x^21 - 14426*x^20 - 3600*x^19 + 67055*x^18 + 37847*x^17 - 204013*x^16 - 156362*x^15 + 410461*x^14 + 372220*x^13 - 539025*x^12 - 547055*x^11 + 444668*x^10 + 495702*x^9 - 213568*x^8 - 265226*x^7 + 51383*x^6 + 77020*x^5 - 4084*x^4 - 10793*x^3 - 398*x^2 + 556*x + 57. Cutting out subspace using f(T_2), where f=x^29 - 2*x^28 - 41*x^27 + 76*x^26 + 754*x^25 - 1276*x^24 - 8211*x^23 + 12462*x^22 + 58875*x^21 - 78450*x^20 - 292361*x^19 + 333284*x^18 + 1029537*x^17 - 972121*x^16 - 2587828*x^15 + 1940186*x^14 + 4606715*x^13 - 2584846*x^12 - 5670730*x^11 + 2171013*x^10 + 4604842*x^9 - 1010476*x^8 - 2255200*x^7 + 172013*x^6 + 550567*x^5 + 19662*x^4 - 38345*x^3 - 2170*x^2 + 696*x + 24. Cutting out subspace using f(T_2), where f=x^49 + 9*x^48 - 35*x^47 - 536*x^46 + 71*x^45 + 14562*x^44 + 18623*x^43 - 238252*x^42 - 518348*x^41 + 2603579*x^40 + 7749620*x^39 - 19813194*x^38 - 77863431*x^37 + 104774744*x^36 + 569023678*x^35 - 355523688*x^34 - 3144064867*x^33 + 455138076*x^32 + 13414095505*x^31 + 2688663590*x^30 - 44683680885*x^29 - 20729659138*x^28 + 116711960041*x^27 + 78878791411*x^26 - 238771256263*x^25 - 204230384491*x^24 + 380321151237*x^23 + 386470200673*x^22 - 466541322190*x^21 - 545777950286*x^20 + 433687384180*x^19 + 575834972057*x^18 - 298870133166*x^17 - 449175559871*x^16 + 148523075302*x^15 + 253971635233*x^14 - 51623516233*x^13 - 101060910378*x^12 + 12312312959*x^11 + 27124578801*x^10 - 2104158898*x^9 - 4612362357*x^8 + 303284083*x^7 + 450448537*x^6 - 37294338*x^5 - 21080345*x^4 + 2360954*x^3 + 247323*x^2 - 20804*x - 1367. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 308085615 Time to this point: 277.85 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2515, a, ^ User error: Identifier 'a' has not been declared or assigned Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 308085615 Time to this point: 278.04 Segmentation fault Magma V2.7-1 Mon Jan 29 2001 08:38:50 on modular [Seed = 341508727] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2517 and weight 2.... I. Manin symbols list. (0.04 s) II. 2-term relations. (1.041 s) III. 3-term relations. Computing quotient by 1120 relations. Form quot and then images (0.789 s) (total time to create space = 1.901 s) Computing cuspidal part of Full Modular symbols space of level 2517, weight 2, and dimension 282 Computing new part of Modular symbols space of level 2517, weight 2, and dimension 279. Computing 3-new part of Modular symbols space of level 2517, weight 2, and dimension 279. Computing space of modular symbols of level 839 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.241 s) III. 3-term relations. Computing quotient by 280 relations. Form quot and then images (0.109 s) (total time to create space = 0.361 s) Computing index-1 degeneracy map from level 2517 to 839. (0.529 s) Computing index-3 degeneracy map from level 2517 to 839. (0.48 s) Computing index-1 degeneracy map from level 839 to 2517. (1.021 s) Computing index-3 degeneracy map from level 839 to 2517. (0.859 s) Computing DualVectorSpace of Modular symbols space of level 2517, weight 2, and dimension 279. Computing complement of Modular symbols space of level 2517, weight 2, and dimension 279 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 282. (0.28 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2517, weight 2, and dimension 3 Computing 839-new part of Modular symbols space of level 2517, weight 2, and dimension 279. Computing space of modular symbols of level 3 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 2517 to 3. (0.059 s) Computing index-839 degeneracy map from level 2517 to 3. (196.97 s) Computing index-1 degeneracy map from level 3 to 2517. (16.949 s) Computing index-839 degeneracy map from level 3 to 2517. (10.599 s) Finding newform decomposition of Modular symbols space of level 2517, weight 2, and dimension 279. Computing cuspidal part of Modular symbols space of level 2517, weight 2, and dimension 279 Decomposing space of level 2517 and dimension 139 using T_2. (will stop at 560) Computing T_2 on dual space of dimension 139. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^139 + 3*x^138 - 201*x^137 - 607*x^136 + 19698*x^135 + 59902*x^134 - 1254370*x^133 - 3842706*x^132 + 58366185*x^131 + 180194839*x^130 - 2115695001*x^129 - 6585569591*x^128 + 62203907994*x^127 + 195308196370*x^126 - 1525000214834*x^125 - 4832293265694*x^124 + 31808031854684*x^123 + 101773559637256*x^122 - 573088069768390*x^121 - 1852619313378286*x^120 + 9025538497416462*x^119 + 29496860637740358*x^118 - 125430068190039276*x^117 - 414700545280664904*x^116 + 1550049537924727241*x^115 + 5188293689830413011*x^114 - 17141736834757018991*x^113 - 58132804783577109393*x^112 + 170536976283435114920*x^111 + 586465304786117411132*x^110 - 1533053831937280553588*x^109 - 5351058749503679304820*x^108 + 12499467764352070500425*x^107 + 44327011918022456943227*x^106 - 92723926214694299607731*x^105 - 334455383648618703369325*x^104 + 627507707288307217283945*x^103 + 2304904443846938739785475*x^102 - 3882882020873625095558571*x^101 - 14542595678364843423271905*x^100 + 22010092103293789521406189*x^99 + 84175195213592808939081819*x^98 - 114474549413032298911075435*x^97 - 447741707232225083321041489*x^96 + 546989556964924456871692837*x^95 + 2191820122307669024237846903*x^94 - 2403718923381381234113131725*x^93 - 9886584079858422068903441843*x^92 + 9722343230063213819291822785*x^91 + 41132892680095450598629787867*x^90 - 36215264987410276261454643313*x^89 - 157974661907552631142255506331*x^88 + 124280676640070167842368947010*x^87 + 560424442192719922373847779670*x^86 - 392982919170782361722201971100*x^85 - 1837310636012100089366786626732*x^84 + 1144927726900741418473645134911*x^83 + 5568279167671830483764799904581*x^82 - 3072559664806898371392308797265*x^81 - 15602900177046578941127107807515*x^80 + 7591484724613909277026409568580*x^79 + 40424743378825680798294064301000*x^78 - 17255940177729191596240152517540*x^77 - 96827586972078389409953217879892*x^76 + 36049611249012230944193738211863*x^75 + 214365544919880751267930587134773*x^74 - 69126190108839875096825621042813*x^73 - 438481777734716148184105987907011*x^72 + 121460191571704519540221720730896*x^71 + 828262644285519331564800466951396*x^70 - 195138800931954177179701585528204*x^69 - 1443862879452751968792755847401472*x^68 + 285877401844856064377190316515703*x^67 + 2321067001191439490619096842346541*x^66 - 380533739101344831834721838290541*x^65 - 3437599339836751635132256527310307*x^64 + 458051867583256581661540086126331*x^63 + 4685630278086779845176796874298437*x^62 - 495297964553335248366432203565387*x^61 - 5870833899413201603591010870918937*x^60 + 476433427438481107952503906743799*x^59 + 6752357718209217362170773315879857*x^58 - 401323147683980377837436564788341*x^57 - 7118141383632798588777349876824351*x^56 + 287649164786455664082761747272633*x^55 + 6865729329135771529295610100418167*x^54 - 164438198288022602103909622605643*x^53 - 6047623871191043337382085832713173*x^52 + 60060264596657936037422144849978*x^51 + 4854435330096843504290231733600614*x^50 + 8567561521633279590740668266764*x^49 - 3542638023939130546467098441647744*x^48 - 39861582375566432378836181892645*x^47 + 2344325756460616037369424083062765*x^46 + 43704372448169602557031173291391*x^45 - 1402686605115270086737613156741487*x^44 - 33733893754539819034405192515527*x^43 + 756430899187604845741582469835495*x^42 + 20866933223974102793397424672447*x^41 - 366360303519824597181988844080003*x^40 - 10758936745754530405673768363376*x^39 + 158735507086920938662967084927260*x^38 + 4684049971009093801667437892538*x^37 - 61259147409073706644172643982194*x^36 - 1722988297128741756549146284880*x^35 + 20954854952639510077444712751256*x^34 + 530875334465006940996350016776*x^33 - 6318987618645341349762895777184*x^32 - 134229116695137867946409595267*x^31 + 1669532791326741566531488796195*x^30 + 26632688093177939290844117915*x^29 - 383804020094279958764475107127*x^28 - 3667596363062057528803216306*x^27 + 76163440370281889242058771166*x^26 + 162433054919339736654767270*x^25 - 12928072830831695102079625198*x^24 + 80802740953798621014040416*x^23 + 1857085909052414501975780652*x^22 - 28846326957326343586733898*x^21 - 222913685222151561316734074*x^20 + 5718659984181325698451560*x^19 + 22018563680899559455770156*x^18 - 804363441228357272661602*x^17 - 1756068058149317036814826*x^16 + 84352952292442056660738*x^15 + 110379914058973802638798*x^14 - 6617718054613627322248*x^13 - 5296879315805813176904*x^12 + 381099540124164282592*x^11 + 185824467305595428792*x^10 - 15516618477475197068*x^9 - 4482455445909952108*x^8 + 420928084954426236*x^7 + 67959834535130544*x^6 - 6963508629978260*x^5 - 562868587965912*x^4 + 61824149991069*x^3 + 1821022455483*x^2 - 222317663445*x + 1041699285 time = 17.44 Factoring characteristic polynomial. [ , , , , , , ] time = 0.56 Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). Charpoly = x^2 - 2*x + 1. Decomposing space of level 2517 and dimension 2 using T_2. (will stop at 560) Computing characteristic polynomial of T_2. x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0.01 Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). Charpoly = x^2 - 4*x + 4. Decomposing space of level 2517 and dimension 2 using T_5. (will stop at 560) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 + 2*x time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x. Cutting out subspace using f(T_5), where f=x + 2. Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Charpoly = x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1. Decomposing space of level 2517 and dimension 5 using T_2. (will stop at 560) Computing characteristic polynomial of T_2. x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Charpoly = x^5 + 10*x^4 + 40*x^3 + 80*x^2 + 80*x + 32. Decomposing space of level 2517 and dimension 5 using T_5. (will stop at 560) Computing T_5 on dual space of dimension 5. T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). Computing characteristic polynomial of T_5. x^5 - 18*x^3 - 12*x^2 + 49*x + 12 time = 0 Factoring characteristic polynomial. [ , , ] time = 0 Cutting out subspace using f(T_5), where f=x + 3. Cutting out subspace using f(T_5), where f=x^2 - 4*x - 1. Cutting out subspace using f(T_5), where f=x^2 + x - 4. Cutting out subspace using f(T_2), where f=x^2 + x - 1. Cutting out subspace using f(T_2), where f=x^28 - 42*x^26 + 8*x^25 + 779*x^24 - 298*x^23 - 8371*x^22 + 4832*x^21 + 57373*x^20 - 44689*x^19 - 259428*x^18 + 259208*x^17 + 768579*x^16 - 974571*x^15 - 1405093*x^14 + 2362096*x^13 + 1277517*x^12 - 3519191*x^11 + 148046*x^10 + 2831065*x^9 - 1360465*x^8 - 766305*x^7 + 853576*x^6 - 216574*x^5 - 27096*x^4 + 22710*x^3 - 3883*x^2 + 222*x - 1. Cutting out subspace using f(T_2), where f=x^29 + 14*x^28 + 54*x^27 - 129*x^26 - 1438*x^25 - 1900*x^24 + 11834*x^23 + 37774*x^22 - 27762*x^21 - 261379*x^20 - 168465*x^19 + 906972*x^18 + 1437685*x^17 - 1429191*x^16 - 4642041*x^15 - 359869*x^14 + 7737885*x^13 + 5190831*x^12 - 6136404*x^11 - 8083470*x^10 + 782961*x^9 + 5087972*x^8 + 1638978*x^7 - 1074612*x^6 - 658387*x^5 + 16347*x^4 + 57475*x^3 + 1059*x^2 - 1868*x + 121. Cutting out subspace using f(T_2), where f=x^35 - 11*x^34 + 5*x^33 + 363*x^32 - 1066*x^31 - 4660*x^30 + 23585*x^29 + 23555*x^28 - 263619*x^27 + 73526*x^26 + 1803908*x^25 - 1880766*x^24 - 8029190*x^23 + 13494113*x^22 + 23266949*x^21 - 56924879*x^20 - 40543583*x^19 + 158705551*x^18 + 26288863*x^17 - 301952348*x^16 + 53743382*x^15 + 391605352*x^14 - 163299553*x^13 - 337648345*x^12 + 202570510*x^11 + 183695417*x^10 - 139719692*x^9 - 57432611*x^8 + 54060471*x^7 + 8764740*x^6 - 10892522*x^5 - 517302*x^4 + 999750*x^3 + 19744*x^2 - 28959*x - 2199. Cutting out subspace using f(T_2), where f=x^38 - 4*x^37 - 51*x^36 + 216*x^35 + 1163*x^34 - 5294*x^33 - 15604*x^32 + 77990*x^31 + 136035*x^30 - 770953*x^29 - 798504*x^28 + 5407101*x^27 + 3114188*x^26 - 27745475*x^25 - 7211092*x^24 + 105893055*x^23 + 3781540*x^22 - 302707406*x^21 + 37726924*x^20 + 647960475*x^19 - 153418064*x^18 - 1031937855*x^17 + 318925695*x^16 + 1208040658*x^15 - 416661896*x^14 - 1021569191*x^13 + 351618972*x^12 + 610386174*x^11 - 186250717*x^10 - 250949552*x^9 + 57472968*x^8 + 68480203*x^7 - 8780316*x^6 - 11547804*x^5 + 280695*x^4 + 1036840*x^3 + 63738*x^2 - 34650*x - 3915. Computing representation of Modular symbols space of level 2517, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 2 Computing T_3 on space of dimension 282. (0.12 s) Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 2 Computing T_5 on space of dimension 282. (0.149 s) Computing T_5 on dual space of dimension 1. T_5 sparse... (0.011 s). %o x p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x - 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 3 4 Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0 s). %o x^2 - 4*x - 1 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 3 4 Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0 s). %o x^2 + x - 4 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^2 + x - 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 28. Goal dimension = 28. Computing T_2 on dual space of dimension 28. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^28 - 42*x^26 + 8*x^25 + 779*x^24 - 298*x^23 - 8371*x^22 + 4832*x^21 + 57373*x^20 - 44689*x^19 - 259428*x^18 + 259208*x^17 + 768579*x^16 - 974571*x^15 - 1405093*x^14 + 2362096*x^13 + 1277517*x^12 - 3519191*x^11 + 148046*x^10 + 2831065*x^9 - 1360465*x^8 - 766305*x^7 + 853576*x^6 - 216574*x^5 - 27096*x^4 + 22710*x^3 - 3883*x^2 + 222*x - 1 p = %o, dimension = %o. 2 28 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 29. Goal dimension = 29. Computing T_2 on dual space of dimension 29. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^29 + 14*x^28 + 54*x^27 - 129*x^26 - 1438*x^25 - 1900*x^24 + 11834*x^23 + 37774*x^22 - 27762*x^21 - 261379*x^20 - 168465*x^19 + 906972*x^18 + 1437685*x^17 - 1429191*x^16 - 4642041*x^15 - 359869*x^14 + 7737885*x^13 + 5190831*x^12 - 6136404*x^11 - 8083470*x^10 + 782961*x^9 + 5087972*x^8 + 1638978*x^7 - 1074612*x^6 - 658387*x^5 + 16347*x^4 + 57475*x^3 + 1059*x^2 - 1868*x + 121 p = %o, dimension = %o. 2 29 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 35. Goal dimension = 35. Computing T_2 on dual space of dimension 35. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^35 - 11*x^34 + 5*x^33 + 363*x^32 - 1066*x^31 - 4660*x^30 + 23585*x^29 + 23555*x^28 - 263619*x^27 + 73526*x^26 + 1803908*x^25 - 1880766*x^24 - 8029190*x^23 + 13494113*x^22 + 23266949*x^21 - 56924879*x^20 - 40543583*x^19 + 158705551*x^18 + 26288863*x^17 - 301952348*x^16 + 53743382*x^15 + 391605352*x^14 - 163299553*x^13 - 337648345*x^12 + 202570510*x^11 + 183695417*x^10 - 139719692*x^9 - 57432611*x^8 + 54060471*x^7 + 8764740*x^6 - 10892522*x^5 - 517302*x^4 + 999750*x^3 + 19744*x^2 - 28959*x - 2199 p = %o, dimension = %o. 2 35 Computing representation of Modular symbols space of level 2517, weight 2, and dimension 38. Goal dimension = 38. Computing T_2 on dual space of dimension 38. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^38 - 4*x^37 - 51*x^36 + 216*x^35 + 1163*x^34 - 5294*x^33 - 15604*x^32 + 77990*x^31 + 136035*x^30 - 770953*x^29 - 798504*x^28 + 5407101*x^27 + 3114188*x^26 - 27745475*x^25 - 7211092*x^24 + 105893055*x^23 + 3781540*x^22 - 302707406*x^21 + 37726924*x^20 + 647960475*x^19 - 153418064*x^18 - 1031937855*x^17 + 318925695*x^16 + 1208040658*x^15 - 416661896*x^14 - 1021569191*x^13 + 351618972*x^12 + 610386174*x^11 - 186250717*x^10 - 250949552*x^9 + 57472968*x^8 + 68480203*x^7 - 8780316*x^6 - 11547804*x^5 + 280695*x^4 + 1036840*x^3 + 63738*x^2 - 34650*x - 3915 p = %o, dimension = %o. 2 38 Computing cuspidal part of Full Modular symbols space of level 839, weight 2, and dimension 71 Computing cuspidal part of Modular symbols space of level 839, weight 2, and dimension 70 Computing new part of Modular symbols space of level 839, weight 2, and dimension 70. Computing 839-new part of Modular symbols space of level 839, weight 2, and dimension 70. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 839 and dimension 70 using T_2. (will stop at 560) Computing T_2 on dual space of dimension 70. Computing DualVectorSpace of Modular symbols space of level 839, weight 2, and dimension 70. Computing complement of Modular symbols space of level 839, weight 2, and dimension 70 Computing representation of Modular symbols space of level 839, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 71. (0.009 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 839, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^70 - x^69 - 106*x^68 + 104*x^67 + 5352*x^66 - 5146*x^65 - 171337*x^64 + 161249*x^63 + 3905689*x^62 - 3593083*x^61 - 67494122*x^60 + 60611396*x^59 + 919196563*x^58 - 804584235*x^57 - 10125551117*x^56 + 8625227727*x^55 + 91883879759*x^54 - 76041027293*x^53 - 696013568726*x^52 + 558598833426*x^51 + 4443933666927*x^50 - 3452096127719*x^49 - 24086425221728*x^48 + 18072322990798*x^47 + 111388949454322*x^46 - 80542775412492*x^45 - 441043890610102*x^44 + 306573915725712*x^43 + 1498313361507504*x^42 - 998489215227438*x^41 - 4371138468711268*x^40 + 2784276334374124*x^39 + 10948900959832052*x^38 - 6643562776980299*x^37 - 23517372918081180*x^36 + 13542052723779061*x^35 + 43217159905891955*x^34 - 23515505607692159*x^33 - 67719440966829532*x^32 + 34650093717450829*x^31 + 90074237996485645*x^30 - 43102663546257309*x^29 - 101111758204834321*x^28 + 44974008134339884*x^27 + 95095286508876226*x^26 - 39055514378665865*x^25 - 74259390407899191*x^24 + 27966039268062977*x^23 + 47612359149328537*x^22 - 16334643136870271*x^21 - 24718317725457183*x^20 + 7687247260909652*x^19 + 10210865662556940*x^18 - 2875185480451365*x^17 - 3282487533656255*x^16 + 841879532506666*x^15 + 797877589560208*x^14 - 189672852615534*x^13 - 141109561222056*x^12 + 32122650286358*x^11 + 17196148841980*x^10 - 3932722547136*x^9 - 1324013956618*x^8 + 323539333136*x^7 + 53937842412*x^6 - 15563043152*x^5 - 570732756*x^4 + 317007105*x^3 - 17615859*x^2 + 270295*x - 517 time = 0.069 Factoring characteristic polynomial. [ , ] time = 0.191 Cutting out subspace using f(T_2), where f=x^19 + 3*x^18 - 18*x^17 - 57*x^16 + 128*x^15 + 439*x^14 - 453*x^13 - 1768*x^12 + 800*x^11 + 4001*x^10 - 501*x^9 - 5079*x^8 - 402*x^7 + 3394*x^6 + 732*x^5 - 1010*x^4 - 296*x^3 + 81*x^2 + 20*x - 1. Cutting out subspace using f(T_2), where f=x^51 - 4*x^50 - 76*x^49 + 317*x^48 + 2677*x^47 - 11730*x^46 - 57955*x^45 + 269307*x^44 + 861849*x^43 - 4299870*x^42 - 9312579*x^41 + 50720612*x^40 + 75313108*x^39 - 458365132*x^38 - 461310236*x^37 + 3247866406*x^36 + 2127152342*x^35 - 18317396169*x^34 - 7115078029*x^33 + 83003669812*x^32 + 15083211552*x^31 - 303781564738*x^30 - 5694909418*x^29 + 899539678946*x^28 - 100025847606*x^27 - 2152268484926*x^26 + 463948933246*x^25 + 4142874250778*x^24 - 1241703237282*x^23 - 6367322309998*x^22 + 2341188083802*x^21 + 7726518104722*x^20 - 3265480810158*x^19 - 7286614417801*x^18 + 3404895717474*x^17 + 5224986528748*x^16 - 2635456144101*x^15 - 2762718586157*x^14 + 1485241463834*x^13 + 1029873883829*x^12 - 590485622639*x^11 - 251916603055*x^10 + 157977231666*x^9 + 35175950137*x^8 - 26450736362*x^7 - 1756677960*x^6 + 2434301198*x^5 - 124568658*x^4 - 89043772*x^3 + 12458636*x^2 - 259955*x + 517. Computing representation of Modular symbols space of level 839, weight 2, and dimension 19. Goal dimension = 19. Computing T_2 on dual space of dimension 19. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^19 + 3*x^18 - 18*x^17 - 57*x^16 + 128*x^15 + 439*x^14 - 453*x^13 - 1768*x^12 + 800*x^11 + 4001*x^10 - 501*x^9 - 5079*x^8 - 402*x^7 + 3394*x^6 + 732*x^5 - 1010*x^4 - 296*x^3 + 81*x^2 + 20*x - 1 p = %o, dimension = %o. 2 19 Computing representation of Modular symbols space of level 839, weight 2, and dimension 51. Computing complement of Modular symbols space of level 839, weight 2, and dimension 51 Computing DualVectorSpace of Modular symbols space of level 839, weight 2, and dimension 20. Goal dimension = 20. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 20. (0.01 s) %o x^20 - 27*x^18 - 3*x^17 + 299*x^16 + 55*x^15 - 1770*x^14 - 409*x^13 + 6104*x^12 + 1601*x^11 - 12504*x^10 - 3576*x^9 + 14835*x^8 + 4600*x^7 - 9450*x^6 - 3206*x^5 + 2734*x^4 + 969*x^3 - 223*x^2 - 61*x + 3 p = 2, dimension = 20. Computing complement of Modular symbols space of level 839, weight 2, and dimension 20 Sorting ... 2.841 seconds. Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.011 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0 s). T_19 sparse... (0 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0 s). T_19 sparse... (0 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 28. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 28. T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 28. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 28. T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 28. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 28. T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 28. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 28. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 28. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 28. T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 28. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_3 on dual space of dimension 29. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 29. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 29. T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 29. T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 29. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). Computing T_17 on dual space of dimension 29. T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). Computing T_19 on dual space of dimension 29. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 29. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 29. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 29. T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 29. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.02 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.019 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 35. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 35. T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 35. T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 35. T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 35. T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 35. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 35. T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 35. T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 35. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 35. T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 35. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.019 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_3 on dual space of dimension 38. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 38. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 38. T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 38. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 38. T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 38. T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 38. T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 38. T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 38. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 38. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 38. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.021 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing q-expansion. T_2 sparse... (0.009 s). T_3 sparse... (0.009 s). T_5 sparse... (0 s). T_7 sparse... (0 s). T_11 sparse... (0.01 s). T_13 sparse... (0.01 s). T_17 sparse... (0.01 s). T_19 sparse... (0.01 s). T_23 sparse... (0 s). T_29 sparse... (0 s). T_31 sparse... (0.011 s). T_37 sparse... (0.009 s). (0.129 s) Computing q-expansion. T_2 sparse... (0.009 s). T_3 sparse... (0.009 s). T_5 sparse... (0 s). T_7 sparse... (0.009 s). T_11 sparse... (0.01 s). T_13 sparse... (0.01 s). T_17 sparse... (0.01 s). T_19 sparse... (0.01 s). T_23 sparse... (0.01 s). T_29 sparse... (0.011 s). T_31 sparse... (0.009 s). T_37 sparse... (0.009 s). (0.12 s) Computing q-expansion. (0.009 s) Computing q-expansion. (0.029 s) Computing q-expansion. (0.031 s) Computing q-expansion. (0.029 s) Computing q-expansion. (0.3 s) Computing q-expansion. (0.39 s) Computing q-expansion. (0.549 s) Computing q-expansion. (1.1 s) Computing character group of torus of J_0(3*839)/F_3. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 341508727 Time to this point: 904.15 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2517, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 904.539 seconds Magma V2.7-1 Mon Jan 29 2001 08:53:56 on modular [Seed = 172302295] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2518 and weight 2.... I. Manin symbols list. (0.05 s) II. 2-term relations. (1.16 s) III. 3-term relations. Computing quotient by 1260 relations. Form quot and then images (0.98 s) (total time to create space = 2.221 s) Computing cuspidal part of Full Modular symbols space of level 2518, weight 2, and dimension 317 Computing new part of Modular symbols space of level 2518, weight 2, and dimension 314. Computing 2-new part of Modular symbols space of level 2518, weight 2, and dimension 314. Computing space of modular symbols of level 1259 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.359 s) III. 3-term relations. Computing quotient by 420 relations. Form quot and then images (0.19 s) (total time to create space = 0.559 s) Computing index-1 degeneracy map from level 2518 to 1259. (1.7 s) Computing index-2 degeneracy map from level 2518 to 1259. (1.54 s) Computing index-1 degeneracy map from level 1259 to 2518. (1.01 s) Computing index-2 degeneracy map from level 1259 to 2518. (0.951 s) Computing DualVectorSpace of Modular symbols space of level 2518, weight 2, and dimension 314. Computing complement of Modular symbols space of level 2518, weight 2, and dimension 314 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 317. (0.289 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^3 - 4*x^2 + 5*x - 2 p = %o, dimension = %o. 2 55 Computing T_3 on space of dimension 317. (0.149 s) Computing T_3 on dual space of dimension 3. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^3 - 12*x^2 + 48*x - 64 p = %o, dimension = %o. 3 3 Computing complement of Modular symbols space of level 2518, weight 2, and dimension 3 Computing 1259-new part of Modular symbols space of level 2518, weight 2, and dimension 314. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0.001 s) II. 2-term relations. (0.001 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0.001 s) (total time to create space = 0.001 s) Computing index-1 degeneracy map from level 2518 to 2. (0.061 s) Computing index-1259 degeneracy map from level 2518 to 2. (442.08 s) Computing index-1 degeneracy map from level 2 to 2518. (34.98 s) Computing index-1259 degeneracy map from level 2 to 2518. (21.37 s) Finding newform decomposition of Modular symbols space of level 2518, weight 2, and dimension 314. Computing cuspidal part of Modular symbols space of level 2518, weight 2, and dimension 314 Decomposing space of level 2518 and dimension 104 using T_3. (will stop at 630) Computing T_3 on dual space of dimension 104. T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^104 - 2*x^103 - 203*x^102 + 406*x^101 + 19884*x^100 - 39776*x^99 - 1252023*x^98 + 2505582*x^97 + 56965165*x^96 - 114072562*x^95 - 1995916419*x^94 + 4000295014*x^93 + 56045542129*x^92 - 112454679398*x^91 - 1296050540181*x^90 + 2604124783264*x^89 + 25171038016888*x^88 - 50660538532168*x^87 - 416636303821887*x^86 + 840214552649022*x^85 + 5944287440060755*x^84 - 12015576754024306*x^83 - 73753502583736166*x^82 + 149485848165722382*x^81 + 801437910662389476*x^80 - 1629433064621718888*x^79 - 7670381321549741380*x^78 + 15650481324749735846*x^77 + 64952567950517218133*x^76 - 133066090256112283502*x^75 - 488413108643342556623*x^74 + 1005217230750085815334*x^73 + 3270705719225433879875*x^72 - 6766844910212551375194*x^71 - 19549279434717230856707*x^70 + 40686744065289472271276*x^69 + 104467964991488174136745*x^68 - 218891643702276360304110*x^67 - 499699400654179710137096*x^66 + 1055052825105893926429736*x^65 + 2141012596848562833558645*x^64 - 4559929327837199041097098*x^63 - 8219395801740271538778271*x^62 + 17679793865212579194114032*x^61 + 28269532396149955992060658*x^60 - 61498555174681928901813080*x^59 - 87062055599660431322814406*x^58 + 191866534189618591011033370*x^57 + 239866278070283315701434660*x^56 - 536545919643463169652604768*x^55 - 590415240975068776046402645*x^54 + 1343584237311592327795942460*x^53 + 1296049419890519796054457295*x^52 - 3008841763108258157483215742*x^51 - 2531524125505002080602808204*x^50 + 6015639512939291440009988198*x^49 + 4387625395036218565966508433*x^48 - 10715761605320257976017446638*x^47 - 6724964739526710737898066192*x^46 + 16965400276411865215013326716*x^45 + 9077710729076662762691992503*x^44 - 23804792709583968650761769234*x^43 - 10737843579241388071179925540*x^42 + 29504379191890225378629053776*x^41 + 11062399707375690835311502810*x^40 - 32179340191457076824224668992*x^39 - 9850312630126268756426856342*x^38 + 30749934553639004021189657178*x^37 + 7506756398142594102589319869*x^36 - 25617006446599857316819520234*x^35 - 4832030024131458704894505640*x^34 + 18499897880640530368164577670*x^33 + 2577775434750764341516942936*x^32 - 11507070926280893788056775648*x^31 - 1105511148946313517089812900*x^30 + 6119574428581436792703929738*x^29 + 359285180525082979684525820*x^28 - 2759265081674187839422256968*x^27 - 75104062237540428934014432*x^26 + 1044740786069629443840046968*x^25 + 1698190463265888293353108*x^24 - 328523159198660119757223168*x^23 + 5911524682740720249302621*x^22 + 84702625177994316170509728*x^21 - 2672643840782969216021460*x^20 - 17638127153228477206343332*x^19 + 688027811142781321704596*x^18 + 2913171649537577352224600*x^17 - 117802698319366676332512*x^16 - 373156976340129211469584*x^15 + 13488261297356743149200*x^14 + 36012536859717488001216*x^13 - 963861596640372915648*x^12 - 2517786322870177142016*x^11 + 33563829921102153216*x^10 + 120561337426899058688*x^9 + 324103409598419968*x^8 - 3629329298089820160*x^7 - 70271916749160448*x^6 + 59642109320724480*x^5 + 2001509484134400*x^4 - 419107085352960*x^3 - 15190142746624*x^2 + 1007705653248*x + 33204469760 time = 5.86 Factoring characteristic polynomial. [ , , , , , , , , ] time = 0.389 Cutting out subspace using f(T_3), where f=x - 1. Cutting out subspace using f(T_3), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0 s). Charpoly = x^2 + 12*x + 35. Decomposing space of level 2518 and dimension 2 using T_3. (will stop at 630) Computing characteristic polynomial of T_3. x^2 + 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Charpoly = x^2 - 8*x + 12. Decomposing space of level 2518 and dimension 2 using T_5. (will stop at 630) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing characteristic polynomial of T_5. x^2 - 4*x time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 4. Cutting out subspace using f(T_5), where f=x. Cutting out subspace using f(T_3), where f=x^3 + 3*x^2 - 1. Cutting out subspace using f(T_3), where f=x^6 - 3*x^5 - 5*x^4 + 16*x^3 + 2*x^2 - 7*x - 1. Cutting out subspace using f(T_3), where f=x^8 + x^7 - 11*x^6 - 5*x^5 + 41*x^4 - 4*x^3 - 51*x^2 + 30*x - 4. Cutting out subspace using f(T_3), where f=x^12 + 7*x^11 - 2*x^10 - 109*x^9 - 165*x^8 + 451*x^7 + 1151*x^6 - 250*x^5 - 2319*x^4 - 1213*x^3 + 879*x^2 + 707*x + 49. Cutting out subspace using f(T_3), where f=x^16 + 7*x^15 - 92*x^13 - 115*x^12 + 460*x^11 + 784*x^10 - 1140*x^9 - 2165*x^8 + 1602*x^7 + 2885*x^6 - 1362*x^5 - 1818*x^4 + 626*x^3 + 463*x^2 - 90*x - 44. Cutting out subspace using f(T_3), where f=x^24 - 7*x^23 - 28*x^22 + 289*x^21 + 141*x^20 - 4912*x^19 + 3468*x^18 + 44485*x^17 - 59708*x^16 - 231885*x^15 + 414644*x^14 + 700658*x^13 - 1536792*x^12 - 1179493*x^11 + 3144672*x^10 + 1048503*x^9 - 3398213*x^8 - 572742*x^7 + 1761118*x^6 + 272332*x^5 - 343164*x^4 - 54584*x^3 + 23168*x^2 + 3264*x - 320. Cutting out subspace using f(T_3), where f=x^32 - 13*x^31 + 13*x^30 + 529*x^29 - 2121*x^28 - 7230*x^27 + 55074*x^26 + 9408*x^25 - 689497*x^24 + 842463*x^23 + 4807504*x^22 - 11081876*x^21 - 18158960*x^20 + 71195892*x^19 + 23594717*x^18 - 272685437*x^17 + 91842819*x^16 + 652658629*x^15 - 507758042*x^14 - 970260420*x^13 + 1123371048*x^12 + 842274707*x^11 - 1378146867*x^10 - 343882698*x^9 + 957451921*x^8 - 11148768*x^7 - 343482470*x^6 + 50376780*x^5 + 48215108*x^4 - 8344408*x^3 - 1044448*x^2 + 73920*x + 3008. Computing representation of Modular symbols space of level 2518, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^3 + 3*x^2 - 1 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 6. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^6 - 3*x^5 - 5*x^4 + 16*x^3 + 2*x^2 - 7*x - 1 p = %o, dimension = %o. 3 6 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 8. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^8 + x^7 - 11*x^6 - 5*x^5 + 41*x^4 - 4*x^3 - 51*x^2 + 30*x - 4 p = %o, dimension = %o. 3 8 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 12. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^12 + 7*x^11 - 2*x^10 - 109*x^9 - 165*x^8 + 451*x^7 + 1151*x^6 - 250*x^5 - 2319*x^4 - 1213*x^3 + 879*x^2 + 707*x + 49 p = %o, dimension = %o. 3 12 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 16. Goal dimension = 16. Computing T_2 on dual space of dimension 16. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^16 - 16*x^15 + 120*x^14 - 560*x^13 + 1820*x^12 - 4368*x^11 + 8008*x^10 - 11440*x^9 + 12870*x^8 - 11440*x^7 + 8008*x^6 - 4368*x^5 + 1820*x^4 - 560*x^3 + 120*x^2 - 16*x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 16. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^16 + 7*x^15 - 92*x^13 - 115*x^12 + 460*x^11 + 784*x^10 - 1140*x^9 - 2165*x^8 + 1602*x^7 + 2885*x^6 - 1362*x^5 - 1818*x^4 + 626*x^3 + 463*x^2 - 90*x - 44 p = %o, dimension = %o. 3 16 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 24. Goal dimension = 24. Computing T_2 on dual space of dimension 24. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^24 + 24*x^23 + 276*x^22 + 2024*x^21 + 10626*x^20 + 42504*x^19 + 134596*x^18 + 346104*x^17 + 735471*x^16 + 1307504*x^15 + 1961256*x^14 + 2496144*x^13 + 2704156*x^12 + 2496144*x^11 + 1961256*x^10 + 1307504*x^9 + 735471*x^8 + 346104*x^7 + 134596*x^6 + 42504*x^5 + 10626*x^4 + 2024*x^3 + 276*x^2 + 24*x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 24. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^24 - 7*x^23 - 28*x^22 + 289*x^21 + 141*x^20 - 4912*x^19 + 3468*x^18 + 44485*x^17 - 59708*x^16 - 231885*x^15 + 414644*x^14 + 700658*x^13 - 1536792*x^12 - 1179493*x^11 + 3144672*x^10 + 1048503*x^9 - 3398213*x^8 - 572742*x^7 + 1761118*x^6 + 272332*x^5 - 343164*x^4 - 54584*x^3 + 23168*x^2 + 3264*x - 320 p = %o, dimension = %o. 3 24 Computing representation of Modular symbols space of level 2518, weight 2, and dimension 32. Goal dimension = 32. Computing T_2 on dual space of dimension 32. T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). %o x^32 - 32*x^31 + 496*x^30 - 4960*x^29 + 35960*x^28 - 201376*x^27 + 906192*x^26 - 3365856*x^25 + 10518300*x^24 - 28048800*x^23 + 64512240*x^22 - 129024480*x^21 + 225792840*x^20 - 347373600*x^19 + 471435600*x^18 - 565722720*x^17 + 601080390*x^16 - 565722720*x^15 + 471435600*x^14 - 347373600*x^13 + 225792840*x^12 - 129024480*x^11 + 64512240*x^10 - 28048800*x^9 + 10518300*x^8 - 3365856*x^7 + 906192*x^6 - 201376*x^5 + 35960*x^4 - 4960*x^3 + 496*x^2 - 32*x + 1 p = %o, dimension = %o. 2 52 Computing T_3 on dual space of dimension 32. T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^32 - 13*x^31 + 13*x^30 + 529*x^29 - 2121*x^28 - 7230*x^27 + 55074*x^26 + 9408*x^25 - 689497*x^24 + 842463*x^23 + 4807504*x^22 - 11081876*x^21 - 18158960*x^20 + 71195892*x^19 + 23594717*x^18 - 272685437*x^17 + 91842819*x^16 + 652658629*x^15 - 507758042*x^14 - 970260420*x^13 + 1123371048*x^12 + 842274707*x^11 - 1378146867*x^10 - 343882698*x^9 + 957451921*x^8 - 11148768*x^7 - 343482470*x^6 + 50376780*x^5 + 48215108*x^4 - 8344408*x^3 - 1044448*x^2 + 73920*x + 3008 p = %o, dimension = %o. 3 32 Computing cuspidal part of Full Modular symbols space of level 1259, weight 2, and dimension 106 Computing cuspidal part of Modular symbols space of level 1259, weight 2, and dimension 105 Computing new part of Modular symbols space of level 1259, weight 2, and dimension 105. Computing 1259-new part of Modular symbols space of level 1259, weight 2, and dimension 105. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) Decomposing space of level 1259 and dimension 105 using T_2. (will stop at 630) Computing T_2 on dual space of dimension 105. Computing DualVectorSpace of Modular symbols space of level 1259, weight 2, and dimension 105. Computing complement of Modular symbols space of level 1259, weight 2, and dimension 105 Computing representation of Modular symbols space of level 1259, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 106. (0.019 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 1259, weight 2, and dimension 1 T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^105 - 159*x^103 + 12241*x^101 - 2*x^100 - 607980*x^99 + 300*x^98 + 21900065*x^97 - 21740*x^96 - 609788311*x^95 + 1014006*x^94 + 13660607573*x^93 - 34218358*x^92 - 253039514776*x^91 + 890371524*x^90 + 3952833514273*x^89 - 18591582978*x^88 - 52853332498901*x^87 + 320127093750*x^86 + 611869772060455*x^85 - 4635743175604*x^84 - 6188674785195241*x^83 + 57293063253638*x^82 + 55085332779529217*x^81 - 611223372108302*x^80 - 434031659920569687*x^79 + 5679235711150780*x^78 + 3041783154447401286*x^77 - 46287514042613174*x^76 - 19034823990006637939*x^75 + 332820587460466126*x^74 + 106699081441109593552*x^73 - 2120997367338763604*x^72 - 537126022831889028825*x^71 + 12024820467450503150*x^70 + 2433216624905885236068*x^69 - 60831777597283725148*x^68 - 9934853379283386157661*x^67 + 275251697371982735386*x^66 + 36604033096424932984895*x^65 - 1116033831581186836200*x^64 - 121796340067307180364151*x^63 + 4060379091451953060104*x^62 + 366168710184779066077405*x^61 - 13268016809897456436430*x^60 - 994799772979294713510425*x^59 + 38961288729734617482690*x^58 + 2441919617669848901263235*x^57 - 102831438145082309507064*x^56 - 5413444228974406596353985*x^55 + 243897624340397484306264*x^54 + 10830307407166227836328037*x^53 - 519579010186416488023980*x^52 - 19533619050902427926104250*x^51 + 993301106426504265935150*x^50 + 31718890651345896355174588*x^49 - 1702022199722164666613140*x^48 - 46294356148468099624887174*x^47 + 2609847835746723435001902*x^46 + 60610659793273617404599019*x^45 - 3574158353452660044940586*x^44 - 71016705200894172444448149*x^43 + 4361184959289182110174158*x^42 + 74262760309662987997081889*x^41 - 4727987215814744039857162*x^40 - 69087463478668248686506123*x^39 + 4538842667039619338537912*x^38 + 56970421760509946486899131*x^37 - 3843544326241773455823002*x^36 - 41464952911534699491648678*x^35 + 2858225803650824300744292*x^34 + 26507549138943509908587231*x^33 - 1856985967408207752614944*x^32 - 14799744051645727517841344*x^31 + 1047888151238310988710876*x^30 + 7169226827233030543240922*x^29 - 510159011516610280876218*x^28 - 2989994375002486981717800*x^27 + 212657885449304377374410*x^26 + 1063860947911710048451767*x^25 - 75253748530038745510198*x^24 - 319432498656572653462220*x^23 + 22392384266664820679024*x^22 + 79875719244161746357467*x^21 - 5543941412533127691306*x^20 - 16365363938030339850113*x^19 + 1128887006501470529470*x^18 + 2691781399079961980019*x^17 - 186624027416392858684*x^16 - 346227277294401120508*x^15 + 24658858845004166288*x^14 + 33639913450936786224*x^13 - 2547116639554051968*x^12 - 2355176079791611392*x^11 + 198177264381438208*x^10 + 111069755235003904*x^9 - 10857674510431232*x^8 - 3175163092495360*x^7 + 371675826589696*x^6 + 44603502759936*x^5 - 6521942900736*x^4 - 141177274368*x^3 + 38234750976*x^2 - 849346560*x time = 0.389 Factoring characteristic polynomial. [ , , , , ] time = 0.429 Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x + 2. Cutting out subspace using f(T_2), where f=x^37 + 6*x^36 - 30*x^35 - 239*x^34 + 317*x^33 + 4292*x^32 - 364*x^31 - 45979*x^30 - 25532*x^29 + 327622*x^28 + 315454*x^27 - 1638615*x^26 - 2072587*x^25 + 5913068*x^24 + 8999769*x^23 - 15561186*x^22 - 27638105*x^21 + 29747591*x^20 + 61678129*x^19 - 40366220*x^18 - 100857587*x^17 + 36533968*x^16 + 120308639*x^15 - 17961164*x^14 - 102959903*x^13 - 1289409*x^12 + 61212895*x^11 + 8613577*x^10 - 23863267*x^9 - 5916418*x^8 + 5451398*x^7 + 1895554*x^6 - 547905*x^5 - 263115*x^4 - 1625*x^3 + 6732*x^2 + 354*x - 15. Cutting out subspace using f(T_2), where f=x^65 - 9*x^64 - 68*x^63 + 839*x^62 + 1617*x^61 - 36626*x^60 + 2246*x^59 + 993176*x^58 - 1168774*x^57 - 18695448*x^56 + 37228294*x^55 + 258221387*x^54 - 703943096*x^53 - 2689387757*x^52 + 9501522323*x^51 + 21241169754*x^50 - 97992407148*x^49 - 124207240732*x^48 + 799383798949*x^47 + 484593187570*x^46 - 5262267652405*x^45 - 611100611278*x^44 + 28289559722300*x^43 - 7719735808660*x^42 - 125011984797661*x^41 + 75378626851082*x^40 + 455104276001110*x^39 - 411526376131963*x^38 - 1362176256538655*x^37 + 1640104222517734*x^36 + 3328167294769607*x^35 - 5111932894046554*x^34 - 6537706587383565*x^33 + 12792833453179060*x^32 + 10007177335406085*x^31 - 25975836338538370*x^30 - 11071310807490604*x^29 + 42896004969066288*x^28 + 6662625036882785*x^27 - 57430636162631791*x^26 + 3547805845008483*x^25 + 61841271437144402*x^24 - 15180192474621387*x^23 - 52841745424130629*x^22 + 21767644448445627*x^21 + 35081311102504227*x^20 - 20298756794517941*x^19 - 17485347900079133*x^18 + 13527484720047052*x^17 + 6138837377687281*x^16 - 6551047312708879*x^15 - 1290826807734234*x^14 + 2276147973821528*x^13 + 45163993044688*x^12 - 548101394079984*x^11 + 61549174523744*x^10 + 85824958172736*x^9 - 19147008786816*x^8 - 7680645072640*x^7 + 2669852552704*x^6 + 255879460864*x^5 - 177762504704*x^4 + 9657806848*x^3 + 4061585408*x^2 - 648806400*x + 28311552. Computing representation of Modular symbols space of level 1259, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1259, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1259, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1259, weight 2, and dimension 37. Goal dimension = 37. Computing T_2 on dual space of dimension 37. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^37 + 6*x^36 - 30*x^35 - 239*x^34 + 317*x^33 + 4292*x^32 - 364*x^31 - 45979*x^30 - 25532*x^29 + 327622*x^28 + 315454*x^27 - 1638615*x^26 - 2072587*x^25 + 5913068*x^24 + 8999769*x^23 - 15561186*x^22 - 27638105*x^21 + 29747591*x^20 + 61678129*x^19 - 40366220*x^18 - 100857587*x^17 + 36533968*x^16 + 120308639*x^15 - 17961164*x^14 - 102959903*x^13 - 1289409*x^12 + 61212895*x^11 + 8613577*x^10 - 23863267*x^9 - 5916418*x^8 + 5451398*x^7 + 1895554*x^6 - 547905*x^5 - 263115*x^4 - 1625*x^3 + 6732*x^2 + 354*x - 15 p = %o, dimension = %o. 2 37 Computing representation of Modular symbols space of level 1259, weight 2, and dimension 65. Computing complement of Modular symbols space of level 1259, weight 2, and dimension 65 Computing DualVectorSpace of Modular symbols space of level 1259, weight 2, and dimension 41. Goal dimension = 41. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 41. (0.051 s) %o x^41 + 6*x^40 - 37*x^39 - 287*x^38 + 491*x^37 + 6145*x^36 - 1149*x^35 - 77925*x^34 - 48736*x^33 + 651659*x^32 + 770052*x^31 - 3778777*x^30 - 6246497*x^29 + 15490649*x^28 + 33339568*x^27 - 44517140*x^26 - 126114896*x^25 + 84677279*x^24 + 348511980*x^23 - 82770727*x^22 - 711090036*x^21 - 50971266*x^20 + 1068509068*x^19 + 331446582*x^18 - 1164324184*x^17 - 597413095*x^16 + 889699200*x^15 + 635398858*x^14 - 444617078*x^13 - 433488827*x^12 + 120812805*x^11 + 186490082*x^10 - 3209183*x^9 - 46240381*x^8 - 7539614*x^7 + 5135967*x^6 + 1590419*x^5 - 37389*x^4 - 42870*x^3 - 2019*x^2 + 90*x p = 2, dimension = 41. Computing complement of Modular symbols space of level 1259, weight 2, and dimension 41 Sorting ... 3.41 seconds. Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 172302295 Time to this point: 1139.97 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2518, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 1140.349 seconds Magma V2.7-1 Mon Jan 29 2001 09:13:02 on modular [Seed = 997471579] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2519 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.84 s) III. 3-term relations. Computing quotient by 920 relations. Form quot and then images (0.58 s) (total time to create space = 1.471 s) Computing cuspidal part of Full Modular symbols space of level 2519, weight 2, and dimension 232 Computing new part of Modular symbols space of level 2519, weight 2, and dimension 229. Computing 11-new part of Modular symbols space of level 2519, weight 2, and dimension 229. Computing space of modular symbols of level 229 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.06 s) III. 3-term relations. Computing quotient by 78 relations. Form quot and then images (0.02 s) (total time to create space = 0.089 s) Computing index-1 degeneracy map from level 2519 to 229. (0.1 s) Computing index-11 degeneracy map from level 2519 to 229. (0.31 s) Computing index-1 degeneracy map from level 229 to 2519. (0.67 s) Computing index-11 degeneracy map from level 229 to 2519. (0.77 s) Computing DualVectorSpace of Modular symbols space of level 2519, weight 2, and dimension 229. Computing complement of Modular symbols space of level 2519, weight 2, and dimension 229 Computing representation of Modular symbols space of level 2519, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 232. (0.239 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2519, weight 2, and dimension 3 Computing 229-new part of Modular symbols space of level 2519, weight 2, and dimension 229. Computing space of modular symbols of level 11 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 4 relations. Form quot and then images (0.009 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 2519 to 11. (0.039 s) Computing index-229 degeneracy map from level 2519 to 11. (17.81 s) Computing index-1 degeneracy map from level 11 to 2519. (2.519 s) Computing index-229 degeneracy map from level 11 to 2519. (2.33 s) Finding newform decomposition of Modular symbols space of level 2519, weight 2, and dimension 229. Computing cuspidal part of Modular symbols space of level 2519, weight 2, and dimension 229 Decomposing space of level 2519 and dimension 191 using T_2. (will stop at 460) Computing T_2 on dual space of dimension 191. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). Computing characteristic polynomial of T_2. x^191 - 3*x^190 - 285*x^189 + 863*x^188 + 39876*x^187 - 121920*x^186 - 3651172*x^185 + 11276012*x^184 + 246065036*x^183 - 767902216*x^182 - 13016087386*x^181 + 41063264454*x^180 + 562777493704*x^179 - 1795656410108*x^178 - 20451902891262*x^177 + 66030345038358*x^176 + 637533789250628*x^175 - 2083822360783224*x^174 - 17312414247484040*x^173 + 57319564076444012*x^172 + 414534764692791875*x^171 - 1391077515822480197*x^170 - 8837766469840821715*x^169 + 30078369445907979941*x^168 + 169108839675464414009*x^167 - 584112461969991379927*x^166 - 2923570845987507807773*x^165 + 10256093924346509305107*x^164 + 45920999648342461233194*x^163 - 163743051226704634177438*x^162 - 658452619167013805297004*x^161 + 2388537501563407084166476*x^160 + 8654161984494753809060670*x^159 - 31966290793052532148104442*x^158 - 104626817897865679591472898*x^157 + 393919994494529923432918034*x^156 + 1167096496692112946073886928*x^155 - 4483798278824033594914035564*x^154 - 12044071904901113062975811334*x^153 + 47272277309685293856672019070*x^152 + 115253155316398321589505226813*x^151 - 462751668149483613189695766995*x^150 - 1024772413834779119568735833609*x^149 + 4215096614507018210860380855899*x^148 + 8481381916083754787623123459253*x^147 - 35794553522021473000782284283247*x^146 - 65439368723551539195024516878609*x^145 + 283867795246773266061980199122499*x^144 + 471326759524316390179384978410864*x^143 - 2105542697198700209783992323941172*x^142 - 3172549485955237250906448292508078*x^141 + 14626756441381559566583085396293134*x^140 + 19976130579730615315280356217552728*x^139 - 95277721857320891007769844582378344*x^138 - 117751889905341158416284297300462424*x^137 + 582585784955067820524197958243663940*x^136 + 650188652850053757461798524111051115*x^135 - 3347090477804463242719938704738433193*x^134 - 3364422541819508802021070622596987931*x^133 + 18083424361149990124063356067821960501*x^132 + 16318687927430700296173090530097555426*x^131 - 91943897965119763210607976600375378474*x^130 - 74195770435267931764402077289866323652*x^129 + 440228074387021842449134671842722536552*x^128 + 316160347194558001406318930890116705897*x^127 - 1986057791469931364284852856946876162971*x^126 - 1262017644354211281103666465162994035301*x^125 + 8446519813572561150661628041837284859119*x^124 + 4715191451021615864129116452075138562976*x^123 - 33877852003332970327379830346019089590984*x^122 - 16468709883730666222876952053502919253980*x^121 + 128190610861250082622668087032556780684692*x^120 + 53669412510341377768849038573951771687791*x^119 - 457741630896186489322983660716293818964397*x^118 - 162737845040542752398520416009178283603181*x^117 + 1542775700319160974998220416555189688750163*x^116 + 457217092346543922472591182339225144884041*x^115 - 4908758123770556712056004665658402304682319*x^114 - 1182467923340420432417912035414776709293525*x^113 + 14745861579589504309543297073618069524644883*x^112 + 2784787716454954626433139667313632002419859*x^111 - 41823203508956038969225015699309443415890801*x^110 - 5855897015529363981481439888194622257990289*x^109 + 111997517241984142707533572463792990676466811*x^108 + 10546839285463557843949719782597467776669344*x^107 - 283149428874896643193047755236474372561388216*x^106 - 14476943445813509533908604287418601904691830*x^105 + 675754110906070662937486868539872138380294922*x^104 + 7244046294285235585673541272351708396714437*x^103 - 1522139540025052844229180047971298649112101887*x^102 + 41413482781712551233753134628721685423757427*x^101 + 3235323624319133650057217173781559175839059015*x^100 - 203150227621306981309230724659148212692462417*x^99 - 6487253976936483737216815473433185077986094517*x^98 + 623785071287213484467948852467781387314328499*x^97 + 12267159478339060047790829195384999824082698731*x^96 - 1562971851029485133029774563520494487724122939*x^95 - 21867770049219459892759794442577392472546372427*x^94 + 3425752170737725238292773796028679881127199217*x^93 + 36733042903409303361910639370480987143058410053*x^92 - 6758287314624597496961503165414563107102940956*x^91 - 58115565688337344198533743248851672080767383884*x^90 + 12173389597562028770680666908249720755612007206*x^89 + 86552295505090610844625039833149013608768630038*x^88 - 20182373029006773030556952697700412342599468696*x^87 - 121271346180432507272218037258382502247276731536*x^86 + 30946256975850783023900794290712259629473143320*x^85 + 159752989212989934970913950589148403309561668560*x^84 - 44015510218407595699464483538983614224990960169*x^83 - 197716340465781839258141652378753580139535593241*x^82 + 58177140504151131030688336968887710021557919769*x^81 + 229722415752244622147795503477581121301207583481*x^80 - 71532426224392115546550722073909385131005852966*x^79 - 250361540200944055634515601722527819439627289090*x^78 + 81861090808404720591046396938869505975895715898*x^77 + 255706570870153587453750559412033484539289237342*x^76 - 87200865194284862336078405551287721782032189757*x^75 - 244512881838793401759459493624103777299218024117*x^74 + 86444970528112019972017986401074673202040060541*x^73 + 218670409649534042045649768527309059459808973297*x^72 - 79712739485656351668898653742617725760459608994*x^71 - 182690080979360351626874825010313673395229076026*x^70 + 68325082108878683903039499935785838480565625178*x^69 + 142412519968557761782112354367158707776079019670*x^68 - 54388122889482862171241562258124307869465351479*x^67 - 103448012355284920225482110300604790088272411171*x^66 + 40162789684669491763269156834845681244068573803*x^65 + 69924227617480708046555034633332821312606037507*x^64 - 27477925263607996675675433158678967762984340494*x^63 - 43914778030018352492916010624916135547839999806*x^62 + 17391970446790442625309495048037097757833062790*x^61 + 25584017855484907232009112726305268636328238750*x^60 - 10167196261544820676240496592777511341128580996*x^59 - 13802154959347526933729819085343798451166183040*x^58 + 5479468892045587137769754048572788668478587744*x^57 + 6882287838708133007103493121098951609394832612*x^56 - 2716856302460244344769624105136516135392800891*x^55 - 3165564173379854502903380852146725708108355799*x^54 + 1236497066877591300684737088116426383443339963*x^53 + 1340158895900974596416244588814623530827809351*x^52 - 515247933325201256173451390803908848858389217*x^51 - 520984009845072966002226964766777309646775201*x^50 + 196025858089568794852851387558189174814359815*x^49 + 185499452055583425316897903563164031379329047*x^48 - 67877272886088103517795601612083951711159799*x^47 - 60324886631890431628854838311935395462059867*x^46 + 21317292565731533526851479605104933478969469*x^45 + 17862974814544597358410735424795819173101145*x^44 - 6048341777826779942655318916328569622227071*x^43 - 4800033065175610359265974740782640203024463*x^42 + 1543553527883845706563029662026868302510885*x^41 + 1166095774507442579280165790364629697079109*x^40 - 352544850943502726188896405490360660098406*x^39 - 255031968878300803663814896183808130706974*x^38 + 71651534892048908944828652101224304931878*x^37 + 49975858564180367951063657210484137134106*x^36 - 12872822273825406241840019632267326036869*x^35 - 8727279417860519186167793528701639838093*x^34 + 2028510252296727989044673719928692916857*x^33 + 1349729850524344259133775564932424224365*x^32 - 277776712026328448759330346344673502567*x^31 - 183538991991832361721815840861702938163*x^30 + 32680773627198968272858337574633996913*x^29 + 21759731177457613225718498623410081229*x^28 - 3256448799716240720253842041362644092*x^27 - 2226846686210787903797564824160655828*x^26 + 269687447580650495338375988918326724*x^25 + 194393852800894492734911252653710212*x^24 - 18077094325736087551171749622384469*x^23 - 14270732696438509517307887122341401*x^22 + 940885140282947835710662752151661*x^21 + 865999101245586300383723813934769*x^20 - 35147870119960342634199557263652*x^19 - 42545203879902755459797101532288*x^18 + 751557468371512287065646250400*x^17 + 1650038470194952882690676213076*x^16 + 3407696646141679694217186626*x^15 - 49014359851317547932312882098*x^14 - 870022441981052755078995140*x^13 + 1076477205824491511382404396*x^12 + 30634656312634096439265113*x^11 - 16800144060566524738182399*x^10 - 559441416822755233425505*x^9 + 178236668254094736011155*x^8 + 5656443548216177447875*x^7 - 1213164693067310706137*x^6 - 29059177600792567155*x^5 + 4812699107331704317*x^4 + 57427849812776545*x^3 - 9164620265762539*x^2 - 18035758941807*x + 5549751509769 time = 72.19 Factoring characteristic polynomial. [ , , , ] time = 1.12 Cutting out subspace using f(T_2), where f=x^30 + x^29 - 37*x^28 - 33*x^27 + 607*x^26 + 478*x^25 - 5819*x^24 - 4011*x^23 + 36179*x^22 + 21699*x^21 - 153174*x^20 - 79797*x^19 + 451563*x^18 + 205095*x^17 - 932730*x^16 - 372802*x^15 + 1341984*x^14 + 478042*x^13 - 1322085*x^12 - 424138*x^11 + 865425*x^10 + 249768*x^9 - 358564*x^8 - 90661*x^7 + 86776*x^6 + 17648*x^5 - 10619*x^4 - 1283*x^3 + 481*x^2 - 18*x - 1. Cutting out subspace using f(T_2), where f=x^34 + 3*x^33 - 41*x^32 - 125*x^31 + 752*x^30 + 2337*x^29 - 8154*x^28 - 25926*x^27 + 58190*x^26 + 190149*x^25 - 287963*x^24 - 972292*x^23 + 1014546*x^22 + 3561584*x^21 - 2572956*x^20 - 9455703*x^19 + 4696685*x^18 + 18199577*x^17 - 6106835*x^16 - 25142954*x^15 + 5513213*x^14 + 24411854*x^13 - 3242185*x^12 - 16081421*x^11 + 987217*x^10 + 6803918*x^9 + 87749*x^8 - 1702240*x^7 - 188499*x^6 + 220830*x^5 + 51952*x^4 - 8347*x^3 - 4277*x^2 - 540*x - 23. Cutting out subspace using f(T_2), where f=x^61 - 4*x^60 - 89*x^59 + 368*x^58 + 3723*x^57 - 15989*x^56 - 97268*x^55 + 436411*x^54 + 1778586*x^53 - 8397001*x^52 - 24168197*x^51 + 121158214*x^50 + 252816909*x^49 - 1361556542*x^48 - 2079663784*x^47 + 12218854876*x^46 + 13608520800*x^45 - 89084554766*x^44 - 71042429811*x^43 + 534041226813*x^42 + 293606134456*x^41 - 2654513435684*x^40 - 935239115266*x^39 + 11002209092861*x^38 + 2122074344127*x^37 - 38156087911025*x^36 - 2404110034644*x^35 + 110905673843807*x^34 - 4804697149304*x^33 - 270192953210762*x^32 + 35273398644787*x^31 + 550942047325401*x^30 - 111305073768190*x^29 - 937562989380843*x^28 + 244106667010528*x^27 + 1325733946104903*x^26 - 407851948398288*x^25 - 1548321552270386*x^24 + 535075359549995*x^23 + 1481791592436424*x^22 - 556635042516395*x^21 - 1150344160187510*x^20 + 459127078414136*x^19 + 715068561015117*x^18 - 298294836848840*x^17 - 350023749744083*x^16 + 150801517186377*x^15 + 132009331556963*x^14 - 58244405407105*x^13 - 37252832956797*x^12 + 16744031643950*x^11 + 7550959431374*x^10 - 3452340883549*x^9 - 1034424513359*x^8 + 483622266049*x^7 + 86566714946*x^6 - 42350251166*x^5 - 3577398258*x^4 + 2009363741*x^3 + 25168568*x^2 - 37108047*x + 1343079. Cutting out subspace using f(T_2), where f=x^66 - 3*x^65 - 105*x^64 + 321*x^63 + 5220*x^62 - 16295*x^61 - 163442*x^60 + 522206*x^59 + 3616646*x^58 - 11860191*x^57 - 60158517*x^56 + 203158610*x^55 + 781089326*x^54 - 2727264520*x^53 - 8113731846*x^52 + 29433557699*x^51 + 68560726369*x^50 - 259945066833*x^49 - 476545899763*x^48 + 1902484272254*x^47 + 2743818440655*x^46 - 11643236709358*x^45 - 13132925024827*x^44 + 59963326319829*x^43 + 52262570877241*x^42 - 260968536280882*x^41 - 172275681261901*x^40 + 962184460906554*x^39 + 466097508893707*x^38 - 3008308427386286*x^37 - 1015895202314978*x^36 + 7972901576262385*x^35 + 1714214011266758*x^34 - 17882020473968613*x^33 - 2013356026793480*x^32 + 33840906707499947*x^31 + 933720800136610*x^30 - 53806155230185627*x^29 + 2270733339970446*x^28 + 71465366370707742*x^27 - 7039845124997938*x^26 - 78709660514250991*x^25 + 11229294724313179*x^24 + 71216909852847190*x^23 - 12515495823630032*x^22 - 52322378361840104*x^21 + 10388321599882014*x^20 + 30758824116058305*x^19 - 6512478259752169*x^18 - 14202478332693541*x^17 + 3064461624025041*x^16 + 5029401164929260*x^15 - 1061388602945077*x^14 - 1323887672906338*x^13 + 261931151533485*x^12 + 248307248473685*x^11 - 43862949057693*x^10 - 31237281519508*x^9 + 4631418356049*x^8 + 2396430631432*x^7 - 273916533101*x^6 - 93787759482*x^5 + 7406014516*x^4 + 1176802621*x^3 - 74530339*x^2 - 3071956*x + 179657. Computing representation of Modular symbols space of level 2519, weight 2, and dimension 30. Goal dimension = 30. Computing T_2 on dual space of dimension 30. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^30 + x^29 - 37*x^28 - 33*x^27 + 607*x^26 + 478*x^25 - 5819*x^24 - 4011*x^23 + 36179*x^22 + 21699*x^21 - 153174*x^20 - 79797*x^19 + 451563*x^18 + 205095*x^17 - 932730*x^16 - 372802*x^15 + 1341984*x^14 + 478042*x^13 - 1322085*x^12 - 424138*x^11 + 865425*x^10 + 249768*x^9 - 358564*x^8 - 90661*x^7 + 86776*x^6 + 17648*x^5 - 10619*x^4 - 1283*x^3 + 481*x^2 - 18*x - 1 p = %o, dimension = %o. 2 30 Computing representation of Modular symbols space of level 2519, weight 2, and dimension 34. Goal dimension = 34. Computing T_2 on dual space of dimension 34. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). %o x^34 + 3*x^33 - 41*x^32 - 125*x^31 + 752*x^30 + 2337*x^29 - 8154*x^28 - 25926*x^27 + 58190*x^26 + 190149*x^25 - 287963*x^24 - 972292*x^23 + 1014546*x^22 + 3561584*x^21 - 2572956*x^20 - 9455703*x^19 + 4696685*x^18 + 18199577*x^17 - 6106835*x^16 - 25142954*x^15 + 5513213*x^14 + 24411854*x^13 - 3242185*x^12 - 16081421*x^11 + 987217*x^10 + 6803918*x^9 + 87749*x^8 - 1702240*x^7 - 188499*x^6 + 220830*x^5 + 51952*x^4 - 8347*x^3 - 4277*x^2 - 540*x - 23 p = %o, dimension = %o. 2 34 Computing representation of Modular symbols space of level 2519, weight 2, and dimension 61. Goal dimension = 61. Computing T_2 on dual space of dimension 61. T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). %o x^61 - 4*x^60 - 89*x^59 + 368*x^58 + 3723*x^57 - 15989*x^56 - 97268*x^55 + 436411*x^54 + 1778586*x^53 - 8397001*x^52 - 24168197*x^51 + 121158214*x^50 + 252816909*x^49 - 1361556542*x^48 - 2079663784*x^47 + 12218854876*x^46 + 13608520800*x^45 - 89084554766*x^44 - 71042429811*x^43 + 534041226813*x^42 + 293606134456*x^41 - 2654513435684*x^40 - 935239115266*x^39 + 11002209092861*x^38 + 2122074344127*x^37 - 38156087911025*x^36 - 2404110034644*x^35 + 110905673843807*x^34 - 4804697149304*x^33 - 270192953210762*x^32 + 35273398644787*x^31 + 550942047325401*x^30 - 111305073768190*x^29 - 937562989380843*x^28 + 244106667010528*x^27 + 1325733946104903*x^26 - 407851948398288*x^25 - 1548321552270386*x^24 + 535075359549995*x^23 + 1481791592436424*x^22 - 556635042516395*x^21 - 1150344160187510*x^20 + 459127078414136*x^19 + 715068561015117*x^18 - 298294836848840*x^17 - 350023749744083*x^16 + 150801517186377*x^15 + 132009331556963*x^14 - 58244405407105*x^13 - 37252832956797*x^12 + 16744031643950*x^11 + 7550959431374*x^10 - 3452340883549*x^9 - 1034424513359*x^8 + 483622266049*x^7 + 86566714946*x^6 - 42350251166*x^5 - 3577398258*x^4 + 2009363741*x^3 + 25168568*x^2 - 37108047*x + 1343079 p = %o, dimension = %o. 2 61 Computing representation of Modular symbols space of level 2519, weight 2, and dimension 66. Goal dimension = 66. Computing T_2 on dual space of dimension 66. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^66 - 3*x^65 - 105*x^64 + 321*x^63 + 5220*x^62 - 16295*x^61 - 163442*x^60 + 522206*x^59 + 3616646*x^58 - 11860191*x^57 - 60158517*x^56 + 203158610*x^55 + 781089326*x^54 - 2727264520*x^53 - 8113731846*x^52 + 29433557699*x^51 + 68560726369*x^50 - 259945066833*x^49 - 476545899763*x^48 + 1902484272254*x^47 + 2743818440655*x^46 - 11643236709358*x^45 - 13132925024827*x^44 + 59963326319829*x^43 + 52262570877241*x^42 - 260968536280882*x^41 - 172275681261901*x^40 + 962184460906554*x^39 + 466097508893707*x^38 - 3008308427386286*x^37 - 1015895202314978*x^36 + 7972901576262385*x^35 + 1714214011266758*x^34 - 17882020473968613*x^33 - 2013356026793480*x^32 + 33840906707499947*x^31 + 933720800136610*x^30 - 53806155230185627*x^29 + 2270733339970446*x^28 + 71465366370707742*x^27 - 7039845124997938*x^26 - 78709660514250991*x^25 + 11229294724313179*x^24 + 71216909852847190*x^23 - 12515495823630032*x^22 - 52322378361840104*x^21 + 10388321599882014*x^20 + 30758824116058305*x^19 - 6512478259752169*x^18 - 14202478332693541*x^17 + 3064461624025041*x^16 + 5029401164929260*x^15 - 1061388602945077*x^14 - 1323887672906338*x^13 + 261931151533485*x^12 + 248307248473685*x^11 - 43862949057693*x^10 - 31237281519508*x^9 + 4631418356049*x^8 + 2396430631432*x^7 - 273916533101*x^6 - 93787759482*x^5 + 7406014516*x^4 + 1176802621*x^3 - 74530339*x^2 - 3071956*x + 179657 p = %o, dimension = %o. 2 66 Computing cuspidal part of Full Modular symbols space of level 229, weight 2, and dimension 19 Computing cuspidal part of Modular symbols space of level 229, weight 2, and dimension 18 Computing new part of Modular symbols space of level 229, weight 2, and dimension 18. Computing 229-new part of Modular symbols space of level 229, weight 2, and dimension 18. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 229 and dimension 18 using T_2. (will stop at 460) Computing T_2 on dual space of dimension 18. Computing DualVectorSpace of Modular symbols space of level 229, weight 2, and dimension 18. Computing complement of Modular symbols space of level 229, weight 2, and dimension 18 Computing representation of Modular symbols space of level 229, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 19. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 229, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^18 - 25*x^16 - 2*x^15 + 253*x^14 + 34*x^13 - 1339*x^12 - 210*x^11 + 4009*x^10 + 586*x^9 - 6870*x^8 - 732*x^7 + 6457*x^6 + 280*x^5 - 2941*x^4 + 104*x^3 + 472*x^2 - 44*x - 1 time = 0 Factoring characteristic polynomial. [ , , ] time = 0.019 Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x^6 + 4*x^5 - 12*x^3 - 3*x^2 + 9*x - 1. Cutting out subspace using f(T_2), where f=x^11 - 5*x^10 - 4*x^9 + 50*x^8 - 26*x^7 - 165*x^6 + 152*x^5 + 193*x^4 - 207*x^3 - 50*x^2 + 52*x + 1. Computing representation of Modular symbols space of level 229, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 229, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^6 + 4*x^5 - 12*x^3 - 3*x^2 + 9*x - 1 p = %o, dimension = %o. 2 6 Computing representation of Modular symbols space of level 229, weight 2, and dimension 11. Computing complement of Modular symbols space of level 229, weight 2, and dimension 11 Computing DualVectorSpace of Modular symbols space of level 229, weight 2, and dimension 8. Goal dimension = 8. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 8. (0 s) %o x^8 + 2*x^7 - 11*x^6 - 24*x^5 + 21*x^4 + 51*x^3 - 10*x^2 - 25*x + 3 p = 2, dimension = 8. Computing complement of Modular symbols space of level 229, weight 2, and dimension 8 Computing cuspidal part of Full Modular symbols space of level 11, weight 2, and dimension 2 Computing cuspidal part of Modular symbols space of level 11, weight 2, and dimension 1 Computing new part of Modular symbols space of level 11, weight 2, and dimension 1. Computing 11-new part of Modular symbols space of level 11, weight 2, and dimension 1. Decomposing space of level 11 and dimension 1 using T_2. (will stop at 460) Computing T_2 on dual space of dimension 1. Computing DualVectorSpace of Modular symbols space of level 11, weight 2, and dimension 1. Goal dimension = 1. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 1. Computing T_2 on space of dimension 2. (0 s) (0 s) %o x + 2 p = 2, dimension = 1. T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x + 2 time = 0.009 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 2. Sorting ... 0.019 seconds. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 997471579 Time to this point: 976.47 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2519, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 976.639 seconds Magma V2.7-1 Mon Jan 29 2001 09:29:19 on modular [Seed = 930626214] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2521 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.75 s) III. 3-term relations. Computing quotient by 842 relations. Form quot and then images (0.5 s) (total time to create space = 1.29 s) Computing cuspidal part of Full Modular symbols space of level 2521, weight 2, and dimension 210 Computing new part of Modular symbols space of level 2521, weight 2, and dimension 209. Computing 2521-new part of Modular symbols space of level 2521, weight 2, and dimension 209. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2521, weight 2, and dimension 209. Computing 2521-new part of Modular symbols space of level 2521, weight 2, and dimension 209. Computing cuspidal part of Modular symbols space of level 2521, weight 2, and dimension 209 Decomposing space of level 2521 and dimension 209 using T_2. (will stop at 421) Computing T_2 on dual space of dimension 209. Computing DualVectorSpace of Modular symbols space of level 2521, weight 2, and dimension 209. Computing complement of Modular symbols space of level 2521, weight 2, and dimension 209 Computing representation of Modular symbols space of level 2521, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 210. (0.5 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2521, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^209 + 3*x^208 - 306*x^207 - 920*x^206 + 46063*x^205 + 138799*x^204 - 4547297*x^203 - 13733395*x^202 + 331129520*x^201 + 1002388026*x^200 - 18968532205*x^199 - 57558317861*x^198 + 890239718057*x^197 + 2707951062697*x^196 - 35202035920301*x^195 - 107345588467721*x^194 + 1196974718839568*x^193 + 3659375902188780*x^192 - 35547588950945011*x^191 - 108958412365716401*x^190 + 933358861519225121*x^189 + 2868471942687702571*x^188 - 21881330588602292742*x^187 - 67429433995189083672*x^186 + 461738370039066462585*x^185 + 1426815226374683811725*x^184 - 8829706876783885085485*x^183 - 27361237243102185014001*x^182 + 153887911311992981708434*x^181 + 478225521673356305868116*x^180 - 2456361836863547787612874*x^179 - 7655610201864389895911024*x^178 + 36061381341170392216517807*x^177 + 112721989855380123297815201*x^176 - 488708781398431549500118338*x^175 - 1532194305577000079454502092*x^174 + 6133586866754843031954409811*x^173 + 19288260423852738874927342625*x^172 - 71493910014837816612247430798*x^171 - 225516588231325009553175654812*x^170 + 775902278557370661587631038526*x^169 + 2455058564228758233338664424734*x^168 - 7857811318902495991815103782747*x^167 - 24941035262528330664705914505845*x^166 + 74408421001270693062465961759450*x^165 + 236921023669111005336121953930292*x^164 - 660005333295931261666209224250017*x^163 - 2108170792512043658573281596293913*x^162 + 5492591902068506694143531207015487*x^161 + 17600216740339751037587125290223967*x^160 - 42947849938138717417284157230166392*x^159 - 138059687846991238279273389583226844*x^158 + 315941899400124511486709492105118053*x^157 + 1018864529267571026914801946925227583*x^156 - 2189206118883609841361118944737627406*x^155 - 7082306469750595148345353207812994120*x^154 + 14303479774864152911560697916108508407*x^153 + 46419378489072661262242400835343954127*x^152 - 88204200389553234301961519223126625804*x^151 - 287145645410341009289087730819565873364*x^150 + 513813206999342670964493881938284630690*x^149 + 1677852925832857123447713143039789897484*x^148 - 2829620887820806212692058699471059265224*x^147 - 9268014651295858520243893929608139811626*x^146 + 14742208234502218380105008806755728741076*x^145 + 48428182432589219732315769397371067345998*x^144 - 72707781290975823802559299637344537055352*x^143 - 239526418707280087241545901806255754039748*x^142 + 339646304005105719220377363622135538785688*x^141 + 1121986437318460505182629520683240139485534*x^140 - 1503547064441491881226245762234191184002583*x^139 - 4979753525003937254919341026387586516454021*x^138 + 6310190741905238249112670603381266418410776*x^137 + 20950528113245068813351442847934457995730982*x^136 - 25117173544262494573979462389744274888309390*x^135 - 83580514277381302719336457218906583524467438*x^134 + 94852122209022340913425448737427878391539834*x^133 + 316279186630558971459532263659091996828575638*x^132 - 339934659221045462930511077814204971199523192*x^131 - 1135538653365121071177350149978958587515083164*x^130 + 1156431815014103258717970626934582396049940669*x^129 + 3868902729862772240912770973846883030000300305*x^128 - 3735130570524538629451307657979967723763493766*x^127 - 12511131099028562060826358732261025692166009256*x^126 + 11455641055456381067681609543638514324012992351*x^125 + 38404017337351923500851080586148144478716725271*x^124 - 33366442727566274024864925529635484580028627084*x^123 - 111906994507421855083782244783721267196737468362*x^122 + 92301615370533082649951211586624178227192286313*x^121 + 309562738495228198218305334685320586820443067763*x^120 - 242511837885671582382137286953723276717683485630*x^119 - 812910926727366567537043585371580131580846641384*x^118 + 605173532357207308418990279393008949541780781012*x^117 + 2026347370035788492036250447067738723533409298326*x^116 - 1434277918555662515764604987420876333498631253375*x^115 - 4794213405987776934927256786888141035075948751693*x^114 + 3228198759830031956974667617018886557451791650252*x^113 + 10764438735236342245412244577381359175105101165318*x^112 - 6899411898781042935784982316662443119889606490842*x^111 - 22932753462706612717640454459746884762804375854158*x^110 + 13999871406013771724510927628057884251104707299234*x^109 + 46346201846141196750449459902860048327522405508446*x^108 - 26965924241602706691512345537163471240746842158440*x^107 - 88827937687150155482880915681508447442589741401960*x^106 + 49293363398485439289382710506389263015404356227692*x^105 + 161409328278267994562065952150472647128896948199784*x^104 - 85492701045784152140776519337866147113743535394570*x^103 - 277970645457929627448351931061311764640762643104284*x^102 + 140638743218013237488202985477763208843111723742947*x^101 + 453512496169665309847362235985308077545652142563741*x^100 - 219364184386645298719185150459621871931835005964592*x^99 - 700662767229733345644926927038139813633585850767642*x^98 + 324295787595675774071308544327381113103153036601675*x^97 + 1024584705256984111876046135228860383692832470125581*x^96 - 454193798988987506481637232918287389538646454402497*x^95 - 1417342656995223159795067312082295180646231637902719*x^94 + 602355611398570220096954496513868048195825356815980*x^93 + 1853693554113053368682451700902475092393633194948018*x^92 - 756032908830193042581056005465250212377296338404603*x^91 - 2290672798154606333742081290173732828451810041884547*x^90 + 897518353117989350309498601586339161453817283945442*x^89 + 2672718811045585721270502632679287794364717486950308*x^88 - 1007100098092825118767686923582145383297394271697072*x^87 - 2942305297195943334883049188901080902611281687647934*x^86 + 1067360257276673112056814083567196361990219687718097*x^85 + 3053659371469184548558934028737268929485725424896317*x^84 - 1067601547782213864021782536539930443474204989792263*x^83 - 2985243277275089694275017958791942728978768544771393*x^82 + 1006893305240111649638248558815626385898543312044853*x^81 + 2746410261075696429605272412742171962355231019333321*x^80 - 894567007460863012481365255604692083609483318622864*x^79 - 2375465797266908995070918278107695834825779170635872*x^78 + 747887337924861989967292709629501306266800099966405*x^77 + 1929612898223529585054504093663835523781423443407145*x^76 - 587690044822943548533346495905198768162539628197696*x^75 - 1470406485664318497494872289455601461445637911152640*x^74 + 433507757939967813847663639011058418046868329475084*x^73 + 1049841165647470016678674585163018127345984591439812*x^72 - 299762884278480471763692840025986300717797174453829*x^71 - 701398991112402221606311192210885188502274109866289*x^70 + 194013251334957482302192262103790337825855200401299*x^69 + 437884118136563194178193924284496829931461250292359*x^68 - 117337439784540030586828475964913731100766096533568*x^67 - 255070977993027160882650765254049915730402807360562*x^66 + 66192064523284330771177142013083807862185902525721*x^65 + 138414346858545000006762878834416951737233089552431*x^64 - 34759891368665646010077334865128376052738346378273*x^63 - 69852439933133017013502227555815745832738662784815*x^62 + 16955548371450401129594853153349011160747868364169*x^61 + 32724475533567853971172068603850154519600133209725*x^60 - 7664310691136989538902118671008176556538970114653*x^59 - 14203925678062230449460025722856085473876540306111*x^58 + 3202036058244801327585670230594627540897675215577*x^57 + 5700084851670154493723154177212039386292220072163*x^56 - 1232869441868967691954675679466936360761219458804*x^55 - 2110167632214626021193963133667605499430844700914*x^54 + 436067285226620654859568650009111107198350208860*x^53 + 718896783405417402451620688725537824672850061154*x^52 - 141181656351926910075996813391166011816284867673*x^51 - 224801118680618274794912531617149156472460505263*x^50 + 41670803113597504336163769665401668296951872559*x^49 + 64340970576128915100837689582750272353758716645*x^48 - 11160889684212516735787272259046079671868181250*x^47 - 16803579720588311378956072204613395838255655132*x^46 + 2697909349138270772532142199064738444903189516*x^45 + 3991026791778292328538212075558734352056563708*x^44 - 584794548582967877679465060781751520529087129*x^43 - 858881028761671310999504689106917217961591039*x^42 + 112756085632665842628807800760064961961920426*x^41 + 166789173964928690731794349950185448192083338*x^40 - 19138215922035443181456032775919024674649164*x^39 - 29093467378494755014624424797117021802445966*x^38 + 2818125253265302506690178382033232979123774*x^37 + 4534777595817619881437372207026269105491604*x^36 - 351994085898517066017420622274819046005786*x^35 - 627847146422281611299279778582936149296268*x^34 + 35802242986910772112140593767374443471691*x^33 + 76676728797075685587393550940233241608823*x^32 - 2691768391182689218927507976236870035624*x^31 - 8192134442564988086344248473512816573768*x^30 + 97518111421647209663966343109325538609*x^29 + 758079697707718429478121356532845033529*x^28 + 9531407530201847427155728895881402458*x^27 - 60012458621191184667769225044876972646*x^26 - 2305494885371388695730225273904967686*x^25 + 4000475574903317183514926928051330900*x^24 + 263843986384129271097201753196507739*x^23 - 219878916726609929185711592982635669*x^22 - 21114994903714251121576162169366456*x^21 + 9671692219118693411471360686873116*x^20 + 1264434832574765282481660808806115*x^19 - 324900082651423300380757222594891*x^18 - 57050694457379620629100334348645*x^17 + 7630221859851314955212403809213*x^16 + 1899153448068468042763732724830*x^15 - 97225115839397700917574996224*x^14 - 44512433693666680466754725215*x^13 - 386259383738777717644924037*x^12 + 672530745575158092205335230*x^11 + 38770226720944679673267082*x^10 - 5378360238435861748987811*x^9 - 615024804149686849176731*x^8 + 7932777520437355870530*x^7 + 3791235566956862872542*x^6 + 139877418801720941621*x^5 - 5693912535127773109*x^4 - 550456829821727447*x^3 - 14676241007265105*x^2 - 143112581251641*x - 284949049905 time = 5.65 Factoring characteristic polynomial. [ , ] time = 1.879 Cutting out subspace using f(T_2), where f=x^97 + 9*x^96 - 97*x^95 - 1096*x^94 + 4009*x^93 + 64047*x^92 - 77990*x^91 - 2390878*x^90 - 156586*x^89 + 64025710*x^88 + 57617595*x^87 - 1309207829*x^86 - 1997930680*x^85 + 21240763897*x^84 + 43602947657*x^83 - 280387978846*x^82 - 712904156915*x^81 + 3062487432611*x^80 + 9315692133656*x^79 - 27975129812294*x^78 - 100635519630730*x^77 + 214885930484056*x^76 + 917724072511218*x^75 - 1387357971603741*x^74 - 7165654136773321*x^73 + 7460378576626252*x^72 + 48395235151570749*x^71 - 32542594359944317*x^70 - 284859563337470349*x^69 + 106773870474584621*x^68 + 1469646128446500054*x^67 - 188945854035642557*x^66 - 6674496293274636627*x^65 - 531605497281359204*x^64 + 26769853736433562525*x^63 + 6936730195171895694*x^62 - 95040320346914432994*x^61 - 39598048883051596897*x^60 + 299150601233709910240*x^59 + 166721615534023544049*x^58 - 835584291965199542436*x^57 - 572487126204449545669*x^56 + 2071789945469926605906*x^55 + 1664359255101505973769*x^54 - 4558756171531449017371*x^53 - 4169935348599180338536*x^52 + 8894914847871446614028*x^51 + 9088028574924648164722*x^50 - 15368749338153648411071*x^49 - 17316264715043807519751*x^48 + 23468657469549019023672*x^47 + 28917326291596588809035*x^46 - 31591111468588302999401*x^45 - 42355879809568332265484*x^44 + 37361699821188004481979*x^43 + 54387734720906156070755*x^42 - 38659365770523791264696*x^41 - 61129197955985812096983*x^40 + 34814109641758278115801*x^39 + 59990820127380667708112*x^38 - 27101571958293396163376*x^37 - 51233597595238984512656*x^36 + 18076174973282901264762*x^35 + 37915576217338989955189*x^34 - 10203134697519974613434*x^33 - 24189194619677755549784*x^32 + 4784407581203278591820*x^31 + 13220881430098944605999*x^30 - 1805772319616503759808*x^29 - 6144817590537378069095*x^28 + 513218438636089482266*x^27 + 2407268266060489801810*x^26 - 88711529583166869263*x^25 - 786508043533860916122*x^24 - 3968938215664235272*x^23 + 211571477409860966391*x^22 + 9256668213655587588*x^21 - 46115412214368984622*x^20 - 3730230579740015404*x^19 + 7978488933043943005*x^18 + 943825041539737829*x^17 - 1065208074313932695*x^16 - 168812926867851572*x^15 + 105192012104225706*x^14 + 21671424690105977*x^13 - 7132618546681690*x^12 - 1947430894734950*x^11 + 278220088640213*x^10 + 114885624295922*x^9 - 1894141028022*x^8 - 3850618756973*x^7 - 306265826835*x^6 + 44391459241*x^5 + 9073955225*x^4 + 596543769*x^3 + 16593508*x^2 + 172968*x + 351. Cutting out subspace using f(T_2), where f=x^112 - 6*x^111 - 155*x^110 + 989*x^109 + 11542*x^108 - 79019*x^107 - 548941*x^106 + 4077585*x^105 + 18687661*x^104 - 152777023*x^103 - 483163602*x^102 + 4430029813*x^101 + 9805645775*x^100 - 103477186998*x^99 - 158671353797*x^98 + 2001050587497*x^97 + 2043391159859*x^96 - 32676616892433*x^95 - 20274756013760*x^94 + 457339448395572*x^93 + 136060721066559*x^92 - 5549532251082344*x^91 - 170403023837474*x^90 + 58915972436560279*x^89 - 11451145353998214*x^88 - 551224575224384458*x^87 + 213742015220350002*x^86 + 4571945128465955752*x^85 - 2545328386483028601*x^84 - 33777931877885061651*x^83 + 23869729363151156468*x^82 + 223163206983203886283*x^81 - 187838842764315591177*x^80 - 1322661817403688667570*x^79 + 1276537577161056202621*x^78 + 7050519253572202271943*x^77 - 7611614595087350576511*x^76 - 33870011325226898784342*x^75 + 40214693670901839460116*x^74 + 146859070477328208265214*x^73 - 189497142694676715094585*x^72 - 575386125573389483040126*x^71 + 800033350524915688925667*x^70 + 2038445549608025323522563*x^69 - 3036004693951936707138157*x^68 - 6532232502742618588323714*x^67 + 10379494913906058432648780*x^66 + 18933237767641687624972215*x^65 - 32019073740434556216484863*x^64 - 49613533544663321355369684*x^63 + 89213594824609898140915317*x^62 + 117441810385135485686964400*x^61 - 224629281331781827401499813*x^60 - 250804000443877500766261374*x^59 + 511160231677996153086356137*x^58 + 482341817703603772183858689*x^57 - 1050948781684302371106202561*x^56 - 833365881037509777402651151*x^55 + 1951033684061152802325657268*x^54 + 1289399854491154378131414787*x^53 - 3267256895491832921505860334*x^52 - 1778939526395863450958444398*x^51 + 4929084578272258493170924306*x^50 + 2175915249705192385249541679*x^49 - 6687945488919607651938171218*x^48 - 2340317135764605333480465579*x^47 + 8144889468357686844419219911*x^46 + 2186290113240137980396058421*x^45 - 8881779635133678259018064992*x^44 - 1738078372755231960537626111*x^43 + 8647960019603043292754315994*x^42 + 1130380887794403916331536309*x^41 - 7493856269566121808227294410*x^40 - 544418253431181122170603175*x^39 + 5757505119918920215608118878*x^38 + 119851548646567773018344855*x^37 - 3904918901706781409679907769*x^36 + 98968186584505284080618359*x^35 + 2326308209944545200406071353*x^34 - 154187799997275500199772901*x^33 - 1210328705690657922473253568*x^32 + 123854220755512231110982405*x^31 + 546317147100741100727897177*x^30 - 73063567260606774329336908*x^29 - 212310465481396897638251611*x^28 + 34106051855575206993809992*x^27 + 70410045527239945990924532*x^26 - 12890558235622017884119867*x^25 - 19722045687693333433997150*x^24 + 3963513717838803642711184*x^23 + 4609656163624323495878291*x^22 - 986978797555034738961217*x^21 - 886281292487519389990714*x^20 + 196903333910470094472029*x^19 + 137794702108679392122538*x^18 - 30956732916274351595599*x^17 - 16968207208976500590714*x^16 + 3749354488404607477498*x^15 + 1613001899391637269952*x^14 - 339309250832133695632*x^13 - 114592356891372696477*x^12 + 22013388109584447691*x^11 + 5835738880458915091*x^10 - 966632833267011100*x^9 - 201820742188748386*x^8 + 26465325622714370*x^7 + 4419598460927941*x^6 - 401308209934022*x^5 - 55774350670325*x^4 + 2884609782252*x^3 + 347789085053*x^2 - 7674034751*x - 811820655. Computing representation of Modular symbols space of level 2521, weight 2, and dimension 97. Goal dimension = 97. Computing T_2 on dual space of dimension 97. T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^97 + 9*x^96 - 97*x^95 - 1096*x^94 + 4009*x^93 + 64047*x^92 - 77990*x^91 - 2390878*x^90 - 156586*x^89 + 64025710*x^88 + 57617595*x^87 - 1309207829*x^86 - 1997930680*x^85 + 21240763897*x^84 + 43602947657*x^83 - 280387978846*x^82 - 712904156915*x^81 + 3062487432611*x^80 + 9315692133656*x^79 - 27975129812294*x^78 - 100635519630730*x^77 + 214885930484056*x^76 + 917724072511218*x^75 - 1387357971603741*x^74 - 7165654136773321*x^73 + 7460378576626252*x^72 + 48395235151570749*x^71 - 32542594359944317*x^70 - 284859563337470349*x^69 + 106773870474584621*x^68 + 1469646128446500054*x^67 - 188945854035642557*x^66 - 6674496293274636627*x^65 - 531605497281359204*x^64 + 26769853736433562525*x^63 + 6936730195171895694*x^62 - 95040320346914432994*x^61 - 39598048883051596897*x^60 + 299150601233709910240*x^59 + 166721615534023544049*x^58 - 835584291965199542436*x^57 - 572487126204449545669*x^56 + 2071789945469926605906*x^55 + 1664359255101505973769*x^54 - 4558756171531449017371*x^53 - 4169935348599180338536*x^52 + 8894914847871446614028*x^51 + 9088028574924648164722*x^50 - 15368749338153648411071*x^49 - 17316264715043807519751*x^48 + 23468657469549019023672*x^47 + 28917326291596588809035*x^46 - 31591111468588302999401*x^45 - 42355879809568332265484*x^44 + 37361699821188004481979*x^43 + 54387734720906156070755*x^42 - 38659365770523791264696*x^41 - 61129197955985812096983*x^40 + 34814109641758278115801*x^39 + 59990820127380667708112*x^38 - 27101571958293396163376*x^37 - 51233597595238984512656*x^36 + 18076174973282901264762*x^35 + 37915576217338989955189*x^34 - 10203134697519974613434*x^33 - 24189194619677755549784*x^32 + 4784407581203278591820*x^31 + 13220881430098944605999*x^30 - 1805772319616503759808*x^29 - 6144817590537378069095*x^28 + 513218438636089482266*x^27 + 2407268266060489801810*x^26 - 88711529583166869263*x^25 - 786508043533860916122*x^24 - 3968938215664235272*x^23 + 211571477409860966391*x^22 + 9256668213655587588*x^21 - 46115412214368984622*x^20 - 3730230579740015404*x^19 + 7978488933043943005*x^18 + 943825041539737829*x^17 - 1065208074313932695*x^16 - 168812926867851572*x^15 + 105192012104225706*x^14 + 21671424690105977*x^13 - 7132618546681690*x^12 - 1947430894734950*x^11 + 278220088640213*x^10 + 114885624295922*x^9 - 1894141028022*x^8 - 3850618756973*x^7 - 306265826835*x^6 + 44391459241*x^5 + 9073955225*x^4 + 596543769*x^3 + 16593508*x^2 + 172968*x + 351 p = %o, dimension = %o. 2 97 Computing representation of Modular symbols space of level 2521, weight 2, and dimension 112. Computing complement of Modular symbols space of level 2521, weight 2, and dimension 112 Computing DualVectorSpace of Modular symbols space of level 2521, weight 2, and dimension 98. Goal dimension = 98. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 98. (0.61 s) %o x^98 + 6*x^97 - 124*x^96 - 805*x^95 + 7297*x^94 + 52020*x^93 - 270131*x^92 - 2156908*x^91 + 7016048*x^90 + 64495468*x^89 - 134459535*x^88 - 1482060614*x^87 + 1929692807*x^86 + 27234555937*x^85 - 20119344034*x^84 - 411196821817*x^83 + 128259779623*x^82 + 5201199903356*x^81 + 128229835823*x^80 - 55922206213262*x^79 - 16710130193848*x^78 + 516792489376246*x^77 + 273066281059050*x^76 - 4140530189137395*x^75 - 3003580221962098*x^74 + 28957340986946215*x^73 + 26014099421691993*x^72 - 177728299814656564*x^71 - 187231780257637398*x^70 + 961352560486995668*x^69 + 1149324517022746191*x^68 - 4597884239375142719*x^67 - 6107658731167708956*x^66 + 19491883382542550677*x^65 + 28364670228277640137*x^64 - 73372831014128791881*x^63 - 115850510932430120076*x^62 + 245522912157691702085*x^61 + 417944747882864700931*x^60 - 730730188167106186671*x^59 - 1335749138567270174583*x^58 + 1934265749691149081639*x^57 + 3789251324083275242913*x^56 - 4551010581308273843949*x^55 - 9551833936835966938678*x^54 + 9506333165995166713577*x^53 + 21404720893668987629636*x^52 - 17596715968689691677362*x^51 - 42632835062927592905237*x^50 + 28789983299417137713462*x^49 + 75417451614680441582925*x^48 - 41488646117050468261981*x^47 - 118343090343378069426506*x^46 + 52417454596196576732719*x^45 + 164429339249893001278431*x^44 - 57697364742657857375182*x^43 - 201822569933242259476961*x^42 + 54848899355585561697105*x^41 + 218201703509715714406750*x^40 - 44451508797894166639291*x^39 - 207074032340435399287712*x^38 + 30071118279641203977472*x^37 + 171776967758999854802730*x^36 - 16312948702509713839097*x^35 - 123949863349536944479001*x^34 + 6420209472882168290518*x^33 + 77351991440236545241172*x^32 - 1132341313510891169461*x^31 - 41468416609913337577805*x^30 - 727500631687866789671*x^29 + 18947671210248223689551*x^28 + 867612950152221355012*x^27 - 7310516327764636274693*x^26 - 520373454784360308333*x^25 + 2355555192385918513094*x^24 + 223478292056853672207*x^23 - 625457764015927311585*x^22 - 73885416855335747386*x^21 + 134616006063366938462*x^20 + 19169180672263989217*x^19 - 22991641757592091186*x^18 - 3896683198933146182*x^17 + 3026811296073946513*x^16 + 611630792707780422*x^15 - 293904611622571141*x^14 - 72146892616999621*x^13 + 19450424745310120*x^12 + 6120512772845063*x^11 - 719774641624717*x^10 - 346551013915788*x^9 + 1831804327093*x^8 + 11245590444084*x^7 + 963188939746*x^6 - 124100422498*x^5 - 26625321906*x^4 - 1773037799*x^3 - 49607556*x^2 - 518553*x - 1053 p = 2, dimension = 98. Computing complement of Modular symbols space of level 2521, weight 2, and dimension 98 Sorting ... 0.009 seconds. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 930626214 Time to this point: 715.4 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2521, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 715.519 seconds Magma V2.7-1 Mon Jan 29 2001 09:41:34 on modular [Seed = 661137303] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2522 and weight 2.... I. Manin symbols list. (0.07 s) II. 2-term relations. (1.3 s) III. 3-term relations. Computing quotient by 1372 relations. Form quot and then images (1.091 s) (total time to create space = 2.501 s) Computing cuspidal part of Full Modular symbols space of level 2522, weight 2, and dimension 346 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 661137303 Time to this point: 4.23 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2522, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 4.250 seconds Magma V2.7-1 Mon Jan 29 2001 09:41:42 on modular [Seed = 627713421] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2526 and weight 2.... I. Manin symbols list. (0.08 s) II. 2-term relations. (1.6 s) III. 3-term relations. Computing quotient by 1688 relations. Form quot and then images (1.53 s) (total time to create space = 3.251 s) Computing cuspidal part of Full Modular symbols space of level 2526, weight 2, and dimension 426 Computing new part of Modular symbols space of level 2526, weight 2, and dimension 419. Computing 2-new part of Modular symbols space of level 2526, weight 2, and dimension 419. Computing space of modular symbols of level 1263 and weight 2.... I. Manin symbols list. (0.021 s) II. 2-term relations. (0.509 s) III. 3-term relations. Computing quotient by 564 relations. Form quot and then images (0.28 s) (total time to create space = 0.821 s) Computing index-1 degeneracy map from level 2526 to 1263. (4.569 s) Computing index-2 degeneracy map from level 2526 to 1263. (4.52 s) Computing index-1 degeneracy map from level 1263 to 2526. (1.431 s) Computing index-2 degeneracy map from level 1263 to 2526. (1.431 s) Computing DualVectorSpace of Modular symbols space of level 2526, weight 2, and dimension 419. Computing complement of Modular symbols space of level 2526, weight 2, and dimension 419 Computing representation of Modular symbols space of level 2526, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 426. (0.311 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.021 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 System error: Out of memory. All virtual memory has been exhausted so Magma cannot perform this statement. >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2526, a, ^ Runtime error: Variable 'a' has not been initialized Total time: 237.810 seconds Magma V2.7-1 Mon Jan 29 2001 09:49:32 on modular [Seed = 594290161] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2530 and weight 2.... I. Manin symbols list. (0.1 s) II. 2-term relations. (1.62 s) III. 3-term relations. Computing quotient by 1728 relations. Form quot and then images (1.589 s) (total time to create space = 3.36 s) Computing cuspidal part of Full Modular symbols space of level 2530, weight 2, and dimension 440 Computing new part of Modular symbols space of level 2530, weight 2, and dimension 425. Computing 2-new part of Modular symbols space of level 2530, weight 2, and dimension 425. Computing space of modular symbols of level 1265 and weight 2.... I. Manin symbols list. (0.009 s) II. 2-term relations. (0.519 s) III. 3-term relations. Computing quotient by 576 relations. Form quot and then images (0.301 s) (total time to create space = 0.839 s) Computing index-1 degeneracy map from level 2530 to 1265. (4.929 s) Computing index-2 degeneracy map from level 2530 to 1265. (4.851 s) Computing index-1 degeneracy map from level 1265 to 2530. (1.289 s) Computing index-2 degeneracy map from level 1265 to 2530. (1.39 s) Computing DualVectorSpace of Modular symbols space of level 2530, weight 2, and dimension 425. Computing complement of Modular symbols space of level 2530, weight 2, and dimension 425 Computing representation of Modular symbols space of level 2530, weight 2, and dimension 15. Goal dimension = 15. Computing T_2 on space of dimension 440. (0.32 s) Computing T_2 on dual space of dimension 15. T_2 sparse... (0.011 s). T_2 sparse... (0.019 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.02 s). %o x^15 - 22*x^14 + 224*x^13 - 1400*x^12 + 6006*x^11 - 18732*x^10 + 43876*x^9 - 78592*x^8 + 108545*x^7 - 115598*x^6 + 94164*x^5 - 57624*x^4 + 25648*x^3 - 7840*x^2 + 1472*x - 128 p = %o, dimension = %o. 2 86 Computing T_3 on space of dimension 440. (0.28 s) Computing T_3 on dual space of dimension 15. T_3 sparse... (0.021 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.021 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.02 s). T_3 sparse... (0.009 s). %o x^15 - 60*x^14 + 1680*x^13 - 29120*x^12 + 349440*x^11 - 3075072*x^10 + 20500480*x^9 - 105431040*x^8 + 421724160*x^7 - 1312030720*x^6 + 3148873728*x^5 - 5725224960*x^4 + 7633633280*x^3 - 7046430720*x^2 + 4026531840*x - 1073741824 p = %o, dimension = %o. 3 15 Computing complement of Modular symbols space of level 2530, weight 2, and dimension 15 Computing 5-new part of Modular symbols space of level 2530, weight 2, and dimension 425. Computing space of modular symbols of level 506 and weight 2.... I. Manin symbols list. (0.009 s) II. 2-term relations. (0.24 s) III. 3-term relations. Computing quotient by 288 relations. Form quot and then images (0.129 s) (total time to create space = 0.389 s) Computing index-1 degeneracy map from level 2530 to 506. (0.87 s) Computing index-5 degeneracy map from level 2530 to 506. (1.009 s) Computing index-1 degeneracy map from level 506 to 2530. (1.37 s) Computing index-5 degeneracy map from level 506 to 2530. (1.71 s) Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 594290161 Time to this point: 419.69 Segmentation fault Magma V2.7-1 Mon Jan 29 2001 10:03:19 on modular [Seed = 458497666] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2531 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.77 s) III. 3-term relations. Computing quotient by 844 relations. Form quot and then images (0.5 s) (total time to create space = 1.31 s) Computing cuspidal part of Full Modular symbols space of level 2531, weight 2, and dimension 212 Computing new part of Modular symbols space of level 2531, weight 2, and dimension 211. Computing 2531-new part of Modular symbols space of level 2531, weight 2, and dimension 211. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2531, weight 2, and dimension 211. Computing 2531-new part of Modular symbols space of level 2531, weight 2, and dimension 211. Computing cuspidal part of Modular symbols space of level 2531, weight 2, and dimension 211 Decomposing space of level 2531 and dimension 211 using T_2. (will stop at 422) Computing T_2 on dual space of dimension 211. Computing DualVectorSpace of Modular symbols space of level 2531, weight 2, and dimension 211. Computing complement of Modular symbols space of level 2531, weight 2, and dimension 211 Computing representation of Modular symbols space of level 2531, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 212. (0.491 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2531, weight 2, and dimension 1 T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^211 + 2*x^210 - 315*x^209 - 626*x^208 + 48832*x^207 + 96414*x^206 - 4966448*x^205 - 9740692*x^204 + 372744277*x^203 + 726102982*x^202 - 22016623398*x^201 - 42590692452*x^200 + 1065895041270*x^199 + 2047326164544*x^198 - 43496624750434*x^197 - 82940570720288*x^196 + 1527024922213192*x^195 + 2890181364179762*x^194 - 46842603109145681*x^193 - 87986190137505368*x^192 + 1271009826357386534*x^191 + 2368875757608083560*x^190 - 30806782125392338617*x^189 - 56961747171631205026*x^188 + 672430237105557180647*x^187 + 1233246315048597441550*x^186 - 13307174309928563315205*x^185 - 24203291502887438794630*x^184 + 240129385894669054149677*x^183 + 433050535683226954221668*x^182 - 3970549875585844305001550*x^181 - 7098484323403937767745380*x^180 + 60414019248991659793544350*x^179 + 107050759651193460808334538*x^178 - 848995457990798498251896809*x^177 - 1490761387617923476458569996*x^176 + 11054919759740904159870775636*x^175 + 19231854230220960178267535854*x^174 - 133759646220932717809869881217*x^173 - 230496268290713326306913834238*x^172 + 1507683836425415261974246278496*x^171 + 2572948661858949988797554677128*x^170 - 15866721954981569563292785923989*x^169 - 26810034606258424715766041488740*x^168 + 156216931209267528521584848478555*x^167 + 261296339870161374974127058118018*x^166 - 1441499921079547478043753884779670*x^165 - 2386267717699490069894925491219096*x^164 + 12486738561077351692562104180639179*x^163 + 20452938321703442110446445548412228*x^162 - 101686515927841472991477759358652060*x^161 - 164768300529888660095562722795771412*x^160 + 779520178960160311020685589172826302*x^159 + 1249227161863304304887305117388748672*x^158 - 5631899491788803589969141017755773636*x^157 - 8924248311013761728101245526778829310*x^156 + 38389253153182206759459363300613347599*x^155 + 60134942495139476375066925128176324014*x^154 - 247121169859862818251351701781334870311*x^153 - 382581904950475447260339913151577586606*x^152 + 1503601512346606307782632351266353364779*x^151 + 2300065897147494517125883305730707472504*x^150 - 8654008583219073865977380726412091964032*x^149 - 13077143550521861622371000172139807090102*x^148 + 47148538242630487168447738099457149273284*x^147 + 70363291775163915764541598385731730285650*x^146 - 243308935461177531288179822454207208825040*x^145 - 358518912877175179889952996721402227912582*x^144 + 1189952652305573855317190570106259869065863*x^143 + 1730824923535096468231986930160806862923808*x^142 - 5518211135758970971026522274169368272813859*x^141 - 7921078823006837674554628688057733363519740*x^140 + 24274665648589052929136990915024818084556073*x^139 + 34379131548727402343362437342387877760674340*x^138 - 101334992374801299922852690513773792477962212*x^137 - 141563048136230157700489829645977584302901428*x^136 + 401567677933841500510789486135773653984524482*x^135 + 553211983916120402760030152902323772548067782*x^134 - 1511023435367422259191134486619017721607447070*x^133 - 2052298391373359115274930219406067616091372844*x^132 + 5400027052830451902635443296726101373470475220*x^131 + 7229306396625990154531348104297402576003781906*x^130 - 18332094987780934744603860378969766201898952156*x^129 - 24184669965421261421807947352062595011562957906*x^128 + 59126146631123280097812978880616420036581894154*x^127 + 76847956847042017733499886935345542060635643264*x^126 - 181192253055610035436805240002239742338571532388*x^125 - 231961546176441000705161667144539476544116054354*x^124 + 527612896346493849171883919690032041148256162470*x^123 + 665144896201687633472411282221155337901424025996*x^122 - 1459863969861540970727397463764931034218521701252*x^121 - 1811927740976995781218665515173264812820481469102*x^120 + 3838121668703959174661877147460405541699254155759*x^119 + 4689003839107362037699311639225987075382450534912*x^118 - 9587503074609296700866692512449711400128268555772*x^117 - 11526818549859781836327849537460795645133845976984*x^116 + 22752383131977658123938303642973736043935958625177*x^115 + 26914419619720094025022708373696447790785312691718*x^114 - 51288526931166685892110580140173989926285851415282*x^113 - 59682694810576160119370506718757940744191823418454*x^112 + 109800948348688021053288565276418428483938471197268*x^111 + 125667934343621867545967997547499696461666823723602*x^110 - 223196934008880051125621895855926675383975588534911*x^109 - 251201142030881272238188508432344215585110762065052*x^108 + 430678703710052114040167313827179343521317974883373*x^107 + 476575583886255281479291814247075819056156927570180*x^106 - 788626222958156653630259964030492828905818119493671*x^105 - 857887500067715281341435254459184024033938525293136*x^104 + 1369915675597686996898695172438335927353866527784937*x^103 + 1464791146881191163486422243848663704923308792186864*x^102 - 2256605392446478372180937175694038714590710390669822*x^101 - 2371423552926447031739457858237844536871933481940376*x^100 + 3523487176842155761151360321650844167930498957883490*x^99 + 3638767013502829656943687262904709793218368078679036*x^98 - 5212456170861059388512498259401131485049200681185671*x^97 - 5289524471691084952383202770551657981290260287220944*x^96 + 7302015766441963446529709874404867616513342299476674*x^95 + 7280868648040070810327528389029048050879663244136046*x^94 - 9681254472108456531779178984965547655732229990814711*x^93 - 9484655702696388261877010189070430840484411792844544*x^92 + 12140763587212587376575254478249232330314622363179938*x^91 + 11686361823775481978675315997818063187022548446146256*x^90 - 14391332126495473053607313586084195712910687083087378*x^89 - 13610783835521699831466478118718629317462947156680208*x^88 + 16113461114817289928738419751856350697831737287779497*x^87 + 14973998319092003434424860754257173633204266239606596*x^86 - 17028548213670246739544267808596260436970039657754364*x^85 - 15549809206843647685663548044125240637488890537202420*x^84 + 16971099768862872569346408447529182870885943988160670*x^83 + 15230093952669561014639920425850129647734982715923626*x^82 - 15936815273052561155705649689932350773846605337175742*x^81 - 14057313302501008029089536051624775652818974988584274*x^80 + 14087669185042669902494254594468754894462018184704503*x^79 + 12216002835761026540893309773375606707979012439449804*x^78 - 11710594974460032553942001795664803388285409583996588*x^77 - 9985249461921972257996462690377267753557870210148278*x^76 + 9144168375082142432537602288955937628961361344434748*x^75 + 7668965590026540162232689047700106947423546033172284*x^74 - 6699196086867028400077486948961295029103600842634526*x^73 - 5528085739030343720107795721711931558904441834963512*x^72 + 4599004847090378705573957672979648240529262823854439*x^71 + 3735505605068057594541388827043127060646128935173222*x^70 - 2954443296836571039220602460108093165406698259219434*x^69 - 2363191484159458683129163181702197023745731372389918*x^68 + 1773457041757153199953436594281384252757913594556384*x^67 + 1397720067837444395783062230063234977156648353548714*x^66 - 993143281885133406416399223607841786023392620856689*x^65 - 771729706645515104199428348544225440789458825961586*x^64 + 517973785460472556385071855956924764223188228422555*x^63 + 397133974210031935702219097659285946568261456275956*x^62 - 251134461487213412360259160944539602507448211656687*x^61 - 190145190031277674341963281610213531064778649161796*x^60 + 112963548516492777406966881194144825491359731667727*x^59 + 84547592612182786615721609949847448485127893139322*x^58 - 47039140354120653928952803109157241180064480426595*x^57 - 34842670907528037381340631721940686219216106485352*x^56 + 18090063291418845432068808164930564726390773333368*x^55 + 13279185205428779390095153642391927864584414781732*x^54 - 6408471426245809609357538998913271548764370079550*x^53 - 4669364145779225280597709029994176718981999920084*x^52 + 2085285228244672156697813453109321558017298354684*x^51 + 1510980667833117504305172557336959113357450370432*x^50 - 621308310036157666048466229357381867358062744965*x^49 - 448709106379007417565717753515608749341740574282*x^48 + 168912479768515090621244183750963245753026532763*x^47 + 121914310122372114121678784457492510918078212870*x^46 - 41737818092681871937330239990747092090589199773*x^45 - 30205198362337062733154349130530224967706329136*x^44 + 9332330914975523442672168241980359787323851744*x^43 + 6799172871600633808195920838956310845966444812*x^42 - 1878646113376237080960327553886434341740722910*x^41 - 1384916572559749311317978015962364494829752110*x^40 + 338485383629249325790159041053087334235470622*x^39 + 254120457078184225960710837437681158383843306*x^38 - 54205594701806019723948736161564110584296688*x^37 - 41796203324147880898008708471452167031178690*x^36 + 7649947406171443437331063932474815846667996*x^35 + 6127518187971195804702621684372904074554220*x^34 - 941209766978052359049992959150475030769513*x^33 - 795676852718605417578723049234081275478486*x^32 + 99498321343076873238105831509986587181256*x^31 + 90857891521964594309765925939036450122390*x^30 - 8847257410837003167119353926646014784989*x^29 - 9048052346809464669207832256471193640818*x^28 + 638588489306842794136756464481082067648*x^27 + 778219034459533882139443842161512140800*x^26 - 34732132065236038063788656330740221761*x^25 - 57148124206813409543880808572162128324*x^24 + 1112713745493895352069694765568963691*x^23 + 3533388392823784434885156493827457740*x^22 + 17752602481441583983060624205058754*x^21 - 180763515326781379533748132024804658*x^20 - 5258022515684981904918319166225231*x^19 + 7481322116263726104807671998036616*x^18 + 397811194787699145242127947484667*x^17 - 242909112914823669189690845593252*x^16 - 19002668872747913558990858396072*x^15 + 5911945430522787121037671183928*x^14 + 629566533957516032927273628912*x^13 - 99792856512903851379641274240*x^12 - 14417687584889584800172079808*x^11 + 978497461720054608158154752*x^10 + 216449070807586542268432640*x^9 - 1861904384174981796473344*x^8 - 1884127865224154557445120*x^7 - 64414327795792358168576*x^6 + 6728576781015318978560*x^5 + 513968017625830457344*x^4 + 6069584538135101440*x^3 - 321132006027362304*x^2 - 5769347230400512*x + 53799061291008 time = 5.56 Factoring characteristic polynomial. [ , ] time = 1.67 Cutting out subspace using f(T_2), where f=x^89 + 7*x^88 - 98*x^87 - 784*x^86 + 4431*x^85 + 42130*x^84 - 120184*x^83 - 1446588*x^82 + 2081059*x^81 + 35659612*x^80 - 20550764*x^79 - 672241603*x^78 - 8274412*x^77 + 10080625403*x^76 + 4504569337*x^75 - 123485825128*x^74 - 97259223777*x^73 + 1259315852599*x^72 + 1345739349760*x^71 - 10841342059990*x^70 - 14212621503246*x^69 + 79613899276516*x^68 + 121715946834652*x^67 - 502648652722920*x^66 - 870923085741012*x^65 + 2744489845621077*x^64 + 5299561371180928*x^63 - 13014679538931086*x^62 - 27740807503767577*x^61 + 53757039278559501*x^60 + 125906745816861431*x^59 - 193721627692764614*x^58 - 498253508563799050*x^57 + 609312461424811749*x^56 + 1725967412730419583*x^55 - 1671214822087580905*x^54 - 5247717273835937814*x^53 + 3987495226320332113*x^52 + 14028591551751335603*x^51 - 8239838854368951748*x^50 - 33003518181673567654*x^49 + 14638005606164414891*x^48 + 68343755555665773083*x^47 - 22081770861121849097*x^46 - 124521203748024198754*x^45 + 27669421933322296847*x^44 + 199411056658369386748*x^43 - 27516178551407513120*x^42 - 280235912487451146265*x^41 + 19142532027403142329*x^40 + 344847507252911791621*x^39 - 3995989902249862232*x^38 - 370565814286098372837*x^37 - 12355942494451186744*x^36 + 346556886635484956417*x^35 + 23337957426540187460*x^34 - 280925864941492116059*x^33 - 25577422731573451608*x^32 + 196430856831982090763*x^31 + 20617963898003236555*x^30 - 117789854365078386039*x^29 - 12904765314055836342*x^28 + 60152007571920027372*x^27 + 6337641150726265270*x^26 - 25938046845403112701*x^25 - 2414141527472988148*x^24 + 9345426018595684588*x^23 + 688536733536956237*x^22 - 2776569056633750869*x^21 - 134703610978417484*x^20 + 668957785158996607*x^19 + 12941958302006448*x^18 - 127928205581617735*x^17 + 1490867195900265*x^16 + 18890818305536753*x^15 - 792065847667684*x^14 - 2079352688919104*x^13 + 142516525017673*x^12 + 163202137820709*x^11 - 14368738754962*x^10 - 8663919004107*x^9 + 833443103270*x^8 + 294640106554*x^7 - 25957642697*x^6 - 6127302850*x^5 + 371829785*x^4 + 72156321*x^3 - 1259264*x^2 - 378293*x - 9861. Cutting out subspace using f(T_2), where f=x^122 - 5*x^121 - 182*x^120 + 942*x^119 + 16051*x^118 - 86290*x^117 - 913616*x^116 + 5121510*x^115 + 37712051*x^114 - 221445984*x^113 - 1202465634*x^112 + 7436026025*x^111 + 30800552198*x^110 - 201873145965*x^109 - 650608397729*x^108 + 4554463950412*x^107 + 11541476917704*x^106 - 87112993237574*x^105 - 174135303443486*x^104 + 1434017264114658*x^103 + 2253297266517973*x^102 - 20555769162892608*x^101 - 25115750650660828*x^100 + 258976226038936816*x^99 + 241092332406739703*x^98 - 2889331386089576419*x^97 - 1979480288117436812*x^96 + 28722244929707471887*x^95 + 13632319526472964993*x^94 - 255700078014955354100*x^93 - 74773299768658253572*x^92 + 2047248121093949806710*x^91 + 272648427522846545541*x^90 - 14793428039765490230582*x^89 + 106300191860257026983*x^88 + 96761958342094653675305*x^87 - 12755812222611930685430*x^86 - 574305790475118762450371*x^85 + 139692658246580629412407*x^84 + 3099322079707046073146884*x^83 - 1064325501598087510966974*x^82 - 15233457658181364671662720*x^81 + 6610315241562414154322497*x^80 + 68284478202917033645756393*x^79 - 35243117235257340663132683*x^78 - 279444919314772772593854932*x^77 + 165160353715582332529895777*x^76 + 1044884158364929216548666746*x^75 - 689126276712706392460747319*x^74 - 3571765751477688034807697956*x^73 + 2579914255908935328778477948*x^72 + 11165869580060901970002701659*x^71 - 8708783430026170195255025131*x^70 - 31927324955089588564342335499*x^69 + 26591765813812535468700795418*x^68 + 83498451028610946612151752436*x^67 - 73599842454815432651187651167*x^66 - 199687513890159680248903748753*x^65 + 184885225699892643635381844296*x^64 + 436536639983381772613487981110*x^63 - 421809882912316295450919301331*x^62 - 871892509174917321971139613531*x^61 + 874188006359608460779519159588*x^60 + 1589979482187616598213129958648*x^59 - 1645412860038693428435960336160*x^58 - 2645228299858356728578796598069*x^57 + 2811126085879298327189384451135*x^56 + 4011266054774664023038542304845*x^55 - 4355441353189543048836337861598*x^54 - 5538607428896651849084709140978*x^53 + 6112309062276381055721962065116*x^52 + 6955496187804218617945694631016*x^51 - 7757821000187076474132324690246*x^50 - 7934627690551458232922101726929*x^49 + 8888683146305256620601003321706*x^48 + 8211298862849666771667464387009*x^47 - 9173906743328903860550390405681*x^46 - 7697458731070143788039154673421*x^45 + 8507221417143904563751009867305*x^44 + 6525748688189664980366686975620*x^43 - 7067363869975962014207602100554*x^42 - 4994223096996295676499612798756*x^41 + 5241786448447521714171256323530*x^40 + 3443015818840487072868400950252*x^39 - 3457234102270349091300610292933*x^38 - 2132743779264220414902998782069*x^37 + 2018322252655371279798716462086*x^36 + 1183324054040772642968073014142*x^35 - 1037261539866651384961899701088*x^34 - 585759350664890638506565541556*x^33 + 466214360476543302027094555521*x^32 + 257400812063093822568041054348*x^31 - 181819762045808147969414393978*x^30 - 99774372086628974643924894759*x^29 + 60923935377738151602287398789*x^28 + 33843696339193496922443036744*x^27 - 17321304679290339618302930687*x^26 - 9946275368464755494085973886*x^25 + 4109394125359265851353395262*x^24 + 2501544715379344148329951423*x^23 - 794587477767323219657623690*x^22 - 530260338648071264755668613*x^21 + 120697011169310173840918107*x^20 + 92946783916616303052269996*x^19 - 13451383975624961445730533*x^18 - 13150651638749117428082155*x^17 + 917271107100485360117684*x^16 + 1455054237809230834772912*x^15 - 3869332612453305534760*x^14 - 120530783518699880815088*x^13 - 6946096581540777759296*x^12 + 7003266028132659738304*x^11 + 798795730283258384128*x^10 - 254848552789695466240*x^9 - 44712956376667490816*x^8 + 4400005804554324992*x^7 + 1265707930968053760*x^6 + 8463793173864448*x^5 - 13730582391488512*x^4 - 863861703376896*x^3 + 2788781457408*x^2 + 794363232256*x - 5455740928. Computing representation of Modular symbols space of level 2531, weight 2, and dimension 87. Goal dimension = 87. Computing T_2 on dual space of dimension 87. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). %o x^87 + 6*x^86 - 99*x^85 - 652*x^84 + 4607*x^83 + 33973*x^82 - 133169*x^81 - 1130477*x^80 + 2651342*x^79 + 26994130*x^78 - 37767122*x^77 - 492767312*x^76 + 377776481*x^75 + 7153737545*x^74 - 2240471900*x^73 - 84833576023*x^72 - 2435998898*x^71 + 837634765418*x^70 + 248418424028*x^69 - 6984683926310*x^68 - 3582556627426*x^67 + 49717483824912*x^66 + 34410748183121*x^65 - 304599867527893*x^64 - 257027155314838*x^63 + 1616533100653057*x^62 + 1575616361433751*x^61 - 7468217297862133*x^60 - 8136965744465375*x^59 + 30148165787829787*x^58 + 35934990736824279*x^57 - 106642368320221978*x^56 - 136990143736238860*x^55 + 331192078258547384*x^54 + 453565932617209579*x^53 - 904185556190191600*x^52 - 1309532045001865091*x^51 + 2171368237320186400*x^50 + 3305284509064385442*x^49 - 4587004731482861671*x^48 - 7303135762976778951*x^47 + 8519940186345256525*x^46 + 14131764723557963785*x^45 - 13900575046296588645*x^44 - 23938073914848714635*x^43 + 19892612937224301856*x^42 + 35454898119036015196*x^41 - 24922566818222616347*x^40 - 45827500806358089383*x^39 + 27272455128089203955*x^38 + 51556633607231153899*x^37 - 25994600885703607533*x^36 - 50310333009799927852*x^35 + 21511072137929390821*x^34 + 42401353118537358631*x^33 - 15396238611060814065*x^32 - 30702336977183252197*x^31 + 9488127462716119397*x^30 + 18978870993921058181*x^29 - 5006539707465498867*x^28 - 9939049888418977374*x^27 + 2245601669554059110*x^26 + 4368935381064040255*x^25 - 847640937479141792*x^24 - 1594046558596839249*x^23 + 265350608673821280*x^22 + 476232985961031982*x^21 - 67355552986609564*x^20 - 114591381667826229*x^19 + 13357478891646319*x^18 + 21767201890701501*x^17 - 1929426114900460*x^16 - 3187667650974612*x^15 + 169333551339876*x^14 + 350607738617685*x^13 - 1412817989653*x^12 - 28306013928886*x^11 - 1801768161399*x^10 + 1664821536403*x^9 + 236733824966*x^8 - 71723045733*x^7 - 13755065477*x^6 + 2089908001*x^5 + 369288403*x^4 - 29385260*x^3 - 4033737*x^2 + 86781*x + 10280 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 458497666 Time to this point: 170.65 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2531, a, ^ User error: Identifier 'a' has not been declared or assigned Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 458497666 Time to this point: 170.89 Segmentation fault Magma V2.7-1 Mon Jan 29 2001 10:08:56 on modular [Seed = 425091679] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2533 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.83 s) III. 3-term relations. Computing quotient by 900 relations. Form quot and then images (0.571 s) (total time to create space = 1.441 s) Computing cuspidal part of Full Modular symbols space of level 2533, weight 2, and dimension 226 Computing new part of Modular symbols space of level 2533, weight 2, and dimension 223. Computing 17-new part of Modular symbols space of level 2533, weight 2, and dimension 223. Computing space of modular symbols of level 149 and weight 2.... I. Manin symbols list. (0.011 s) II. 2-term relations. (0.04 s) III. 3-term relations. Computing quotient by 50 relations. Form quot and then images (0.009 s) (total time to create space = 0.06 s) Computing index-1 degeneracy map from level 2533 to 149. (0.091 s) Computing index-17 degeneracy map from level 2533 to 149. (0.459 s) Computing index-1 degeneracy map from level 149 to 2533. (0.67 s) Computing index-17 degeneracy map from level 149 to 2533. (0.809 s) Computing DualVectorSpace of Modular symbols space of level 2533, weight 2, and dimension 223. Computing complement of Modular symbols space of level 2533, weight 2, and dimension 223 Computing representation of Modular symbols space of level 2533, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 226. (0.231 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2533, weight 2, and dimension 3 Computing 149-new part of Modular symbols space of level 2533, weight 2, and dimension 223. Computing space of modular symbols of level 17 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 6 relations. Form quot and then images (0.009 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 2533 to 17. (0.039 s) Computing index-149 degeneracy map from level 2533 to 17. (8.731 s) Computing index-1 degeneracy map from level 17 to 2533. (1.56 s) Computing index-149 degeneracy map from level 17 to 2533. (1.349 s) Finding newform decomposition of Modular symbols space of level 2533, weight 2, and dimension 223. Computing cuspidal part of Modular symbols space of level 2533, weight 2, and dimension 223 Decomposing space of level 2533 and dimension 197 using T_2. (will stop at 450) Computing T_2 on dual space of dimension 197. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^197 - 3*x^196 - 292*x^195 + 880*x^194 + 41894*x^193 - 126858*x^192 - 3936878*x^191 + 11980550*x^190 + 272545931*x^189 - 833721677*x^188 - 14823313330*x^187 + 45591801310*x^186 + 659623970589*x^185 - 2040363405035*x^184 - 24695843459184*x^183 + 76845900190344*x^182 + 793918512640099*x^181 - 2485888684909669*x^180 - 22257820045663500*x^179 + 70150064136156300*x^178 + 550841314742835208*x^177 - 1748037216625115744*x^176 - 12152249498191231548*x^175 + 38842530601862681272*x^174 + 240911866610655763873*x^173 - 775877801924732253759*x^172 - 4320508633513279466328*x^171 + 14025632173343407197920*x^170 + 70491665811423944223251*x^169 - 230758314568689512821349*x^168 - 1051375845979524010916476*x^167 + 3472175434097259803666636*x^166 + 14394463969308498350437882*x^165 - 47980960996745977051128722*x^164 - 181556190145121014565458472*x^163 + 611131851134581209619839012*x^162 + 2116246719450601595934635492*x^161 - 7197432298408555004918195292*x^160 - 22858877225794571510672125312*x^159 + 78597487141161648345336069832*x^158 + 229365103153590984267781341058*x^157 - 797808212550435150140657504386*x^156 - 2142450129959479384072011697072*x^155 + 7543904206177680388637463379524*x^154 + 18664857624732187009075775700129*x^153 - 66580286028781402860032411871411*x^152 - 151912824286580995236407139416860*x^151 + 549413436261005695873628213184836*x^150 + 1156808309754351577606306065587390*x^149 - 4245497999094463002822444754037642*x^148 - 8252620610792202189976934008416724*x^147 + 30763367270184890962641421216138520*x^146 + 55218453324995555494734172935142476*x^145 - 209291357482925116892069296220235952*x^144 - 346876354623158226753035381079288166*x^143 + 1338319948152805173198341224812882850*x^142 + 2047585461550403039827578474056249890*x^141 - 8051690932020952824268238618394006178*x^140 - 11366095333884921732382411495863086070*x^139 + 45615547978979306271965558500312574170*x^138 + 59368563766357259209893161120579449181*x^137 - 243542321625801877901040831981543682887*x^136 - 291946196701285175404117120987459584226*x^135 + 1226222209012436546166120603300265333294*x^134 + 1352157245771416525697845665263380735683*x^133 - 5825830641708990539015737482857789647057*x^132 - 5900093957876147471016304084056907954392*x^131 + 26131663940822577814387444552132501231824*x^130 + 24259317974416779091674259902242721506030*x^129 - 110711161601743353770015155019777685683098*x^128 - 93997443947437668986308608880998307256416*x^127 + 443195523826367869707921065055514467200040*x^126 + 343199726780730740976462560078273506393889*x^125 - 1676929831744970921206522512064598149391159*x^124 - 1180557717445276144483114231953429351609148*x^123 + 5998722351222846217356054637511859484772180*x^122 + 3824592760959732450966681648261718833999804*x^121 - 20291293042975755973524076642653776705414556*x^120 - 11662986729153702428898000967506506187494512*x^119 + 64912067278681904986277660623763723061810424*x^118 + 33452884006604720361255346324507777627630643*x^117 - 196399002041258086756921753972644038400841057*x^116 - 90158732787960216546990599544628509979621596*x^115 + 562031831920594780278940166686436120864616784*x^114 + 227994713598640773426910845300457880392210754*x^113 - 1521166764617681335720984725316201667488389794*x^112 - 539957480955773119658035885624378827219044738*x^111 + 3893593722497370779970229511628220564820562702*x^110 + 1194472590395083847542655434928567025378602124*x^109 - 9423739843157589051354775627478774275426775240*x^108 - 2459060058550785656849569093248497269049867818*x^107 + 21563199011236979769897024804894818597858147166*x^106 + 4685740334667623631805585100917113129411979864*x^105 - 46635447514801413526781109850486543578393838024*x^104 - 8194689842443264894921231019863364163572887192*x^103 + 95302706544769800406223918327476278892060612120*x^102 + 12967032861281520696915579413663085008404955461*x^101 - 183963021190654539929564444159506431610067927023*x^100 - 18068097463967347443556661170296308239199397310*x^99 + 335288587203686840321009263541803964003986674678*x^98 + 20812551346361492823374575806223053106308259529*x^97 - 576730383698342278918980293435630228767178030211*x^96 - 15880513775741022046907643692059682174378474126*x^95 + 935774402139218029535495899293618367813459721718*x^94 - 5137000674684160659252197548824120184700942671*x^93 - 1431419886821258851313837202557080519050943158023*x^92 + 53084726304536444578485310428810840693738669348*x^91 + 2062945623984625432306476293847002868147218598804*x^90 - 138896685128182010603053974278060304086141989339*x^89 - 2799198477578770608459740519114265513344947009999*x^88 + 269542300537809486487155618234817298140439213392*x^87 + 3573362300981557577922822719266515925164908876524*x^86 - 443244039777680994083766510528975699712413242612*x^85 - 4288059663636658017791685573390750908094784722236*x^84 + 645933096268498051528082923000982942814461105812*x^83 + 4832782732309676709399044166997478772731416617892*x^82 - 851201212498972212334317162140034516797768297971*x^81 - 5110535868815895274141352394452821638786122111803*x^80 + 1025062929834145029577928902856021355794379843294*x^79 + 5065407743772208402751234309051209992895961384082*x^78 - 1134778774110071386477372848353495301559215076787*x^77 - 4700579574762213211707084164862799828134102589887*x^76 + 1158757160963661634317050731684501140917312510492*x^75 + 4078962629371697412577467394723769504322623769084*x^74 - 1093498893958042782928703770742976705308955464373*x^73 - 3305532291150627201095956075621819892644481446637*x^72 + 954527768403498052880650162095763393865646143144*x^71 + 2498133851232614965629120011976206955213574830412*x^70 - 770916942777595580840118817223063176918518925591*x^69 - 1757989685713876007192448376587766698741045832431*x^68 + 575919303582152580857810720313474618932908937500*x^67 + 1150107194997595695049596243922667738328885723324*x^66 - 397709441375131099431655397400820546502853806956*x^65 - 698272187994609154731602446983230694755121708364*x^64 + 253626282116481145496862829447215843714228435934*x^63 + 392701801575676048911619586481080839670682504258*x^62 - 149175646399815937542725522241160869895269509178*x^61 - 204164475019474512010068372739457610594226712646*x^60 + 80801047703302682725720323672035423524428598894*x^59 + 97912805782436982450997009211920151588202273082*x^58 - 40233413497700895798005977367894722854288481561*x^57 - 43214955761678737814315093953494946252935832653*x^56 + 18379822356422195351976328738873602611451430830*x^55 + 17509816250084281476664044400980705047589741862*x^54 - 7686213078628075907483961607704076364505582227*x^53 - 6495573449905496670904087503857965676971443611*x^52 + 2935138703219866550377150120237216037420925710*x^51 + 2199820807056249879137530639613313696646620230*x^50 - 1020728935393239847037184821202829290495981086*x^49 - 678012245775371772142319062678230257087524102*x^48 + 322302866292542627158141391166734415324126860*x^47 + 189541825679535431891247281537916240067187492*x^46 - 92102998689112129711776828374960075098761806*x^45 - 47885527045129483425462905237173154333876002*x^44 + 23735043536028920137757707524941670784908038*x^43 + 10889591955903188354663905190589164694547742*x^42 - 5494360442081340166498058660092766462810922*x^41 - 2219456138947356033568493671921475571970366*x^40 + 1137616092767868387464798796871605357072768*x^39 + 403504504554654705537878723507993793477260*x^38 - 209691783171533654034918194540562267835259*x^37 - 65094933381076181125129468416253394336027*x^36 + 34230851511899760035082265328044881358726*x^35 + 9264634205640784178985769528591211149710*x^34 - 4920408383754019448462612684894117773760*x^33 - 1155814396758782720088495932460806451020*x^32 + 618780051434005903279961787840168620578*x^31 + 125481628936427605985578134909010951394*x^30 - 67589109622972533687726928930373079486*x^29 - 11758427772614379003391231918394628722*x^28 + 6359850391484013202522253322384507132*x^27 + 942221682302308232782823279722916544*x^26 - 510666936184783700590584184437368630*x^25 - 63880889078701734228206386041943406*x^24 + 34607099340407464690018439175095178*x^23 + 3619951802968475940877208194909210*x^22 - 1953784922552330474766565177866564*x^21 - 169070183997435777873177428884100*x^20 + 90465476606658391176787186120350*x^19 + 6404913177815595093190543148018*x^18 - 3370369547979698896958945852159*x^17 - 193271011512093482980827145099*x^16 + 98647660682249973749888006150*x^15 + 4551712231771128596200748514*x^14 - 2200044570908989207062217165*x^13 - 81735766629947351263490537*x^12 + 35905166277696775764250774*x^11 + 1086791002907706374351514*x^10 - 405426782195482194930957*x^9 - 10239801718788289972369*x^8 + 2911655577431193733650*x^7 + 63612356628041186006*x^6 - 11520049455370528834*x^5 - 233986556726864414*x^4 + 18522904460199500*x^3 + 446099131806204*x^2 - 3917557159143*x - 101408068755 time = 58.58 Factoring characteristic polynomial. [ , , , ] time = 1.36 Cutting out subspace using f(T_2), where f=x^47 + 14*x^46 + 30*x^45 - 463*x^44 - 2473*x^43 + 4527*x^42 + 56948*x^41 + 32166*x^40 - 701666*x^39 - 1318068*x^38 + 5215644*x^37 + 16717259*x^36 - 22316630*x^35 - 128115135*x^34 + 25987496*x^33 + 671473668*x^32 + 331838901*x^31 - 2506402810*x^30 - 2623333310*x^29 + 6684389330*x^28 + 10812569773*x^27 - 12272165746*x^26 - 29987724849*x^25 + 13379901720*x^24 + 59562951660*x^23 - 1580756695*x^22 - 86166623885*x^21 - 22921385742*x^20 + 90479683693*x^19 + 44678764215*x^18 - 67783586842*x^17 - 47031832370*x^16 + 35148896831*x^15 + 31585980208*x^14 - 12051981553*x^13 - 13878958907*x^12 + 2558364996*x^11 + 3912028869*x^10 - 313951810*x^9 - 669428171*x^8 + 26181673*x^7 + 62576321*x^6 - 2778601*x^5 - 2619801*x^4 + 168999*x^3 + 28872*x^2 - 1758*x - 37. Cutting out subspace using f(T_2), where f=x^48 + 13*x^47 + 12*x^46 - 545*x^45 - 2086*x^44 + 8816*x^43 + 60227*x^42 - 47394*x^41 - 920022*x^40 - 582502*x^39 + 8914410*x^38 + 14019423*x^37 - 58168607*x^36 - 143726519*x^35 + 255071835*x^34 + 951712330*x^33 - 674830509*x^32 - 4493644065*x^31 + 379180388*x^30 + 15732980928*x^29 + 5412934625*x^28 - 41515509667*x^27 - 28102506463*x^26 + 82817325707*x^25 + 80366007722*x^24 - 123863308417*x^23 - 157437529816*x^22 + 135726911131*x^21 + 223133046999*x^20 - 103418334564*x^19 - 232001679011*x^18 + 47337222264*x^17 + 176132286793*x^16 - 4217935471*x^15 - 95835144881*x^14 - 10300432194*x^13 + 36107223169*x^12 + 7548219487*x^11 - 8873952777*x^10 - 2625078849*x^9 + 1268172962*x^8 + 494375100*x^7 - 77173912*x^6 - 45467580*x^5 - 1207314*x^4 + 1326603*x^3 + 179878*x^2 + 7773*x + 105. Cutting out subspace using f(T_2), where f=x^51 - 16*x^50 + 50*x^49 + 527*x^48 - 3796*x^47 - 3081*x^46 + 91708*x^45 - 134607*x^44 - 1175023*x^43 + 3620401*x^42 + 8421160*x^41 - 46594075*x^40 - 22033026*x^39 + 384407515*x^38 - 201794584*x^37 - 2198674285*x^36 + 2816349291*x^35 + 8861195273*x^34 - 18372980336*x^33 - 24175949192*x^32 + 79944065096*x^31 + 36091225608*x^30 - 251732117997*x^29 + 21026037050*x^28 + 588737271991*x^27 - 282585570029*x^26 - 1024042205334*x^25 + 849766902018*x^24 + 1298586070991*x^23 - 1576204158510*x^22 - 1134859672331*x^21 + 2029889732074*x^20 + 572587797832*x^19 - 1860819259135*x^18 - 4761658075*x^17 + 1203717946483*x^16 - 236264725423*x^15 - 531593713165*x^14 + 188288094645*x^13 + 150158699110*x^12 - 75940119629*x^11 - 23605584334*x^10 + 17186059889*x^9 + 1195476198*x^8 - 2059625302*x^7 + 151785677*x^6 + 105438829*x^5 - 18616030*x^4 - 610251*x^3 + 304804*x^2 - 17224*x + 201. Cutting out subspace using f(T_2), where f=x^51 - 14*x^50 + 20*x^49 + 605*x^48 - 2784*x^47 - 9341*x^46 + 83212*x^45 + 15629*x^44 - 1324215*x^43 + 1696463*x^42 + 13120896*x^41 - 32177799*x^40 - 82832684*x^39 + 330655883*x^38 + 290200432*x^37 - 2285428791*x^36 + 69251979*x^35 + 11346525047*x^34 - 7491896736*x^33 - 41345967238*x^32 + 49936407462*x^31 + 109865455072*x^30 - 200327764005*x^29 - 202976899262*x^28 + 567245277735*x^27 + 216099131991*x^26 - 1187440075002*x^25 + 33065122712*x^24 + 1861938855163*x^23 - 615891392456*x^22 - 2177807329065*x^21 + 1278646610130*x^20 + 1863612391836*x^19 - 1571651912653*x^18 - 1119723434797*x^17 + 1307075092871*x^16 + 431718410033*x^15 - 755170400213*x^14 - 79418391111*x^13 + 301723304084*x^12 - 9598176791*x^11 - 82185767412*x^10 + 8958694743*x^9 + 15090567566*x^8 - 2128960442*x^7 - 1841682313*x^6 + 252197847*x^5 + 143875182*x^4 - 15088981*x^3 - 6521542*x^2 + 361158*x + 129863. Computing representation of Modular symbols space of level 2533, weight 2, and dimension 47. Goal dimension = 47. Computing T_2 on dual space of dimension 47. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 425091679 Time to this point: 594.53 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2533, a, ^ User error: Identifier 'a' has not been declared or assigned Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 425091679 Time to this point: 594.67 Segmentation fault Magma V2.7-1 Mon Jan 29 2001 10:28:28 on modular [Seed = 324824225] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2534 and weight 2.... I. Manin symbols list. (0.07 s) II. 2-term relations. (1.36 s) III. 3-term relations. Computing quotient by 1456 relations. Form quot and then images (1.221 s) (total time to create space = 2.691 s) Computing cuspidal part of Full Modular symbols space of level 2534, weight 2, and dimension 368 Computing new part of Modular symbols space of level 2534, weight 2, and dimension 361. Computing 2-new part of Modular symbols space of level 2534, weight 2, and dimension 361. Computing space of modular symbols of level 1267 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.439 s) III. 3-term relations. Computing quotient by 488 relations. Form quot and then images (0.24 s) (total time to create space = 0.689 s) Computing index-1 degeneracy map from level 2534 to 1267. (2.57 s) Computing index-2 degeneracy map from level 2534 to 1267. (2.58 s) Computing index-1 degeneracy map from level 1267 to 2534. (1.1 s) Computing index-2 degeneracy map from level 1267 to 2534. (0.979 s) Computing DualVectorSpace of Modular symbols space of level 2534, weight 2, and dimension 361. Computing complement of Modular symbols space of level 2534, weight 2, and dimension 361 Computing representation of Modular symbols space of level 2534, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 368. (0.271 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 68 Computing T_3 on space of dimension 368. (0.2 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 2534, weight 2, and dimension 7 Computing 7-new part of Modular symbols space of level 2534, weight 2, and dimension 361. Computing space of modular symbols of level 362 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.15 s) III. 3-term relations. Computing quotient by 182 relations. Form quot and then images (0.071 s) (total time to create space = 0.231 s) Computing index-1 degeneracy map from level 2534 to 362. (0.309 s) Computing index-7 degeneracy map from level 2534 to 362. (0.55 s) Computing index-1 degeneracy map from level 362 to 2534. (1.09 s) Computing index-7 degeneracy map from level 362 to 2534. (1.221 s) Computing 181-new part of Modular symbols space of level 2534, weight 2, and dimension 361. Computing space of modular symbols of level 14 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 8 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 2534 to 14. (0.071 s) Computing index-181 degeneracy map from level 2534 to 14. (17.719 s) Computing index-1 degeneracy map from level 14 to 2534. (3.39 s) Computing index-181 degeneracy map from level 14 to 2534. (3.609 s) Finding newform decomposition of Modular symbols space of level 2534, weight 2, and dimension 361. Computing cuspidal part of Modular symbols space of level 2534, weight 2, and dimension 361 Decomposing space of level 2534 and dimension 89 using T_3. (will stop at 728) Computing T_3 on dual space of dimension 89. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^89 - 178*x^87 + 15221*x^85 - 16*x^84 - 832774*x^83 + 2536*x^82 + 32758034*x^81 - 192224*x^80 - 986983352*x^79 + 9277744*x^78 + 23695622721*x^77 - 320317232*x^76 - 465619609390*x^75 + 8425331240*x^74 + 7633493366270*x^73 - 175585024408*x^72 - 105904692381392*x^71 + 2976926624064*x^70 + 1256875323083396*x^69 - 41839554407848*x^68 - 12866622109502688*x^67 + 494234794691640*x^66 + 114349092849329384*x^65 - 4957837525909624*x^64 - 886677654959341284*x^63 + 42565038873769264*x^62 + 6021775341388037709*x^61 - 314608061188104576*x^60 - 35921033306783754152*x^59 + 2010646003735135600*x^58 + 188590273593322366988*x^57 - 11145476909951292064*x^56 - 872573481295326265168*x^55 + 53695898165113012832*x^54 + 3560243149043379149666*x^53 - 225076088153304834224*x^52 - 12810698048628200143148*x^51 + 820998183854595627088*x^50 + 40630586545026354689835*x^49 - 2604229072411823832416*x^48 - 113461864020560097084094*x^47 + 7172136531544049415968*x^46 + 278516577730114136973679*x^45 - 17105294593811963179392*x^44 - 599650335225888195994442*x^43 + 35197092696561093297912*x^42 + 1129214705459175966983693*x^41 - 62163559897391412899040*x^40 - 1853534175892059623019458*x^39 + 93569746036924664900400*x^38 + 2641143819091803215511024*x^37 - 118845165649894440948624*x^36 - 3251262870557097192506540*x^35 + 125518426714062835359840*x^34 + 3438148407856864303485851*x^33 - 107667491684409902142712*x^32 - 3102759468714824859897530*x^31 + 71780782221262035829936*x^30 + 2371326769968112621339550*x^29 - 33371503085749764743800*x^28 - 1521130426708751911110412*x^27 + 6306201343869596617496*x^26 + 810413105126864489360662*x^25 + 5367293531472808096240*x^24 - 354153271276131593297784*x^23 - 6443865579492986257136*x^22 + 125052016569976202264152*x^21 + 3815960399197095871416*x^20 - 35024917082895013764778*x^19 - 1523609772504361488976*x^18 + 7601897370339823122252*x^17 + 433471994182267640720*x^16 - 1240281031046798996860*x^15 - 87845866749536656720*x^14 + 145960527419366337177*x^13 + 12312789267179075048*x^12 - 11680335152750875308*x^11 - 1123980569472309544*x^10 + 581478654838328518*x^9 + 59809792398687816*x^8 - 15696637264184868*x^7 - 1489119825596864*x^6 + 195537761227817*x^5 + 11125602800640*x^4 - 1029764736000*x^3 time = 6.379 Factoring characteristic polynomial. [ , , , , , , , , , , , , , , ] time = 0.281 Cutting out subspace using f(T_3), where f=x - 3. Cutting out subspace using f(T_3), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^4 + 12*x^3 + 46*x^2 + 60*x + 25. Decomposing space of level 2534 and dimension 4 using T_3. (will stop at 728) Computing characteristic polynomial of T_3. x^4 - 4*x^3 + 6*x^2 - 4*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Charpoly = x^4 - 8*x^3 + 22*x^2 - 24*x + 9. Decomposing space of level 2534 and dimension 4 using T_5. (will stop at 728) Computing T_5 on dual space of dimension 4. T_5 sparse... (0.02 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing characteristic polynomial of T_5. x^4 + 3*x^3 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Charpoly = x^3 - 7*x^2 + 11*x - 5. Decomposing space of level 2534 and dimension 3 using T_3. (will stop at 728) Computing characteristic polynomial of T_3. x^3 - 3*x^2 + 3*x - 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Charpoly = x^3 + x^2 - 5*x + 3. Decomposing space of level 2534 and dimension 3 using T_5. (will stop at 728) Computing T_5 on dual space of dimension 3. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). Computing characteristic polynomial of T_5. x^3 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Charpoly = x^3 - 10*x^2 + 32*x - 32. Decomposing space of level 2534 and dimension 3 using T_11. (will stop at 728) Computing T_11 on dual space of dimension 3. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing characteristic polynomial of T_11. x^3 - 5*x^2 - 9*x + 45 time = 0 Factoring characteristic polynomial. [ , , ] time = 0.01 Cutting out subspace using f(T_11), where f=x - 5. Cutting out subspace using f(T_11), where f=x - 3. Cutting out subspace using f(T_11), where f=x + 3. Cutting out subspace using f(T_5), where f=x + 3. Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Charpoly = x^3 - x^2 - x + 1. Decomposing space of level 2534 and dimension 3 using T_3. (will stop at 728) Computing characteristic polynomial of T_3. x^3 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Charpoly = x^3 + 3*x^2 - 9*x - 27. Decomposing space of level 2534 and dimension 3 using T_5. (will stop at 728) Computing T_5 on dual space of dimension 3. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing characteristic polynomial of T_5. x^3 - 2*x^2 - 4*x + 8 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). Charpoly = x^2 + 14*x + 49. Decomposing space of level 2534 and dimension 2 using T_3. (will stop at 728) Computing characteristic polynomial of T_3. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Charpoly = x^2 + 4*x + 4. Decomposing space of level 2534 and dimension 2 using T_5. (will stop at 728) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing characteristic polynomial of T_5. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Charpoly = x^2 - 10*x + 25. Decomposing space of level 2534 and dimension 2 using T_11. (will stop at 728) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). Computing characteristic polynomial of T_11. x^2 - 3*x - 4 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_11), where f=x - 4. Cutting out subspace using f(T_11), where f=x + 1. Cutting out subspace using f(T_5), where f=x + 2. Cutting out subspace using f(T_3), where f=x + 3. Cutting out subspace using f(T_3), where f=x^2 + x - 5. Cutting out subspace using f(T_3), where f=x^2 + 2*x - 1. Cutting out subspace using f(T_3), where f=x^4 + x^3 - 4*x^2 - 4*x + 1. Cutting out subspace using f(T_3), where f=x^4 + 3*x^3 - 4*x^2 - 15*x - 7. Cutting out subspace using f(T_3), where f=x^6 + 3*x^5 - 9*x^4 - 29*x^3 + 5*x^2 + 28*x - 11. Cutting out subspace using f(T_3), where f=x^7 - x^6 - 13*x^5 + 9*x^4 + 53*x^3 - 10*x^2 - 73*x - 32. Cutting out subspace using f(T_3), where f=x^7 + 6*x^6 + 6*x^5 - 20*x^4 - 32*x^3 + 7*x^2 + 13*x - 1. Cutting out subspace using f(T_3), where f=x^10 - 8*x^9 + 10*x^8 + 68*x^7 - 197*x^6 + 8*x^5 + 426*x^4 - 292*x^3 - 123*x^2 + 72*x + 19. Cutting out subspace using f(T_3), where f=x^10 - 2*x^9 - 20*x^8 + 32*x^7 + 139*x^6 - 134*x^5 - 444*x^4 + 102*x^3 + 545*x^2 + 224*x + 25. Cutting out subspace using f(T_3), where f=x^14 - 6*x^13 - 14*x^12 + 137*x^11 - 9*x^10 - 1146*x^9 + 896*x^8 + 4455*x^7 - 4557*x^6 - 8788*x^5 + 8675*x^4 + 8927*x^3 - 5942*x^2 - 4053*x + 416. Cutting out subspace using f(T_3), where f=x^14 + 5*x^13 - 18*x^12 - 113*x^11 + 88*x^10 + 915*x^9 + 2*x^8 - 3283*x^7 - 776*x^6 + 5059*x^5 + 1071*x^4 - 2620*x^3 - 459*x^2 + 353*x + 47. J0( N: 2534 ) NewformDecomposition( M: Modular symbols space of level 2534, weight 2, and dimension... ) Decomposition_recurse( M: Modular symbols space of level 2534, weight 2, and dimension..., p: 3, stop: 728, proof: false, elliptic_only: false, random_op: true ) ModularSymbolsDual( M: Modular symbols space of level 2534, weight 2, and dimension..., V: Vector space of degree 368, dimension 14 over Rational Field ) In file "/home/was/modsym/modsym.m", line 548, column 4: >> assert V subset DualRepresentation(M); ^ Runtime error in assert: Assertion failed >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2534, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 1157.980 seconds Magma V2.7-1 Mon Jan 29 2001 11:06:27 on modular [Seed = 122188746] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2537 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.811 s) III. 3-term relations. Computing quotient by 880 relations. Form quot and then images (0.549 s) (total time to create space = 1.41 s) Computing cuspidal part of Full Modular symbols space of level 2537, weight 2, and dimension 222 Computing new part of Modular symbols space of level 2537, weight 2, and dimension 219. Computing 43-new part of Modular symbols space of level 2537, weight 2, and dimension 219. Computing space of modular symbols of level 59 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.02 s) III. 3-term relations. Computing quotient by 20 relations. Form quot and then images (0 s) (total time to create space = 0.031 s) Computing index-1 degeneracy map from level 2537 to 59. (0.069 s) Computing index-43 degeneracy map from level 2537 to 59. (1.511 s) Computing index-1 degeneracy map from level 59 to 2537. (0.849 s) Computing index-43 degeneracy map from level 59 to 2537. (1.04 s) Computing DualVectorSpace of Modular symbols space of level 2537, weight 2, and dimension 219. Computing complement of Modular symbols space of level 2537, weight 2, and dimension 219 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 222. (0.23 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2537, weight 2, and dimension 3 Computing 59-new part of Modular symbols space of level 2537, weight 2, and dimension 219. Computing space of modular symbols of level 43 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.011 s) III. 3-term relations. Computing quotient by 16 relations. Form quot and then images (0.009 s) (total time to create space = 0.021 s) Computing index-1 degeneracy map from level 2537 to 43. (0.049 s) Computing index-59 degeneracy map from level 2537 to 43. (2.27 s) Computing index-1 degeneracy map from level 43 to 2537. (0.921 s) Computing index-59 degeneracy map from level 43 to 2537. (0.989 s) Finding newform decomposition of Modular symbols space of level 2537, weight 2, and dimension 219. Computing cuspidal part of Modular symbols space of level 2537, weight 2, and dimension 219 Decomposing space of level 2537 and dimension 203 using T_2. (will stop at 440) Computing T_2 on dual space of dimension 203. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^203 - x^202 - 302*x^201 + 298*x^200 + 44851*x^199 - 43659*x^198 - 4366684*x^197 + 4192028*x^196 + 313483063*x^195 - 296709099*x^194 - 17697083882*x^193 + 16509405898*x^192 + 818192424735*x^191 - 752075502403*x^190 - 31858100968238*x^189 + 28844292567542*x^188 + 1066247346912114*x^187 - 950569680775130*x^186 - 31154097915650946*x^185 + 27338397253265998*x^184 + 804434160690337370*x^183 - 694575985287984950*x^182 - 18537470816538494038*x^181 + 15742871827828335922*x^180 + 384325051839686400943*x^179 - 320894457223564061475*x^178 - 7217033314272322205272*x^177 + 5922031882231448425664*x^176 + 123453276246408670790532*x^175 - 99511646637717911489244*x^174 - 1933054185883675146905064*x^173 + 1529949988408817309069376*x^172 + 27823192513005175690920772*x^171 - 21612063196359629281695460*x^170 - 369469009004250248197370878*x^169 + 281519549659729078158752270*x^168 + 4540948184060674760371708160*x^167 - 3392299516154144790914337904*x^166 - 51800758382817246737105705954*x^165 + 37919868043068331078271759130*x^164 + 549831324117673311913802166605*x^163 - 394183828312753440642832573413*x^162 - 5442376964066547877246795646944*x^161 + 3818925712198022203044525207344*x^160 + 50335116922463491450067275921190*x^159 - 34549364678402635460167227744910*x^158 - 435755944783864403637710093262220*x^157 + 292381365955964713399732595095356*x^156 + 3536647495931892845765084694935250*x^155 - 2318161687761157254342693651216054*x^154 - 26948344675331769132923185509060712*x^153 + 17243455477266363226910872396844376*x^152 + 193026476636472561698160402048524183*x^151 - 120484102245743532631799919419389863*x^150 - 1301194622718818660381353464088660822*x^149 + 791664317836511291734525158158677046*x^148 + 8263297865560596174070925327410590687*x^147 - 4896519215023176996176418339747604083*x^146 - 49482237944958587245662462424885387580*x^145 + 28533232100985589509266081818717410704*x^144 + 279632041646616030980732286169195280508*x^143 - 156772716073699800857172026335342039676*x^142 - 1492397460173521695394118925891288192204*x^141 + 812727877588841204274214338625589077236*x^140 + 7527049051069231838534909919931099945295*x^139 - 3977748545387240555718695817295161600575*x^138 - 35896938267890108934091901009041237028068*x^137 + 18389715049245665703487089472549175393376*x^136 + 161957669793536664250282273197459857836735*x^135 - 80344101887416238352578494191455518876263*x^134 - 691587866604224510982655420756336965706124*x^133 + 331848431993101775848615298596553351823072*x^132 + 2796135284511185497457527606659095824227756*x^131 - 1296190701001321987681560912295814090259664*x^130 - 10707094014034934679863180971928913621289280*x^129 + 4789061497447263933296313415929207330706772*x^128 + 38841948676244284454672306573430893495218884*x^127 - 16740437220702109102406714681082146975068428*x^126 - 133516970396047029470254562668986491814019424*x^125 + 55370040386366902718138693240197357330526784*x^124 + 434956473773974015618782848500817438247961328*x^123 - 173303075302332694591777106760340370059267996*x^122 - 1342997754748267509305569719412035330141816632*x^121 + 513296355512946287980729039796405293564509796*x^120 + 3930523103678408043182675439945378847664058696*x^119 - 1438610724510900047923635741635768965804320864*x^118 - 10903755131866949953841802047842259686614363424*x^117 + 3814960189548400354049713907030769380414710992*x^116 + 28670659221316690822878430421975804607231734216*x^115 - 9570668632870760462113115197208830393238749008*x^114 - 71449750446433945184280056748961600962240033434*x^113 + 22709587824598317516431255973847106638146176482*x^112 + 168737432572370237599024869030376840928362460926*x^111 - 50953580023576628456343627568590634657310604654*x^110 - 377569448348110604930334357529900679641433295966*x^109 + 108067773996446469090582232786648886907502287126*x^108 + 800322011677917497245133354562916388781975872280*x^107 - 216572844341487595560566834101044702465688809892*x^106 - 1606585258281406662956378461800898547001238573020*x^105 + 409920384842439010546926224381289207181201111220*x^104 + 3053395984490799908409871911998018176631481265028*x^103 - 732408650191274750330293668504729003609555328024*x^102 - 5492277707892369078639921280376257812353661738920*x^101 + 1234535006260825399096073544865115913667844711700*x^100 + 9346341738236066881610512274638104824369272042622*x^99 - 1961781576909848603470961739367692297850866564378*x^98 - 15040427684229915295221248542640527305100150876502*x^97 + 2936677516446170239135693924519198736527884268710*x^96 + 22876885567307097366636147141758251592346701658681*x^95 - 4137480132546966755475021904353052618631795733177*x^94 - 32871484694312907381663546039942236004114425765376*x^93 + 5480917414933644985221577835643133500388850359908*x^92 + 44593647293126574980925505777894142500429561262458*x^91 - 6818846812335231176222941240711537323112414809630*x^90 - 57079572957650570095181664230448026841811155809632*x^89 + 7956804656810213365565976074930436663316892787628*x^88 + 68887689972020837812649471472974092376677919046876*x^87 - 8695146437126798959149835410660994540480396478536*x^86 - 78330369593586033699085036641316330940687161731030*x^85 + 8882869052457244499002334239696508643618087933286*x^84 + 83848442100823719935593340340127686429514087024079*x^83 - 8465430743977961444560148324507954729802597953375*x^82 - 84422371741880857552768013898576045846905843177138*x^81 + 7506688234074093422674078293145275284853819281214*x^80 + 79874957540776858020711271982200169215618195570482*x^79 - 6173885860198707062005241427591552834955502876326*x^78 - 70944176394221615370183991651063816997245740301264*x^77 + 4690075460202482423660961471337806613527101315704*x^76 + 59088930627377798242434048966185354792622359670974*x^75 - 3272482342026026481703186189050070333604567630734*x^74 - 46097211126187083554303370299297303894062305656480*x^73 + 2080432645081298841157688200772316669925968945936*x^72 + 33641967898841311672456448259334546643361172427827*x^71 - 1190041464459282676297210440581766159599982342683*x^70 - 22937490131665681867633896374541551034026573721078*x^69 + 599238375243846595257382299114647250349646940874*x^68 + 14589656486396517860671588947064368752264816529826*x^67 - 253841164137029315241821227881827415086353511722*x^66 - 8643898613245090745075734152417542871821911708550*x^65 + 79585417882986688118018086853976511998183914050*x^64 + 4762338969796729747189875135838518268499898643941*x^63 - 7426382949239495376781896843444382377921988681*x^62 - 2435582943583455515083878112521914864570242915080*x^61 - 13488579626960895465501189418026975685999454520*x^60 + 1154047324810953791292590153736328604783031395391*x^59 + 13943990539379788897522305868819833459536280921*x^58 - 505571690422016582241019728931726202010457190554*x^57 - 9138545274891314431258259199372120289336675158*x^56 + 204318744339544149153553079142165033407336389071*x^55 + 4806274455767421973237558032614241157020632569*x^54 - 75988480719385886691606450285153638582202586858*x^53 - 2160964462967535136788473988925032691700754290*x^52 + 25939416841033985317961938620819232412409575157*x^51 + 851810649668061856176937109633354408953696443*x^50 - 8104110249696323674127516282014098958152915660*x^49 - 297837258397029083827941060371260384121084548*x^48 + 2310108493154251104005298797909938276521745024*x^47 + 92895462086855924605073738409926573791416436*x^46 - 598779198462015932511896252089441886709238058*x^45 - 25908144680056411475308226118654918185672982*x^44 + 140603016720788299456847130739702196809415608*x^43 + 6464414811856082636752078579895972458892076*x^42 - 29788309366727357505357843171926984263971568*x^41 - 1441990770400695833314993357645386264726224*x^40 + 5668564107296510202406717847178088969861255*x^39 + 287104928557826627001632651557975630294941*x^38 - 964113808051294708783390467641002092948220*x^37 - 50904784562985049654822085322434029895872*x^36 + 145758874233631724771764673974176907442510*x^35 + 8013567290635526916482931043185179148814*x^34 - 19469482131134930609819579840772098016014*x^33 - 1115962257906415338858851670681035666722*x^32 + 2282149230754964017514104182930597573993*x^31 + 136860473895901835951693899042872716055*x^30 - 232972488314315254468226231619313236018*x^29 - 14699719305510709122105100627054502282*x^28 + 20535664431863966090551021126955508337*x^27 + 1373298013612863410892131002591112923*x^26 - 1547748174560643072189787295680123432*x^25 - 110648466375856474483227342054061676*x^24 + 98615626110479384889317180846384060*x^23 + 7607960248089525777932552103686772*x^22 - 5240874199991828499740100855799376*x^21 - 440648756023741051917775031380320*x^20 + 228534660067406482792580971555336*x^19 + 21159429721847413067752290405728*x^18 - 8008497139693139259734591007008*x^17 - 826027478771148831390975311744*x^16 + 219318307292710555907866356208*x^15 + 25580965669565682996461712080*x^14 - 4507275463364024248673140576*x^13 - 608829906224303229872460224*x^12 + 65024787660813836515619008*x^11 + 10665204939513956986116672*x^10 - 573070457911432066965888*x^9 - 129086655912800824438528*x^8 + 1785936724495960425984*x^7 + 974734092228484563968*x^6 + 14958531030483888128*x^5 - 3795322919339851776*x^4 - 133945233114759168*x^3 + 4853399721689088*x^2 + 228033066074112*x time = 50.71 Factoring characteristic polynomial. [ , , , , , , , , ] time = 1.81 Cutting out subspace using f(T_2), where f=x - 2. Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.01 s). Charpoly = x^2 - 4*x + 4. Decomposing space of level 2537 and dimension 2 using T_2. (will stop at 440) Computing characteristic polynomial of T_2. x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.01 s). Charpoly = x^2 - 4*x + 4. Decomposing space of level 2537 and dimension 2 using T_3. (will stop at 440) Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^2 - x time = 0.001 Factoring characteristic polynomial. [ , ] time = 0.001 Cutting out subspace using f(T_3), where f=x - 1. Cutting out subspace using f(T_3), where f=x. Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x + 2. Cutting out subspace using f(T_2), where f=x^3 - 2*x^2 - 2*x + 2. Cutting out subspace using f(T_2), where f=x^41 + 7*x^40 - 29*x^39 - 303*x^38 + 200*x^37 + 5894*x^36 + 3371*x^35 - 68024*x^34 - 86485*x^33 + 517363*x^32 + 931318*x^31 - 2717619*x^30 - 6281294*x^29 + 9999923*x^28 + 29397764*x^27 - 25290466*x^26 - 99638824*x^25 + 40149342*x^24 + 249379634*x^23 - 23838267*x^22 - 464172468*x^21 - 55693809*x^20 + 641710992*x^19 + 176000270*x^18 - 653833752*x^17 - 251241676*x^16 + 484414320*x^15 + 222584328*x^14 - 256056364*x^13 - 129269603*x^12 + 94092791*x^11 + 49139590*x^10 - 23114098*x^9 - 11845059*x^8 + 3537080*x^7 + 1693703*x^6 - 289029*x^5 - 126372*x^4 + 7846*x^3 + 3770*x^2 + 60*x - 12. Cutting out subspace using f(T_2), where f=x^42 + 9*x^41 - 16*x^40 - 368*x^39 - 377*x^38 + 6603*x^37 + 15011*x^36 - 67236*x^35 - 227618*x^34 + 410205*x^33 + 2076763*x^32 - 1312362*x^31 - 12834478*x^30 - 538262*x^29 + 56458504*x^28 + 28323069*x^27 - 180566284*x^26 - 156056238*x^25 + 421182226*x^24 + 505317065*x^23 - 706193996*x^22 - 1115346790*x^21 + 815468074*x^20 + 1746120281*x^19 - 574750484*x^18 - 1950512194*x^17 + 125012124*x^16 + 1535187314*x^15 + 184569748*x^14 - 827202325*x^13 - 209472421*x^12 + 290443415*x^11 + 102753539*x^10 - 61045105*x^9 - 26884594*x^8 + 6484934*x^7 + 3614909*x^6 - 193861*x^5 - 218209*x^4 - 12562*x^3 + 3652*x^2 + 480*x + 16. Cutting out subspace using f(T_2), where f=x^52 - 10*x^51 - 34*x^50 + 650*x^49 - 242*x^48 - 19216*x^47 + 36131*x^46 + 339623*x^45 - 1005163*x^44 - 3943958*x^43 + 16219354*x^42 + 30671016*x^41 - 179883702*x^40 - 147479383*x^39 + 1467775451*x^38 + 216447604*x^37 - 9126619131*x^36 + 2973296931*x^35 + 44105794483*x^34 - 30452646021*x^33 - 167412192351*x^32 + 166745746800*x^31 + 501080493357*x^30 - 639064845560*x^29 - 1180666546858*x^28 + 1837765384300*x^27 + 2173341637556*x^26 - 4068592040887*x^25 - 3077396784325*x^24 + 6994891537530*x^23 + 3257295928381*x^22 - 9332883831078*x^21 - 2431975517057*x^20 + 9591200384979*x^19 + 1092827349022*x^18 - 7485886049736*x^17 - 70463951710*x^16 + 4342674304283*x^15 - 277612939195*x^14 - 1814432351390*x^13 + 207727865860*x^12 + 521523480691*x^11 - 78094741617*x^10 - 96329476718*x^9 + 16985347484*x^8 + 10298334254*x^7 - 2026319441*x^6 - 539586091*x^5 + 110281432*x^4 + 11970687*x^3 - 2362920*x^2 - 93684*x + 15938. Cutting out subspace using f(T_2), where f=x^60 - 3*x^59 - 95*x^58 + 285*x^57 + 4266*x^56 - 12788*x^55 - 120479*x^54 + 360512*x^53 + 2402003*x^52 - 7165693*x^51 - 35975156*x^50 + 106824399*x^49 + 420561442*x^48 - 1240545459*x^47 - 3936580206*x^46 + 11506365480*x^45 + 30031561547*x^44 - 86715644381*x^43 - 189106546217*x^42 + 537384669244*x^41 + 991874489982*x^40 - 2761155460409*x^39 - 4361397969749*x^38 + 11827347870906*x^37 + 16147290915509*x^36 - 42371276690509*x^35 - 50466239140894*x^34 + 127119029480545*x^33 + 133281403608068*x^32 - 319246832360492*x^31 - 297299927680413*x^30 + 669785550781136*x^29 + 558992666545980*x^28 - 1169634270244541*x^27 - 882731345367780*x^26 + 1691005473773664*x^25 + 1164409771197965*x^24 - 2009513057621437*x^23 - 1273476843540750*x^22 + 1944639927410648*x^21 + 1143403654123642*x^20 - 1514423300313148*x^19 - 832160820269238*x^18 + 934986991986920*x^17 + 483006716354186*x^16 - 448960310679583*x^15 - 218959519369247*x^14 + 163552772778796*x^13 + 75430029762262*x^12 - 43725792637185*x^11 - 19026801111228*x^10 + 8195784466431*x^9 + 3334268724379*x^8 - 1009768192184*x^7 - 375666626868*x^6 + 74759377098*x^5 + 24274634304*x^4 - 2963895740*x^3 - 781247152*x^2 + 48080880*x + 9314784. Computing representation of Modular symbols space of level 2537, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 2 Computing T_3 on space of dimension 222. (0.08 s) Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 2*x^2 - 2*x + 2 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 41. Goal dimension = 41. Computing T_2 on dual space of dimension 41. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^41 + 7*x^40 - 29*x^39 - 303*x^38 + 200*x^37 + 5894*x^36 + 3371*x^35 - 68024*x^34 - 86485*x^33 + 517363*x^32 + 931318*x^31 - 2717619*x^30 - 6281294*x^29 + 9999923*x^28 + 29397764*x^27 - 25290466*x^26 - 99638824*x^25 + 40149342*x^24 + 249379634*x^23 - 23838267*x^22 - 464172468*x^21 - 55693809*x^20 + 641710992*x^19 + 176000270*x^18 - 653833752*x^17 - 251241676*x^16 + 484414320*x^15 + 222584328*x^14 - 256056364*x^13 - 129269603*x^12 + 94092791*x^11 + 49139590*x^10 - 23114098*x^9 - 11845059*x^8 + 3537080*x^7 + 1693703*x^6 - 289029*x^5 - 126372*x^4 + 7846*x^3 + 3770*x^2 + 60*x - 12 p = %o, dimension = %o. 2 41 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 42. Goal dimension = 42. Computing T_2 on dual space of dimension 42. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^42 + 9*x^41 - 16*x^40 - 368*x^39 - 377*x^38 + 6603*x^37 + 15011*x^36 - 67236*x^35 - 227618*x^34 + 410205*x^33 + 2076763*x^32 - 1312362*x^31 - 12834478*x^30 - 538262*x^29 + 56458504*x^28 + 28323069*x^27 - 180566284*x^26 - 156056238*x^25 + 421182226*x^24 + 505317065*x^23 - 706193996*x^22 - 1115346790*x^21 + 815468074*x^20 + 1746120281*x^19 - 574750484*x^18 - 1950512194*x^17 + 125012124*x^16 + 1535187314*x^15 + 184569748*x^14 - 827202325*x^13 - 209472421*x^12 + 290443415*x^11 + 102753539*x^10 - 61045105*x^9 - 26884594*x^8 + 6484934*x^7 + 3614909*x^6 - 193861*x^5 - 218209*x^4 - 12562*x^3 + 3652*x^2 + 480*x + 16 p = %o, dimension = %o. 2 42 Computing representation of Modular symbols space of level 2537, weight 2, and dimension 50. Goal dimension = 50. Computing T_2 on dual space of dimension 50. T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^50 - 51/4*x^49 - 7/2*x^48 + 5527/8*x^47 - 45683/24*x^46 - 256301/16*x^45 + 3604763/48*x^44 + 1167347/6*x^43 - 71635487/48*x^42 - 23519773/24*x^41 + 114064033/6*x^40 - 168421663/24*x^39 - 1016236411/6*x^38 + 4350199157/24*x^37 + 26368817953/24*x^36 - 87501461489/48*x^35 - 126539971933/24*x^34 + 573904411489/48*x^33 + 894409361009/48*x^32 - 1365959173199/24*x^31 - 2245667010211/48*x^30 + 615126358543/3*x^29 + 586266964983/8*x^28 - 27380118428635/48*x^27 - 94773286529/4*x^26 + 29713651958027/24*x^25 - 10828146184969/48*x^24 - 50565969193967/24*x^23 + 17350401061471/24*x^22 + 45048447931969/16*x^21 - 30925795406147/24*x^20 - 5898806964305/2*x^19 + 4743401040655/3*x^18 + 7217354378107/3*x^17 - 67702266097019/48*x^16 - 36095366210507/24*x^15 + 7415884445483/8*x^14 + 16758559242353/24*x^13 - 21315467537909/48*x^12 - 10938920271335/48*x^11 + 1796080837699/12*x^10 + 765313062805/16*x^9 - 1595574813665/48*x^8 - 134205092147/24*x^7 + 210576004273/48*x^6 + 843912064/3*x^5 - 296913710*x^4 - 184322449/48*x^3 + 153063667/16*x^2 - 110669*x - 209275/2 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 122188746 Time to this point: 631.52 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2537, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 631.799 seconds Magma V2.7-1 Mon Jan 29 2001 11:27:07 on modular [Seed = 21915892] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2539 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.781 s) III. 3-term relations. Computing quotient by 848 relations. Form quot and then images (0.5 s) (total time to create space = 1.311 s) Computing cuspidal part of Full Modular symbols space of level 2539, weight 2, and dimension 212 Computing new part of Modular symbols space of level 2539, weight 2, and dimension 211. Computing 2539-new part of Modular symbols space of level 2539, weight 2, and dimension 211. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2539, weight 2, and dimension 211. Computing 2539-new part of Modular symbols space of level 2539, weight 2, and dimension 211. Computing cuspidal part of Modular symbols space of level 2539, weight 2, and dimension 211 Decomposing space of level 2539 and dimension 211 using T_2. (will stop at 424) Computing T_2 on dual space of dimension 211. Computing DualVectorSpace of Modular symbols space of level 2539, weight 2, and dimension 211. Computing complement of Modular symbols space of level 2539, weight 2, and dimension 211 Computing representation of Modular symbols space of level 2539, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 212. (0.509 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2539, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... 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(0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^211 - 315*x^209 + 2*x^208 + 48829*x^207 - 616*x^206 - 4965525*x^205 + 93344*x^204 + 372604576*x^203 - 9277032*x^202 - 22002756644*x^201 + 680178412*x^200 + 1064879728504*x^199 - 39235261194*x^198 - 43438142862061*x^197 + 1854459333646*x^196 + 1524265078440072*x^195 - 73857780902488*x^194 - 46732869885301471*x^193 + 2529781953755314*x^192 + 1267257938921409923*x^191 - 75688567189155882*x^190 - 30694743015574320243*x^189 + 2002368517942914002*x^188 + 669472214484855678816*x^187 - 47304041472173685506*x^186 - 13237444758668736287004*x^185 + 1006014570529539619750*x^184 + 238649853233549820553616*x^183 - 19390704301706602061554*x^182 - 3942101761264306328870098*x^181 + 340679878352818660631836*x^180 + 59915500702013831114777296*x^179 - 5482580996382196246988194*x^178 - 840994767710035141913570161*x^177 + 81160011224456487224129490*x^176 + 10936827361046149501355797750*x^175 - 1109208724496432683551991466*x^174 - 132150640314652565621067432204*x^173 + 14040976972357556221952019944*x^172 + 1487382229389556921758474788437*x^171 - 165092567894025941525600194944*x^170 - 15628834990368836025214279952706*x^169 + 1807576385135176727026251811478*x^168 + 153621747181997175257177335320829*x^167 - 18470435339132376149981477013966*x^166 - 1415082382155815490673716164070812*x^165 + 176496969809206810548772437055962*x^164 + 12235313535046910214871188512904929*x^163 - 1579991104840083516902698928627792*x^162 - 99445261614897348469066673383815775*x^161 + 13271722762834659582059749537264630*x^160 + 760777349838825671596288785680426875*x^159 - 104756955533285861388099573814082464*x^158 - 5484646200242531034202568110515847476*x^157 + 778012158072684284278254421611577416*x^156 + 37300968286357478068303767933162502068*x^155 - 5443106825494666012349695851572555974*x^154 - 239546326146242481155843020097086557161*x^153 + 35910616174321119329319895651869279856*x^152 + 1453894965726848458692075044558082026938*x^151 - 223628565174394864083350937544835186838*x^150 - 8346206218565425446629778110346415575841*x^149 + 1315622946485821837551648145130763726292*x^148 + 45348354776884404026006937469017260207916*x^147 - 7317599210980753793152818310277062972556*x^146 - 233357677843209581712497761706470788511245*x^145 + 38506770375598906136571761592064777005548*x^144 + 1137923057280587890420686015999408429120918*x^143 - 191823933473145942042988172016872534162628*x^142 - 5260758889414211553468235395422168006525099*x^141 + 905110439684458672108164577514600831684606*x^140 + 23068383060927305811385695027680420047012293*x^139 - 4047074844864181282500179581072507430826114*x^138 - 95980580235932514811462124691510218321695050*x^137 + 17155494339743721644765013916882059629085258*x^136 + 379042786520722696693506967030871151601484853*x^135 - 68967455482023424917089144213534188995669598*x^134 - 1421186556291054412090996110559457400174323717*x^133 + 263025124608763235128219160142444975312387864*x^132 + 5060232152359080732388350907354761051339677546*x^131 - 951859905198354877217029561638061618300543082*x^130 - 17112948318692163013182836394681747119567261580*x^129 + 3269345908909538828603249106577443687232707328*x^128 + 54976061783582039413824403625157405897135032874*x^127 - 10659318283701733335044179762588413459626297994*x^126 - 167786719814134439454689786388762582590006415383*x^125 + 32993431653929091480273727360256874362158687386*x^124 + 486518623817565380029532692620557365470893546356*x^123 - 96958195910154617341256802294716699892780720338*x^122 - 1340307550020924737563558449609588101081219887086*x^121 + 270527359319435226684735870183836873231539858924*x^120 + 3508007654646718646083820148273047199331662882500*x^119 - 716637780266816386578481359796074297515055182108*x^118 - 8722454369719729870349693725057144136092038226860*x^117 + 1802287635177061469896732235041729980706588113160*x^116 + 20601236586295566857353493826467066535015230157975*x^115 - 4302694511128311232637063601477626909993357475944*x^114 - 46212769370577105853041074181228003277037567866710*x^113 + 9749609262737828339645474306571589152339378031100*x^112 + 98438732093828965730349902595910777258998479944650*x^111 - 20964509014826358487688171725626727509433156438184*x^110 - 199071920722351941894357609706155145898308689592308*x^109 + 42769644931061960111618414508988575391013325036768*x^108 + 382104427216532217783833273478929469521795883717652*x^107 - 82760823278592413720242513444042996725329129543934*x^106 - 695910816818368457723959102856962626854544699391845*x^105 + 151851396924212870824047966039127258360696553291514*x^104 + 1202206473754713516853165849931082914121155454691192*x^103 - 264098448816318251085767131217276417498586787555378*x^102 - 1969227415898293057608543152277533677756992523401858*x^101 + 435206615996491192622705089370160645776408134808930*x^100 + 3057200838021148050707672407523991808923733756815572*x^99 - 679231887360897838324365714901137865620887990231388*x^98 - 4496405897690182765274360780066417304569982244141270*x^97 + 1003515962136343756805854577433553308531942681968046*x^96 + 6261875495994675870510064293497612904756181504987569*x^95 - 1402763951119992096365145327597010578148438823233108*x^94 - 8252888134585050154183930269897519772481860540551698*x^93 + 1854165582131490377555881706259414733553565191139982*x^92 + 10287647238313525887857667707180107600207484178413979*x^91 - 2316028121651114430209311891497623970350612561233946*x^90 - 12121624324383256228073493641427810030059800914549273*x^89 + 2731968584640629805247925861646493580260053273605012*x^88 + 13491048861062778109489636068625958245056915724857696*x^87 - 3041064692107177281667812206978402548030781031416946*x^86 - 14172774476339164603936734952624856101721949736848408*x^85 + 3191908547022353742960759453496876200518437230222786*x^84 + 14042686979483793019926321628685000026496376632211837*x^83 - 3156317587505734211166261830667495391861934889885870*x^82 - 13112046575474018933776735352638885627515435784597447*x^81 + 2937781740276459529710329014147667341404447304869000*x^80 + 11527370020270705311249230655697129844652091921311355*x^79 - 2571229422584094324287291650512158276275945992535174*x^78 - 9532760436997719741047013316993768977972023331106588*x^77 + 2113914456992309972453545191630942718914320539597464*x^76 + 7407956599695075269372642872219389546701552176884329*x^75 - 1630680400304657220425511879294506687292192796932028*x^74 - 5403860186512742943327349907430285712217332514580751*x^73 + 1178851431553535532916360403088664941382048884545572*x^72 + 3696075165163287297300604685781179577723685723350938*x^71 - 797615391308245553160684200313340604393051361438192*x^70 - 2367458407907357670239883537136692041453656824039780*x^69 + 504389369330480340853816560239757665864097455701554*x^68 + 1418304605195165012090899725637265849244398697583822*x^67 - 297662742215383551878905463846769178157768424092578*x^66 - 793611051903724648360234826151189149224772524944838*x^65 + 163669371358737632792550744347721496245037360960868*x^64 + 414156714517387928044239308633906495364957058177869*x^63 - 83702353386738479415845371835137733338889570781592*x^62 - 201264814315569576496522390496369932145858112186885*x^61 + 39738959413153186441611904616788546359040944421666*x^60 + 90928691172278679709995454417312763965685995184901*x^59 - 17478961832672469921618943087782028051988112746054*x^58 - 38124182423805368270978905621157572623515560835811*x^57 + 7106695119091700667175823778068743401271083704058*x^56 + 14806478908096645082674364941150171038923743800032*x^55 - 2664488581557424263155957017623137742435078643800*x^54 - 5315980573301385874688717280935693543325514037200*x^53 + 918730969296077681052944454770839399338534464154*x^52 + 1760603607696402645575351418184903237895283919358*x^51 - 290467615400709053556394905201152680613614344676*x^50 - 536640056325072990798379715187469387560608567386*x^49 + 83925345564719659597403742282495098552667454166*x^48 + 150164161147461016915813151651038367296204847885*x^47 - 22076587208478009509414540257347107137238513706*x^46 - 38471641062938453991430141035457727418224584471*x^45 + 5264078177283568284237007077963470782067539162*x^44 + 8997747715471361337468271107431631021174412271*x^43 - 1131985396080183836111648332154514094464076640*x^42 - 1914938055854662142541965941905377600546870906*x^41 + 218173782452234673426389124526272744655176666*x^40 + 369550540500636965253477037996757825397034235*x^39 - 37397730416976754466065766765469342194484750*x^38 - 64416478902931420583283298899802139125767090*x^37 + 5643402644547311738802231214914997302364274*x^36 + 10097936541660003817921012774662326499310432*x^35 - 738973073937425755995919329943829804488272*x^34 - 1416608387385212855150052834244414368806868*x^33 + 82088377213983308662095851279066823495298*x^32 + 176857425837786374535848195724541282123897*x^31 - 7419747189413074890217168521211656921874*x^30 - 19523681315792719368706421462562423052267*x^29 + 493106507149714932286204295936020945906*x^28 + 1891520591068336216270875838793648024501*x^27 - 14986387785353983415679030740674830230*x^26 - 159412758177442381954264689658913948523*x^25 - 1591829792541764779399718625675487618*x^24 + 11562980295094281305026174265453012807*x^23 + 328682165699628584469143578102859172*x^22 - 712481554865349140483646417895410554*x^21 - 33774432007309689151834927013242720*x^20 + 36685533124140409664002384449993955*x^19 + 2459334313910637239529728205396004*x^18 - 1545113381198792478058624246414372*x^17 - 135467394248533743580374309987200*x^16 + 51709954044821266541548952624096*x^15 + 5696616151288583821432617965048*x^14 - 1318357429462507826137650211280*x^13 - 180104863961762510942116419520*x^12 + 23909298270326108177498093184*x^11 + 4135124412035880400095603328*x^10 - 268386994789831059245284608*x^9 - 64979438464823112360519680*x^8 + 1111239096525035975803904*x^7 + 631721803622219106729984*x^6 + 10434630112569373020160*x^5 - 3142325276344621326336*x^4 - 122773770279466909696*x^3 + 5148055994107559936*x^2 + 285801734128205824*x + 1271643696660480 time = 5.931 Factoring characteristic polynomial. [ , , ] time = 1.269 Cutting out subspace using f(T_2), where f=x + 2. Cutting out subspace using f(T_2), where f=x^94 + 10*x^93 - 83*x^92 - 1138*x^91 + 2545*x^90 + 61928*x^89 - 6599*x^88 - 2143719*x^87 - 2285158*x^86 + 52956276*x^85 + 99878056*x^84 - 992282437*x^83 - 2548415458*x^82 + 14623534578*x^81 + 47142950122*x^80 - 173241449465*x^79 - 682494184420*x^78 + 1668518151287*x^77 + 8042889196293*x^76 - 13072730675934*x^75 - 79040006504474*x^74 + 82043587820625*x^73 + 658398996748648*x^72 - 391031351909259*x^71 - 4703268642109058*x^70 + 1147560073269284*x^69 + 29061113009700906*x^68 + 1199673822213615*x^67 - 156323048666312082*x^66 - 43902680012347793*x^65 + 735575956198142135*x^64 + 358635154826168093*x^63 - 3038572127768411104*x^62 - 2037713284479235066*x^61 + 11046847200267061306*x^60 + 9246001294634011493*x^59 - 35402308009103453891*x^58 - 35128163250862816861*x^57 + 100090742210917530520*x^56 + 114233048460699077260*x^55 - 249652788074976816934*x^54 - 321722097615324785620*x^53 + 548957317908465334351*x^52 + 790038861605224634604*x^51 - 1062506838613047513940*x^50 - 1698089544095852468406*x^49 + 1805757003391372661177*x^48 + 3200884386199735306252*x^47 - 2685363050958861792861*x^46 - 5294801673929534400125*x^45 + 3477386856314989842956*x^44 + 7682863901287860706073*x^43 - 3894712494403954775780*x^42 - 9766492123823026521297*x^41 + 3736550148632128479464*x^40 + 10854542103258111235539*x^39 - 3025901169177921112122*x^38 - 10518321224699148057183*x^37 + 2017718818366293215567*x^36 + 8856155310468964147808*x^35 - 1054068045709593300408*x^34 - 6452147943573569877186*x^33 + 375620094915899574898*x^32 + 4047643029327935613193*x^31 - 31253126544156428132*x^30 - 2174084630572235687119*x^29 - 73611541916014178180*x^28 + 993316780881236346561*x^27 + 67266107758545434001*x^26 - 383148370650518148951*x^25 - 36370994603227716198*x^24 + 123690923404049574165*x^23 + 14406407239042138709*x^22 - 33083043138014396117*x^21 - 4409437623698853303*x^20 + 7244257114684292455*x^19 + 1059386731420241288*x^18 - 1280282002550610865*x^17 - 199875433115729143*x^16 + 179456511699471635*x^15 + 29353615963192508*x^14 - 19517720663828233*x^13 - 3299020273420178*x^12 + 1600888973625093*x^11 + 276344490866475*x^10 - 95307512743016*x^9 - 16585313716796*x^8 + 3902305953719*x^7 + 671802241641*x^6 - 101371253906*x^5 - 16685906581*x^4 + 1459830905*x^3 + 213381822*x^2 - 8617700*x - 906664. Cutting out subspace using f(T_2), where f=x^116 - 12*x^115 - 108*x^114 + 1846*x^113 + 3956*x^112 - 136412*x^111 + 43842*x^110 + 6437279*x^109 - 11188018*x^108 - 217391221*x^107 + 608371242*x^106 + 5573804959*x^105 - 21002067608*x^104 - 112120874155*x^103 + 540287784244*x^102 + 1796774417170*x^101 - 11052827192619*x^100 - 22878368159861*x^99 + 186330670781551*x^98 + 223577831769386*x^97 - 2647878304870663*x^96 - 1456942253949732*x^95 + 32218423979117950*x^94 + 1141682982006555*x^93 - 339477613247017138*x^92 + 133749170486347673*x^91 + 3123532786070719681*x^90 - 2404282892599082666*x^89 - 25251621698115278245*x^88 + 28139508220725516721*x^87 + 180160373682183719037*x^86 - 260527637220923433480*x^85 - 1137632022847977794237*x^84 + 2027261758314208535160*x^83 + 6366452766550844419964*x^82 - 13631304368419945682586*x^81 - 31562848761268720378315*x^80 + 80431987273087281153024*x^79 + 138256655092399225548038*x^78 - 420477636170465908827321*x^77 - 531840298634709669761635*x^76 + 1959955531975836952911837*x^75 + 1774815480664254269675641*x^74 - 8181814230793383967340015*x^73 - 5009690744935450766045822*x^72 + 30682410221998230890975966*x^71 + 11251659827653664924065274*x^70 - 103582561619103399319676111*x^69 - 16195060753162670949833474*x^68 + 315239877707385848741017385*x^67 - 8704737105649839251940828*x^66 - 865545814988504730880910088*x^65 + 165931594519540134110091961*x^64 + 2144581801487664754641544288*x^63 - 731327158530208126662252227*x^62 - 4794019219990309153293477842*x^61 + 2299634544338935775840598628*x^60 + 9661885389667559082761916457*x^59 - 5907025263826887713336767034*x^58 - 17535812901226649330152890973*x^57 + 12967621942077731919562730583*x^56 + 28613543307573922022986259506*x^55 - 24824000849305787380755612216*x^54 - 41882695284403768616604078355*x^53 + 41862872649351619213452465264*x^52 + 54835305019928863363110403368*x^51 - 62525948579515850946370519985*x^50 - 63977761657674008207069402151*x^49 + 82930645802080653092121535190*x^48 + 66196129345875878935182388836*x^47 - 97768570272190794580303175953*x^46 - 60347564804198352726522309147*x^45 + 102423642632282311081175148671*x^44 + 48039858279673218231192520688*x^43 - 95237676921411912272088270280*x^42 - 32949817897992103241344092542*x^41 + 78448903710045305554896057846*x^40 + 19048892892399338284629213894*x^39 - 57095604785638900352100811130*x^38 - 8896528132815255047370674790*x^37 + 36597002501306476525630020504*x^36 + 3010296935602204012938835474*x^35 - 20579085690564538232505915882*x^34 - 414526166411159220879131300*x^33 + 10105665769972735291255488888*x^32 - 323072906420676751292913307*x^31 - 4310923740447640343437282016*x^30 + 323837716238054741998608925*x^29 + 1587832944818960722009264038*x^28 - 174682403567719463199164827*x^27 - 501462469036998972622409554*x^26 + 68734023351374159363894737*x^25 + 134705435891615224509407294*x^24 - 21074275496973333244673032*x^23 - 30494000907289274979448763*x^22 + 5125558247214065179988587*x^21 + 5754736262003673329569015*x^20 - 988093127043357504303851*x^19 - 893833186871541329924552*x^18 + 149147081384663037272279*x^17 + 112505999222218780313031*x^16 - 17223562421906866926355*x^15 - 11254742569169721932584*x^14 + 1464156340019285133692*x^13 + 872033238596731005784*x^12 - 85597577861314510280*x^11 - 50429535786764058184*x^10 + 2959909473426373200*x^9 + 2051965096811672064*x^8 - 30067437664527872*x^7 - 52763714252831488*x^6 - 1562995925868544*x^5 + 673149169976320*x^4 + 46715552934912*x^3 - 1494036144128*x^2 - 150595555328*x - 701276160. Computing representation of Modular symbols space of level 2539, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2539, weight 2, and dimension 94. Goal dimension = 94. Computing T_2 on dual space of dimension 94. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). %o x^94 + 10*x^93 - 83*x^92 - 1138*x^91 + 2545*x^90 + 61928*x^89 - 6599*x^88 - 2143719*x^87 - 2285158*x^86 + 52956276*x^85 + 99878056*x^84 - 992282437*x^83 - 2548415458*x^82 + 14623534578*x^81 + 47142950122*x^80 - 173241449465*x^79 - 682494184420*x^78 + 1668518151287*x^77 + 8042889196293*x^76 - 13072730675934*x^75 - 79040006504474*x^74 + 82043587820625*x^73 + 658398996748648*x^72 - 391031351909259*x^71 - 4703268642109058*x^70 + 1147560073269284*x^69 + 29061113009700906*x^68 + 1199673822213615*x^67 - 156323048666312082*x^66 - 43902680012347793*x^65 + 735575956198142135*x^64 + 358635154826168093*x^63 - 3038572127768411104*x^62 - 2037713284479235066*x^61 + 11046847200267061306*x^60 + 9246001294634011493*x^59 - 35402308009103453891*x^58 - 35128163250862816861*x^57 + 100090742210917530520*x^56 + 114233048460699077260*x^55 - 249652788074976816934*x^54 - 321722097615324785620*x^53 + 548957317908465334351*x^52 + 790038861605224634604*x^51 - 1062506838613047513940*x^50 - 1698089544095852468406*x^49 + 1805757003391372661177*x^48 + 3200884386199735306252*x^47 - 2685363050958861792861*x^46 - 5294801673929534400125*x^45 + 3477386856314989842956*x^44 + 7682863901287860706073*x^43 - 3894712494403954775780*x^42 - 9766492123823026521297*x^41 + 3736550148632128479464*x^40 + 10854542103258111235539*x^39 - 3025901169177921112122*x^38 - 10518321224699148057183*x^37 + 2017718818366293215567*x^36 + 8856155310468964147808*x^35 - 1054068045709593300408*x^34 - 6452147943573569877186*x^33 + 375620094915899574898*x^32 + 4047643029327935613193*x^31 - 31253126544156428132*x^30 - 2174084630572235687119*x^29 - 73611541916014178180*x^28 + 993316780881236346561*x^27 + 67266107758545434001*x^26 - 383148370650518148951*x^25 - 36370994603227716198*x^24 + 123690923404049574165*x^23 + 14406407239042138709*x^22 - 33083043138014396117*x^21 - 4409437623698853303*x^20 + 7244257114684292455*x^19 + 1059386731420241288*x^18 - 1280282002550610865*x^17 - 199875433115729143*x^16 + 179456511699471635*x^15 + 29353615963192508*x^14 - 19517720663828233*x^13 - 3299020273420178*x^12 + 1600888973625093*x^11 + 276344490866475*x^10 - 95307512743016*x^9 - 16585313716796*x^8 + 3902305953719*x^7 + 671802241641*x^6 - 101371253906*x^5 - 16685906581*x^4 + 1459830905*x^3 + 213381822*x^2 - 8617700*x - 906664 p = %o, dimension = %o. 2 94 Computing representation of Modular symbols space of level 2539, weight 2, and dimension 114. Computing complement of Modular symbols space of level 2539, weight 2, and dimension 114 Computing DualVectorSpace of Modular symbols space of level 2539, weight 2, and dimension 98. Goal dimension = 98. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). 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(0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). Computing T_2 on space of dimension 98. J0( N: 2539 ) NewformDecomposition( M: Modular symbols space of level 2539, weight 2, and dimension... ) !!( M: Full Modular symbols space of level 2539, weight 2, and dime..., x: Modular symbols space of level 2539, weight 2, and dimension... ) subset( M1: Modular symbols space of level 2539, weight 2, and dimension..., M2: Full Modular symbols space of level 2539, weight 2, and dime... ) Representation( M: Modular symbols space of level 2539, weight 2, and dimension... ) VectorSpace( M: Modular symbols space of level 2539, weight 2, and dimension... ) DualVectorSpace( M: Modular symbols space of level 2539, weight 2, and dimension... ) HeckeOperator( M: Modular symbols space of level 2539, weight 2, and dimension..., n: 2 ) Restrict( A: [0 0 0 0 0 -1 1 0 0 1 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 -1 1..., x: Vector space of degree 212, dimension 98 over Rational Field ) In file "/home/was/modsym/linalg.m", line 264, column 21: >> v := [Coordinates(S, S.i*A) : i in [1..#B]]; ^ Runtime error in 'Coordinates': Argument 2 is not in argument 1 >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2539, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 274.990 seconds Magma V2.7-1 Mon Jan 29 2001 11:36:06 on modular [Seed = 4256338469] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2542 and weight 2.... I. Manin symbols list. (0.06 s) II. 2-term relations. (1.261 s) III. 3-term relations. Computing quotient by 1344 relations. Form quot and then images (1.079 s) (total time to create space = 2.431 s) Computing cuspidal part of Full Modular symbols space of level 2542, weight 2, and dimension 340 Computing new part of Modular symbols space of level 2542, weight 2, and dimension 333. Computing 2-new part of Modular symbols space of level 2542, weight 2, and dimension 333. Computing space of modular symbols of level 1271 and weight 2.... I. Manin symbols list. (0.009 s) II. 2-term relations. (0.391 s) III. 3-term relations. Computing quotient by 448 relations. Form quot and then images (0.209 s) (total time to create space = 0.62 s) Computing index-1 degeneracy map from level 2542 to 1271. (1.979 s) Computing index-2 degeneracy map from level 2542 to 1271. (1.87 s) Computing index-1 degeneracy map from level 1271 to 2542. (1.09 s) Computing index-2 degeneracy map from level 1271 to 2542. (1 s) Computing DualVectorSpace of Modular symbols space of level 2542, weight 2, and dimension 333. Computing complement of Modular symbols space of level 2542, weight 2, and dimension 333 Computing representation of Modular symbols space of level 2542, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 340. (0.241 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 4256338469 Time to this point: 38.75 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2542, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 38.859 seconds Magma V2.7-1 Mon Jan 29 2001 11:37:23 on modular [Seed = 4222915702] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2543 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.781 s) III. 3-term relations. Computing quotient by 848 relations. Form quot and then images (0.509 s) (total time to create space = 1.341 s) Computing cuspidal part of Full Modular symbols space of level 2543, weight 2, and dimension 213 Computing new part of Modular symbols space of level 2543, weight 2, and dimension 212. Computing 2543-new part of Modular symbols space of level 2543, weight 2, and dimension 212. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2543, weight 2, and dimension 212. Computing 2543-new part of Modular symbols space of level 2543, weight 2, and dimension 212. Computing cuspidal part of Modular symbols space of level 2543, weight 2, and dimension 212 Decomposing space of level 2543 and dimension 212 using T_2. (will stop at 424) Computing T_2 on dual space of dimension 212. Computing DualVectorSpace of Modular symbols space of level 2543, weight 2, and dimension 212. Computing complement of Modular symbols space of level 2543, weight 2, and dimension 212 Computing representation of Modular symbols space of level 2543, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 213. (0.52 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2543, weight 2, and dimension 1 T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 4222915702 Time to this point: 6.49 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2543, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 6.530 seconds Magma V2.7-1 Mon Jan 29 2001 11:37:35 on modular [Seed = 4189492856] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2545 and weight 2.... I. Manin symbols list. (0.03 s) II. 2-term relations. (0.951 s) III. 3-term relations. Computing quotient by 1020 relations. Form quot and then images (0.719 s) (total time to create space = 1.72 s) Computing cuspidal part of Full Modular symbols space of level 2545, weight 2, and dimension 256 Computing new part of Modular symbols space of level 2545, weight 2, and dimension 253. Computing 5-new part of Modular symbols space of level 2545, weight 2, and dimension 253. Computing space of modular symbols of level 509 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.149 s) III. 3-term relations. Computing quotient by 170 relations. Form quot and then images (0.06 s) (total time to create space = 0.209 s) Computing index-1 degeneracy map from level 2545 to 509. (0.241 s) Computing index-5 degeneracy map from level 2545 to 509. (0.25 s) Computing index-1 degeneracy map from level 509 to 2545. (0.841 s) Computing index-5 degeneracy map from level 509 to 2545. (0.74 s) Computing DualVectorSpace of Modular symbols space of level 2545, weight 2, and dimension 253. Computing complement of Modular symbols space of level 2545, weight 2, and dimension 253 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 256. (0.269 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2545, weight 2, and dimension 3 Computing 509-new part of Modular symbols space of level 2545, weight 2, and dimension 253. Computing space of modular symbols of level 5 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0.001 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 2545 to 5. (0.051 s) Computing index-509 degeneracy map from level 2545 to 5. (75.61 s) Computing index-1 degeneracy map from level 5 to 2545. (5.7 s) Computing index-509 degeneracy map from level 5 to 2545. (5.179 s) Finding newform decomposition of Modular symbols space of level 2545, weight 2, and dimension 253. Computing cuspidal part of Modular symbols space of level 2545, weight 2, and dimension 253 Decomposing space of level 2545 and dimension 169 using T_2. (will stop at 510) Computing T_2 on dual space of dimension 169. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... 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T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing characteristic polynomial of T_2. x^169 + 3*x^168 - 246*x^167 - 742*x^166 + 29647*x^165 + 89929*x^164 - 2333186*x^163 - 7119138*x^162 + 134853921*x^161 + 414015063*x^160 - 6104056158*x^159 - 18861154134*x^158 + 225322955608*x^157 + 700943186212*x^156 - 6974565762876*x^155 - 21850485780396*x^154 + 184740722537888*x^153 + 583070679993316*x^152 - 4252367528818072*x^151 - 13525773438850196*x^150 + 86091728657355439*x^149 + 276079732417283081*x^148 - 1547957594351389040*x^147 - 5006738599192441404*x^146 + 24915074206439123509*x^145 + 81315788975907395379*x^144 - 361348270045459579850*x^143 - 1190594785034109780262*x^142 + 4748435908391665626316*x^141 + 15802950852193090584848*x^140 - 56803326174598189401480*x^139 - 191052533497302449669568*x^138 + 621068544865735681010823*x^137 + 2112375807301858720206233*x^136 - 6228017949348905082991666*x^135 - 21434671711863351148030054*x^134 + 57451904149645632910590949*x^133 + 200222752630559978652640267*x^132 - 488800475273135106088901000*x^131 - 1726299431957970818592760664*x^130 + 3844260964759917445503672085*x^129 + 13770078741755603818102005779*x^128 - 28002836665801320201009988208*x^127 - 101826784549815560845912167600*x^126 + 189252199985638477544758021117*x^125 + 699315282922381556969756117747*x^124 - 1188425026115177948179831544430*x^123 - 4467401809640210395252333977242*x^122 + 6942999023806137788998128194956*x^121 + 26583371794662819279904466921920*x^120 - 37777882185820765370951476162350*x^119 - 147525011716396634307236564887866*x^118 + 191618900563463433159906107515123*x^117 + 764332369326898119151325176301465*x^116 - 906720056649587407058866235486576*x^115 - 3700492982196339559682410971957508*x^114 + 4004959237640684016430936962441287*x^113 + 16754905118367900556743903483390037*x^112 - 16519709939418456981293039325984036*x^111 - 70994185713445017325638359151211352*x^110 + 63651597832465483014732112510264588*x^109 + 281674930730538355632997120983649452*x^108 - 229125805360698715858878167056646424*x^107 - 1046936606257100373965030082608898156*x^106 + 770513307000372197967926859605494174*x^105 + 3646701109826643307802678699123874566*x^104 - 2420100845986871545497242630565555836*x^103 - 11907188682177427976536204428857857744*x^102 + 7096625569092138912738575124129124801*x^101 + 36452890368143892641459422673247815183*x^100 - 19415589059315634750669155955513448742*x^99 - 104644628196947305257400675091570974982*x^98 + 49513015094031752457839106794614104939*x^97 + 281694307380022543672551155337309104081*x^96 - 117540840739739475148938924984878849608*x^95 - 711042460309347029460199592058196222616*x^94 + 259284806219888412886913703379078121826*x^93 + 1682737513347025419051885655299580679854*x^92 - 530158132877700747322450159446761446580*x^91 - 3732973243205294006596127752189904426516*x^90 + 1001281175504436706184081696489356452747*x^89 + 7760553339868898482881422975621889276617*x^88 - 1737880034539527102394806460669144377070*x^87 - 15113975442916662152583382175169478594682*x^86 + 2750506568367406942125923659330364086687*x^85 + 27563143008257668724953959434766663287589*x^84 - 3918766678118939968269813598020220437268*x^83 - 47046229566348756245417685062561223066072*x^82 + 4908223114950304519589217679058169863253*x^81 + 75112877310605726014589927670286018906183*x^80 - 5128385227171407502828465428534902809672*x^79 - 112100894995651917648377810859162203152308*x^78 + 3795457950071468949531025456241218181795*x^77 + 156272711748820612061223024499682301693577*x^76 - 143553539528692769588264013661862893950*x^75 - 203316045968058316863502086045474529943062*x^74 - 6239999974982498626398789309896051752211*x^73 + 246642601998550064395995404101135423185055*x^72 + 15074684913895265868349283713461955299796*x^71 - 278690112281091354811593396503482328665360*x^70 - 25225470556583774130097629597631256439592*x^69 + 292976851584975601290288197843189190758876*x^68 + 34871829477421120364891230250933449430010*x^67 - 286188742052571856026011679222506585292442*x^66 - 42015218413660593808941763537094578390868*x^65 + 259400811541624001529822232275693039970432*x^64 + 45143388423490496658155150648866979952506*x^63 - 217830299663032052439491875511554453326214*x^62 - 43754150325702849949482588108753826021081*x^61 + 169180718407624329387608888221700819245045*x^60 + 38489971391226563737743803128070992719770*x^59 - 121295764191578955651951573821044510456690*x^58 - 30831742834342599681454735026102698382681*x^57 + 80109877090575560098096037976469460503145*x^56 + 22523661772785145300723944961159342305948*x^55 - 48623564538019073263371345785651741702216*x^54 - 15012083487413721524960266328939492283521*x^53 + 27050362006864534107761293317671563342285*x^52 + 9124597104270425029837127680393672265076*x^51 - 13751604535503900761480631058013833970644*x^50 - 5052210409633443095242447697449354106897*x^49 + 6366220524958141378798800308790672501381*x^48 + 2544034688147643953687020173750004582698*x^47 - 2673033246439730323422084864841973791266*x^46 - 1162490541159505202064345320593189367112*x^45 + 1013076003322927888036018898298143855792*x^44 + 480734010525138967371650009497759755132*x^43 - 344563620232709115386917912753947678480*x^42 - 179330647690762204138541847216961826850*x^41 + 104404680392912281255403382773689893434*x^40 + 60111732301747835394462079551930708820*x^39 - 27915428604525472630757771590156700232*x^38 - 18023336374272954747119378902775093276*x^37 + 6499148885243496745384810419030737624*x^36 + 4807672140347654810613149667755135060*x^35 - 1290981404516136784102827903296906856*x^34 - 1133605473207066919010556512209759926*x^33 + 211111055046453730065694977097683966*x^32 + 234448448401916095348872511155153564*x^31 - 26248887999825216209908512576953820*x^30 - 42127231924997217023341659896692870*x^29 + 1854914285615647778889442962765782*x^28 + 6498725676892194677607876824385924*x^27 + 125824114708144788098656859339324*x^26 - 847457440731692046977089252830982*x^25 - 68186496838127186259610060944182*x^24 + 91464719809957363879705700312280*x^23 + 13046157137937331474176561109584*x^22 - 7919467516728260268877398079600*x^21 - 1680649611866003075401599612892*x^20 + 522007187018042256968344052816*x^19 + 159049988839316543460581137692*x^18 - 23392766399342346677487478732*x^17 - 11132112105521734800876546608*x^16 + 451630385869134713098424524*x^15 + 559208436548205723237344404*x^14 + 21330170122088601701626549*x^13 - 18801924781656609830165637*x^12 - 2001477854818395133268766*x^11 + 361338989086827993420002*x^10 + 69151942963147198723927*x^9 - 2052394909203815439611*x^8 - 1131439842202533280260*x^7 - 42275100744939514508*x^6 + 7066739637838202431*x^5 + 537680706530583089*x^4 - 9153695447557742*x^3 - 1558686187620782*x^2 - 26835574381355*x - 80810780925 time = 31.15 Factoring characteristic polynomial. [ , , , , , , , ] time = 0.859 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). Charpoly = x^4 + 8*x^3 + 24*x^2 + 32*x + 16. Decomposing space of level 2545 and dimension 4 using T_2. (will stop at 510) Computing characteristic polynomial of T_2. x^4 + 4*x^3 + 6*x^2 + 4*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). Charpoly = x^4 + 8*x^3 + 24*x^2 + 32*x + 16. Decomposing space of level 2545 and dimension 4 using T_3. (will stop at 510) Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^4 + 3*x^3 - 5*x^2 - 19*x - 12 time = 0 Factoring characteristic polynomial. [ , , ] time = 0.009 Cutting out subspace using f(T_3), where f=x + 1. Cutting out subspace using f(T_3), where f=x + 3. Cutting out subspace using f(T_3), where f=x^2 - x - 4. Cutting out subspace using f(T_2), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Charpoly = x^4 + 4*x^3 - 4*x^2 - 16*x + 16. Decomposing space of level 2545 and dimension 4 using T_2. (will stop at 510) Computing characteristic polynomial of T_2. x^4 + 2*x^3 - x^2 - 2*x + 1 time = 0.001 Factoring characteristic polynomial. [ ] time = 0.001 Cutting out subspace using f(T_2), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). Charpoly = x^4 + 6*x^3 - 9*x^2 - 54*x + 81. Decomposing space of level 2545 and dimension 4 using T_3. (will stop at 510) Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). Computing characteristic polynomial of T_3. x^4 + 4*x^3 + x^2 - 6*x - 4 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0 s). Charpoly = x^2 + 4*x - 1. Cutting out subspace using f(T_3), where f=x^2 + 2*x - 4. Cutting out subspace using f(T_2), where f=x^2 + 2*x - 1. Cutting out subspace using f(T_2), where f=x^3 - 3*x^2 - x + 5. Cutting out subspace using f(T_2), where f=x^35 + 7*x^34 - 31*x^33 - 309*x^32 + 296*x^31 + 6169*x^30 + 1207*x^29 - 73892*x^28 - 56409*x^27 + 593982*x^26 + 645415*x^25 - 3396312*x^24 - 4323610*x^23 + 14286559*x^22 + 19462462*x^21 - 45094923*x^20 - 61694353*x^19 + 107868745*x^18 + 139691592*x^17 - 195612828*x^16 - 224730514*x^15 + 265867636*x^14 + 251098030*x^13 - 263317854*x^12 - 186658264*x^11 + 180325312*x^10 + 86291420*x^9 - 78192349*x^8 - 22970113*x^7 + 18785717*x^6 + 3664252*x^5 - 2223234*x^4 - 360314*x^3 + 98993*x^2 + 17293*x + 269. Cutting out subspace using f(T_2), where f=x^36 - x^35 - 50*x^34 + 49*x^33 + 1133*x^32 - 1083*x^31 - 15411*x^30 + 14291*x^29 + 140487*x^28 - 125596*x^27 - 907598*x^26 + 776393*x^25 + 4284904*x^24 - 3475027*x^23 - 15026576*x^22 + 11417560*x^21 + 39399422*x^20 - 27611329*x^19 - 77148873*x^18 + 48796436*x^17 + 111905682*x^16 - 61906540*x^15 - 118413524*x^14 + 54617142*x^13 + 89248642*x^12 - 31740650*x^11 - 46215226*x^10 + 10973011*x^9 + 15515013*x^8 - 1721678*x^7 - 3030016*x^6 - 49621*x^5 + 265117*x^4 + 36006*x^3 - 1710*x^2 - 267*x - 1. Cutting out subspace using f(T_2), where f=x^42 - 5*x^41 - 51*x^40 + 286*x^39 + 1144*x^38 - 7497*x^37 - 14535*x^36 + 119388*x^35 + 108837*x^34 - 1290839*x^33 - 383891*x^32 + 10031341*x^31 - 1115522*x^30 - 57855373*x^29 + 23334135*x^28 + 252132138*x^27 - 157305404*x^26 - 837478219*x^25 + 668662179*x^24 + 2123748260*x^23 - 2002342291*x^22 - 4094430103*x^21 + 4373518989*x^20 + 5944439941*x^19 - 7031574545*x^18 - 6405548220*x^17 + 8289124728*x^16 + 5026702209*x^15 - 7073442239*x^14 - 2809558221*x^13 + 4279076623*x^12 + 1094105808*x^11 - 1779287848*x^10 - 293475154*x^9 + 485300946*x^8 + 55226836*x^7 - 80460232*x^6 - 7478702*x^5 + 7038088*x^4 + 617969*x^3 - 232061*x^2 - 13363*x + 1765. Cutting out subspace using f(T_2), where f=x^43 - 3*x^42 - 63*x^41 + 191*x^40 + 1824*x^39 - 5595*x^38 - 32195*x^37 + 100040*x^36 + 387588*x^35 - 1221457*x^34 - 3374148*x^33 + 10795265*x^32 + 21980712*x^31 - 71438312*x^30 - 109441129*x^29 + 361229715*x^28 + 422025530*x^27 - 1412088609*x^26 - 1270997889*x^25 + 4291080468*x^24 + 3005990510*x^23 - 10143048007*x^22 - 5607200936*x^21 + 18579981457*x^20 + 8286518963*x^19 - 26163367315*x^18 - 9750465986*x^17 + 27958866277*x^16 + 9164140379*x^15 - 22250148517*x^14 - 6846994222*x^13 + 12833064070*x^12 + 3981065762*x^11 - 5152065579*x^10 - 1723401875*x^9 + 1348872648*x^8 + 517685975*x^7 - 203042025*x^6 - 96979262*x^5 + 12074006*x^4 + 9402628*x^3 + 404795*x^2 - 291527*x - 34041. Computing representation of Modular symbols space of level 2545, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 4 Computing T_3 on space of dimension 256. (0.1 s) Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x + 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^2 - x - 4 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 2. Goal dimension = 2. %o x^2 + x - 1 p = %o, dimension = %o. 2 4 %o x^2 + 2*x + 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^2 + x - 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^2 + 2*x - 4 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^2 + 2*x - 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 3*x^2 - x + 5 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 2545, weight 2, and dimension 35. Goal dimension = 35. Computing T_2 on dual space of dimension 35. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^35 + 7*x^34 - 31*x^33 - 309*x^32 + 296*x^31 + 6169*x^30 + 1207*x^29 - 73892*x^28 - 56409*x^27 + 593982*x^26 + 645415*x^25 - 3396312*x^24 - 4323610*x^23 + 14286559*x^22 + 19462462*x^21 - 45094923*x^20 - 61694353*x^19 + 107868745*x^18 + 139691592*x^17 - 195612828*x^16 - 224730514*x^15 + 265867636*x^14 + 251098030*x^13 - 263317854*x^12 - 186658264*x^11 + 180325312*x^10 + 86291420*x^9 - 78192349*x^8 - 22970113*x^7 + 18785717*x^6 + 3664252*x^5 - 2223234*x^4 - 360314*x^3 + 98993*x^2 + 17293*x + 269 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 4189492856 Time to this point: 561.24 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2545, a, ^ User error: Identifier 'a' has not been declared or assigned Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 4189492856 Time to this point: 561.42 Segmentation fault Magma V2.7-1 Mon Jan 29 2001 11:55:57 on modular [Seed = 4089222080] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2546 and weight 2.... I. Manin symbols list. (0.06 s) II. 2-term relations. (1.271 s) III. 3-term relations. Computing quotient by 1360 relations. Form quot and then images (1.109 s) (total time to create space = 2.481 s) Computing cuspidal part of Full Modular symbols space of level 2546, weight 2, and dimension 344 Computing new part of Modular symbols space of level 2546, weight 2, and dimension 337. Computing 2-new part of Modular symbols space of level 2546, weight 2, and dimension 337. Computing space of modular symbols of level 1273 and weight 2.... I. Manin symbols list. (0.011 s) II. 2-term relations. (0.4 s) III. 3-term relations. Computing quotient by 456 relations. Form quot and then images (0.209 s) (total time to create space = 0.631 s) Computing index-1 degeneracy map from level 2546 to 1273. (2.01 s) Computing index-2 degeneracy map from level 2546 to 1273. (1.91 s) Computing index-1 degeneracy map from level 1273 to 2546. (1.07 s) Computing index-2 degeneracy map from level 1273 to 2546. (0.75 s) Computing DualVectorSpace of Modular symbols space of level 2546, weight 2, and dimension 337. Computing complement of Modular symbols space of level 2546, weight 2, and dimension 337 Computing representation of Modular symbols space of level 2546, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 344. (0.25 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 64 Computing T_3 on space of dimension 344. (0.17 s) J0( N: 2546 ) NewformDecomposition( M: Modular symbols space of level 2546, weight 2, and dimension... ) IsNew( M: Modular symbols space of level 2546, weight 2, and dimension... ) NewSubspace( M: Modular symbols space of level 2546, weight 2, and dimension... ) NewSubspace( M: Modular symbols space of level 2546, weight 2, and dimension..., p: 2 ) DualVectorSpace( M: Modular symbols space of level 2546, weight 2, and dimension... ) VectorSpace( M: Modular symbols space of level 2546, weight 2, and dimension... ) Restrict( A: [4 -4 4 0 0 0 -4 0 4 0 0 -2 2 -4 2 -2 0 0 4 0 -4 2 2 -4 4 0 ..., x: Vector space of degree 344, dimension 64 over Rational Field ) In file "/home/was/modsym/linalg.m", line 264, column 21: >> v := [Coordinates(S, S.i*A) : i in [1..#B]]; ^ Runtime error in 'Coordinates': Argument 2 is not in argument 1 >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2546, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 42.369 seconds Magma V2.7-1 Mon Jan 29 2001 11:57:20 on modular [Seed = 4055798063] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2549 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.771 s) III. 3-term relations. Computing quotient by 850 relations. Form quot and then images (0.509 s) (total time to create space = 1.31 s) Computing cuspidal part of Full Modular symbols space of level 2549, weight 2, and dimension 213 Computing new part of Modular symbols space of level 2549, weight 2, and dimension 212. Computing 2549-new part of Modular symbols space of level 2549, weight 2, and dimension 212. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2549, weight 2, and dimension 212. Computing 2549-new part of Modular symbols space of level 2549, weight 2, and dimension 212. Computing cuspidal part of Modular symbols space of level 2549, weight 2, and dimension 212 Decomposing space of level 2549 and dimension 212 using T_2. (will stop at 425) Computing T_2 on dual space of dimension 212. Computing DualVectorSpace of Modular symbols space of level 2549, weight 2, and dimension 212. Computing complement of Modular symbols space of level 2549, weight 2, and dimension 212 Computing representation of Modular symbols space of level 2549, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 213. (0.511 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0.001 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2549, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing characteristic polynomial of T_2. x^212 + 2*x^211 - 316*x^210 - 630*x^209 + 49140*x^208 + 97656*x^207 - 5013113*x^206 - 9930440*x^205 + 377380652*x^204 + 745117632*x^203 - 22356390498*x^202 - 43996509010*x^201 + 1085480895515*x^200 + 2129106023902*x^199 - 44421542330647*x^198 - 86838984762148*x^197 + 1563821486619416*x^196 + 3046785735699962*x^195 - 48101290076747043*x^194 - 93397009996458258*x^193 + 1308609071594260530*x^192 + 2532187415196530654*x^191 - 31799644963432758703*x^190 - 61320592912198036260*x^189 + 695835476294161407090*x^188 + 1337142366225794756982*x^187 - 13803711907113748350335*x^186 - 26432804770760493479878*x^185 + 249673318838615974497637*x^184 + 476415098168052785180852*x^183 - 4137700375480583134883433*x^182 - 7867354295831699503807164*x^181 + 63094438462541856446955212*x^180 + 119538524326061191109581714*x^179 - 888516811765077883603093053*x^178 - 1677340007236709112468148330*x^177 + 11592664183160024876141293718*x^176 + 21805677340614562548709021848*x^175 - 140533217540562878021680822200*x^174 - 263383888513950924195676454180*x^173 + 1586892536403602939419137873370*x^172 + 2963299286541931063790768054372*x^171 - 16728737212627838285638080018860*x^170 - 31124601216032426969960020229386*x^169 + 164966669887689078557792977132532*x^168 + 305805568204031830911050802043608*x^167 - 1524496113855525087584442186069450*x^166 - 2815665797600650118988424025679082*x^165 + 13223718936720918376377698181222211*x^164 + 24333933172056097669788700711723050*x^163 - 107822123602317707482178150928218505*x^162 - 197683392321266863959833095227961344*x^161 + 827477923117165111993073354727159600*x^160 + 1511553422879029104115611577905549166*x^159 - 5984261149446019604340912319521608212*x^158 - 10891437588981146504561144606044374552*x^157 + 40825470878057593538161662300395518171*x^156 + 74031751586667153161678975529452211168*x^155 - 262986692779353381214710985662686985575*x^154 - 475159301199204663596266223390025172616*x^153 + 1601002903451618283160489734906712164293*x^152 + 2882204474407874228456303660299354795800*x^151 - 9218115505652180596728359959139546134627*x^150 - 16535329300844405780062973896791499337202*x^149 + 50232505971719340105334012411622350273852*x^148 + 89785634977495825400169246052646142881352*x^147 - 259232195713084308183094674487523001481349*x^146 - 461719479807307829319352740358410083546512*x^145 + 1267631934485393152397796244742619193969806*x^144 + 2249927335751288036813135383773312397387626*x^143 - 5876358746811991924598782470217163952250037*x^142 - 10394213303611547529029887576868284170239636*x^141 + 25835616331004359999031830326942220728183324*x^140 + 45544452483596687599709837031356273440165032*x^139 - 107766675903810637822057967522019858529766869*x^138 - 189349208763582411513797837840196332452416640*x^137 + 426620344045325592527313736272324074433202713*x^136 + 747163982084628468227793676402253054053199834*x^135 - 1603260102345523743446634489174946875248385148*x^134 - 2799052636303131245768234116254181280413924622*x^133 + 5720899355115460196498769486761696342571437887*x^132 + 9957405262078577611833742745932062678782286544*x^131 - 19386281117061726171389018065439552337245949944*x^130 - 33643285856177986553304736467208855801636011572*x^129 + 62394551433514354337305213091257461587462504418*x^128 + 107975551823546232531901594786235997349163772012*x^127 - 190745167502445694647935749790500963873700690932*x^126 - 329204790848698708077556760528008909861899062646*x^125 + 553896991688694113759224712981443438425781543040*x^124 + 953544846149012633551113613032708634799330381870*x^123 - 1527806585600003482784189940218134116250256137749*x^122 - 2623934758654458493912590744142334406398210437464*x^121 + 4002659753766718593155600539374101589260958561942*x^120 + 6859413119009486269986492055996758669156040064902*x^119 - 9959298430516752124802537617745210673561849497166*x^118 - 17033764281793281663503368197106713253601282693672*x^117 + 23531484126934354167314863147452688668185018674494*x^116 + 40176728772515225628651888139852865429111812665080*x^115 - 52787724573458124418054104016212625015577400009473*x^114 - 89993711353754554337233837915248336630566420844722*x^113 + 112404536211971857496748985884111828242170107414155*x^112 + 191398988685492463431017678845284734764417915551088*x^111 - 227136877662511718332713498359776505119638711657595*x^110 - 386416811327569784138461761821216513765390866285306*x^109 + 435422726590729045526417096506730515884874085501241*x^108 + 740359939364579159554561368577732519205021682213480*x^107 - 791592136868153382556544747625418332745148836634296*x^106 - 1345749874473406298613048115102458967044013005029180*x^105 + 1364225319669798205771120253423667129248812465100659*x^104 + 2319884772992467364613028273613407688435546484791894*x^103 - 2227776415419589499263984354202280966037447057864850*x^102 - 3791201746291373745207065360511219466755022797755382*x^101 + 3445426469719648658314739672183193858568075640172703*x^100 + 5870901676241403009879188966921665666902607373151860*x^99 - 5043855837160105630624699303158497755262723918923764*x^98 - 8610727476284274752896603953948009865317773191563904*x^97 + 6985044869373298426883000129708162504780398773100627*x^96 + 11955059698029529197569264415811786361524849670221556*x^95 - 9144834525424909499258273243736541564996775432467776*x^94 - 15703251254264847125373984036711113716304457151957854*x^93 + 11310162903610954380236150405005685322906544172440000*x^92 + 19502077681452951957486876715345824963468758001660648*x^91 - 13203996886204717164854009529947809709406777504612141*x^90 - 22883937687324448526408257320441405474913909423261672*x^89 + 14538219370902082119612219098324808202950330062789331*x^88 + 25352500837214994411985144429020672277911398654183476*x^87 - 15082648112333449089907047001016836655382364602550121*x^86 - 26497686538827144418232942679358780379593362987009536*x^85 + 14728482171538150182508697312846173138013128364200613*x^84 + 26104967264719434366566750625161281779128835775220634*x^83 - 13522708132488854717302080238257338149878498541184744*x^82 - 24219762001851692436197540596513054554417381745945170*x^81 + 11658924048260566202465024087707281836417882439288291*x^80 + 21140852577459330975222665922166029807452496145713852*x^79 - 9426536849203900082489575611227673579171365106443783*x^78 - 17343010707679100478077748298477129792146186516941138*x^77 + 7136611974678100449902101404151595675817395186195155*x^76 + 13356305547196898843503606960305524581142789510311478*x^75 - 5050706966325005770072660563635692780617192249749752*x^74 - 9644579422965909296466906472250018462904510884577030*x^73 + 3335174573149959161171118041905602789370697817347102*x^72 + 6521578893293060483784763592411801841254086669928628*x^71 - 2050548162987776638738092589825354239969798324754460*x^70 - 4123741490151004844442412901381623731682350276250706*x^69 + 1170981962845102363622912213493095571884387871543174*x^68 + 2434737157571742688169083036226883972917616064003408*x^67 - 619339287512871247606020691020369922715849570203857*x^66 - 1340108019555068066027114021146505201964257965734736*x^65 + 302371467898344017204107813057361055261703499590883*x^64 + 686448320206474771093542235845900215535646978212448*x^63 - 135704885124097123171453763433334765108600712899419*x^62 - 326627532663309564864273963350890494368820632110490*x^61 + 55695595823847882821057831426610781252602555197689*x^60 + 144081765423665953005537138279500408224830729347154*x^59 - 20758381293028227354237101793503752344329912856070*x^58 - 58795258229967500824563149065455177907832667857280*x^57 + 6956956089188430652241807272466624555464412684760*x^56 + 22143296644513419151144821777517900172734052363434*x^55 - 2064553688054107905544040119496196940916438308339*x^54 - 7677390972994202512621283640434801247553039565876*x^53 + 527977054572721528990186007739781351018581102794*x^52 + 2443800509595100887990256946314127093736853131304*x^51 - 109704427595548811638943501643201613284281830138*x^50 - 712032720171659299127732750976654704658308797894*x^49 + 15350313535696590499309347922181420905603060667*x^48 + 189275593066229995270924463736908892407898827978*x^47 + 240324518899466094542207087949741380859489727*x^46 - 45738995743999229689224956765244619672264350490*x^45 - 1081346213614552149411713369359237917660809930*x^44 + 10008031303374908484066312416469970258289693038*x^43 + 456506995551895366542883769746117795239877030*x^42 - 1974062230213079950836902014938461014212442468*x^41 - 132768413132293818654831366836343230797946224*x^40 + 349281013151695007664203359244313849088689178*x^39 + 30966562867876129960851756726187859276973318*x^38 - 55127546812168340876888762760060824435075140*x^37 - 6060606966845313743078840221813576154406122*x^36 + 7712327236160491952650480844512362646554092*x^35 + 1012329327948769290331649468890530941622023*x^34 - 949412683296177385566878100051706846128382*x^33 - 145131810087863920056148959801169951335001*x^32 + 101972703430579722646714879647125962167308*x^31 + 17855501282867457149594011577785149002682*x^30 - 9460196929512189746858414738625419075278*x^29 - 1877962620227053796342813208935774802246*x^28 + 748896557528009013025584966045968249618*x^27 + 167732969727189212964280143625364984438*x^26 - 49829812950118269123263087602684463506*x^25 - 12605723056497170662652992483176489827*x^24 + 2732920785467269902934155021048341888*x^23 + 787760864838110794950121938008160014*x^22 - 120280530877778075249699833362244846*x^21 - 40334083241608733976441489863402010*x^20 + 4078450744027430215753931831439610*x^19 + 1661233827723852027844799450987777*x^18 - 98883776235185000205230852569526*x^17 - 53795250123461983683914764452773*x^16 + 1400854226276123655360602128632*x^15 + 1330665863139656911972136104065*x^14 + 985001504735421080778743838*x^13 - 24217380290181705993820222788*x^12 - 530965969498769443899649128*x^11 + 308230718688666457670045861*x^10 + 11854616433192938068455522*x^9 - 2550183537946536450131889*x^8 - 130905421063294921357796*x^7 + 12224550112807673858605*x^6 + 761293917761673934816*x^5 - 27305919463164555729*x^4 - 2136205206486482548*x^3 + 9927705060334402*x^2 + 2269774576615364*x + 32086033319587 time = 5.899 Factoring characteristic polynomial. [ , ] time = 1.08 Cutting out subspace using f(T_2), where f=x^89 + 5*x^88 - 105*x^87 - 556*x^86 + 5250*x^85 + 29698*x^84 - 166123*x^83 - 1014842*x^82 + 3726712*x^81 + 24931457*x^80 - 62864571*x^79 - 469118348*x^78 + 823840864*x^77 + 7033640977*x^76 - 8517442868*x^75 - 86316057173*x^74 + 69339217672*x^73 + 883796538771*x^72 - 430695386803*x^71 - 7658509398482*x^70 + 1803027344818*x^69 + 56775811858036*x^68 - 1708423208019*x^67 - 363103085234446*x^66 - 50974872181019*x^65 + 2016295772904349*x^64 + 572849176768223*x^63 - 9770457125942826*x^62 - 3975328517780589*x^61 + 41474631658608733*x^60 + 21273451962315225*x^59 - 154670487893099651*x^58 - 93647267198615462*x^57 + 507787941569631602*x^56 + 348808307377035240*x^55 - 1469562651227138866*x^54 - 1115657120740929434*x^53 + 3751685268295631425*x^52 + 3090316448853274339*x^51 - 8449745636113283768*x^50 - 7450006692935648496*x^49 + 16782140682589249412*x^48 + 15674152501406627136*x^47 - 29364154447066725607*x^46 - 28813952011159122768*x^45 + 45197425868966305065*x^44 + 46281905804100575867*x^43 - 61077317165591059027*x^42 - 64889404483675770058*x^41 + 72284950639553990673*x^40 + 79262204303385902128*x^39 - 74703365822315300221*x^38 - 84118938235263921764*x^37 + 67185499033507956837*x^36 + 77284371241686645006*x^35 - 52381412346427238121*x^34 - 61193943514597092820*x^33 + 35252120423571279306*x^32 + 41531333067943879155*x^31 - 20383180211579293594*x^30 - 24002862251700523183*x^29 + 10075182086295643367*x^28 + 11722272591063180120*x^27 - 4234252585138587997*x^26 - 4793447613621786631*x^25 + 1504041025016153310*x^24 + 1623516781347874816*x^23 - 448448857193198302*x^22 - 449576139924103050*x^21 + 111277294918174731*x^20 + 100198312131419260*x^19 - 22716489489748141*x^18 - 17626786627608108*x^17 + 3754581902807951*x^16 + 2387298726832355*x^15 - 491326626759363*x^14 - 240674249450195*x^13 + 49356284819951*x^12 + 17191413260172*x^11 - 3643836065004*x^10 - 801312501830*x^9 + 185124408253*x^8 + 20465569554*x^7 - 5776032551*x^6 - 135937039*x^5 + 85841418*x^4 - 3343907*x^3 - 173378*x^2 + 5681*x + 169. Cutting out subspace using f(T_2), where f=x^123 - 3*x^122 - 196*x^121 + 591*x^120 + 18687*x^119 - 56648*x^118 - 1154925*x^117 + 3520648*x^116 + 52024385*x^115 - 159520739*x^114 - 1820850919*x^113 + 5617606865*x^112 + 51549172811*x^111 - 160066034133*x^110 - 1213416609520*x^109 + 3793418119742*x^108 + 24227560913134*x^107 - 76282715464820*x^106 - 416547672834331*x^105 + 1321415736733155*x^104 + 6239678780489343*x^103 - 19951193716593668*x^102 - 82195203602573201*x^101 + 265014859575587362*x^100 + 959372904789933896*x^99 - 3120511767855463567*x^98 - 9983048430378901434*x^97 + 32773793364740347379*x^96 + 93086676023073271284*x^95 - 308603179217614012739*x^94 - 781092340563446879046*x^93 + 2616393194285613700964*x^92 + 5918965126094511834614*x^91 - 20044134317181228367392*x^90 - 40625920031685363666282*x^89 + 139172615480348405438747*x^88 + 253190214742800594999799*x^87 - 877990527994580875996319*x^86 - 1435709341852263412518900*x^85 + 5043126979617601907344209*x^84 + 7419816276535332096149418*x^83 - 26419782479291065901050189*x^82 - 34996021275553858734824551*x^81 + 126410290297777750977509160*x^80 + 150803467388112928257736123*x^79 - 553016545927949618725840361*x^78 - 594194391464663646063741489*x^77 + 2213913334925004786521396332*x^76 + 2142040701363998139503837839*x^75 - 8115380880686166884473789296*x^74 - 7067657022622205565185225669*x^73 + 27248571152504759995110149557*x^72 + 21347941156047734579411576255*x^71 - 83817137278364266784314396284*x^70 - 59030841522945723105024694437*x^69 + 236186273878271946126473630172*x^68 + 149412672505856908299677715550*x^67 - 609538112913259923100672267144*x^66 - 346071850953572782833129967041*x^65 + 1440049554110356205590790431685*x^64 + 733249725792211655182287152440*x^63 - 3112466549795656001926683284016*x^62 - 1420507943447885677548486817571*x^61 + 6149165188765653008986058452540*x^60 + 2514881827971298588181753967548*x^59 - 11093184806447466014324277871632*x^58 - 4066707896289517989237234307543*x^57 + 18250580933952445661505450854286*x^56 + 6003463153322985563848055907364*x^55 - 27342086350094509238959494027092*x^54 - 8087421995971784124727717575827*x^53 + 37236707620638381406053375167505*x^52 + 9938892630149828362125276950359*x^51 - 46008019850346638821623071775798*x^50 - 11141003013974169779186266705193*x^49 + 51455759432785674669497763225853*x^48 + 11391343429648839865859405434558*x^47 - 51958060888714299664621628042550*x^46 - 10625106174329711229740200952794*x^45 + 47230167180599318811420901576695*x^44 + 9040799910177374428394978078733*x^43 - 38520466444679451811752211355063*x^42 - 7015211472821950398341640861104*x^41 + 28082155213909127702793585850816*x^40 + 4958390276878861527951176225293*x^39 - 18220840810091437142615331561943*x^38 - 3184719908611058032837139792246*x^37 + 10470468066647565566973454036242*x^36 + 1851289919899746466432420695090*x^35 - 5298533997070231103447284085988*x^34 - 968180241207326676170114215082*x^33 + 2345650682410223049776306026301*x^32 + 451922070644867352823167227302*x^31 - 901360861357514048518198654695*x^30 - 186438218038852524506998568333*x^29 + 297847295795443656371737334274*x^28 + 67200571193540788124215478757*x^27 - 83666877030931117766017417621*x^26 - 20887039251220923461141374135*x^25 + 19690255185082038329781471800*x^24 + 5515457734571078455124691516*x^23 - 3808116853859860513867286071*x^22 - 1216348910070167075241226198*x^21 + 588961096996226015872773220*x^20 + 219544795926063539652100422*x^19 - 69786777449180369853940286*x^18 - 31634022843050768848946037*x^17 + 5840889469569783614763642*x^16 + 3522799563866450364958698*x^15 - 273983217038616770727186*x^14 - 289821493736781337323471*x^13 - 2693027580474623866691*x^12 + 16433978914769589387598*x^11 + 1380052301013555246291*x^10 - 566036912016073489476*x^9 - 90565639256345757016*x^8 + 8410493260470307039*x^7 + 2587327779459341865*x^6 + 53753724059377718*x^5 - 27240517247913566*x^4 - 2210058236860112*x^3 + 16583549852463*x^2 + 7048462874529*x + 189858185323. Computing representation of Modular symbols space of level 2549, weight 2, and dimension 87. Goal dimension = 87. Computing T_2 on dual space of dimension 87. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). %o x^87 + 5*x^86 - 99*x^85 - 526*x^84 + 4654*x^83 + 26535*x^82 - 137992*x^81 - 854899*x^80 + 2888491*x^79 + 19765283*x^78 - 45208318*x^77 - 349348741*x^76 + 545193630*x^75 + 4910490944*x^74 - 5117585108*x^73 - 56378120469*x^72 + 36850641325*x^71 + 538897675498*x^70 - 189370543801*x^69 - 4349525669798*x^68 + 475324586585*x^67 + 29960781232259*x^66 + 2680507147367*x^65 - 177578464874359*x^64 - 45473080742911*x^63 + 911341507811028*x^62 + 363073027305411*x^61 - 4069173106112733*x^60 - 2124688275285121*x^59 + 15864187627082233*x^58 + 10020277764178520*x^57 - 54140523604126068*x^56 - 39535296257841743*x^55 + 162007517334450711*x^54 + 132965225689665052*x^53 - 425417022676626724*x^52 - 385227469124703627*x^51 + 980352522105819910*x^50 + 967442566227725394*x^49 - 1981174369757178656*x^48 - 2113606205221142574*x^47 + 3505683490987593622*x^46 + 4024370940227911339*x^45 - 5418604513215825640*x^44 - 6681048981874350297*x^43 + 7290914689854305963*x^42 + 9664493248683972399*x^41 - 8500274291077861732*x^40 - 12161512054137726934*x^39 + 8533227919899578080*x^38 + 13278533784623481075*x^37 - 7313158474982930739*x^36 - 12535492537429856616*x^35 + 5286366213339707802*x^34 + 10186278971767507309*x^33 - 3164862052723049557*x^32 - 7085627622751647484*x^31 + 1521766453290045469*x^30 + 4191301511232384234*x^29 - 551754160273762686*x^28 - 2091773105003586792*x^27 + 124564322185656821*x^26 + 872732643258362501*x^25 + 2515109088181020*x^24 - 301178915127007718*x^23 - 17068751341433041*x^22 + 84927390756018578*x^21 + 8704169311390263*x^20 - 19299732730584595*x^19 - 2712603959216602*x^18 + 3480314107162989*x^17 + 593140246572924*x^16 - 489569688929590*x^15 - 93361733147843*x^14 + 52720208276319*x^13 + 10472228231741*x^12 - 4256887652633*x^11 - 809988463936*x^10 + 251540881066*x^9 + 40721935464*x^8 - 10505319171*x^7 - 1194620262*x^6 + 288868230*x^5 + 15673685*x^4 - 4318856*x^3 + 4521*x^2 + 16231*x - 50 p = %o, dimension = %o. 2 0 Computing representation of Modular symbols space of level 2549, weight 2, and dimension 123. Computing complement of Modular symbols space of level 2549, weight 2, and dimension 123 Computing DualVectorSpace of Modular symbols space of level 2549, weight 2, and dimension 90. Goal dimension = 90. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.019 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_2 on space of dimension 90. (0.52 s) %o x^90 + 2*x^89 - 120*x^88 - 241*x^87 + 6918*x^86 + 13948*x^85 - 255217*x^84 - 516473*x^83 + 6771238*x^82 + 13751321*x^81 - 137658942*x^80 - 280524635*x^79 + 2231195908*x^78 + 4562118385*x^77 - 29618365799*x^76 - 60763728569*x^75 + 328287389191*x^74 + 675778885755*x^73 - 3082085003116*x^72 - 6366423238073*x^71 + 24778555540264*x^70 + 51366729823582*x^69 - 172035858782127*x^68 - 357977815610389*x^67 + 1038334383522319*x^66 + 2169220389447406*x^65 - 5476038141944824*x^64 - 11489004656247495*x^63 + 25336042860047889*x^62 + 53400617211950500*x^61 - 103150443013510974*x^60 - 218490843780045326*x^59 + 370364196480683491*x^58 + 788729743165477988*x^57 - 1174555517331859566*x^56 - 2515987573358244586*x^55 + 3293030832940487164*x^54 + 7098656630518419727*x^53 - 8164739356033619936*x^52 - 17720694982673106785*x^51 + 17899230215404202808*x^50 + 39132160761396194900*x^49 - 34672269546361121100*x^48 - 76386611951286607015*x^47 + 59278511330041054053*x^46 + 131639281902443673369*x^45 - 89310371802798339328*x^44 - 199923034577892786628*x^43 + 118342547013097407023*x^42 + 266953164090581300847*x^41 - 137592647615276069891*x^40 - 312489978732473006605*x^39 + 139991159231681978899*x^38 + 319542313739299722129*x^37 - 124272125858837225505*x^36 - 284234526071487173139*x^35 + 95950293524684621543*x^34 + 218833950967362557766*x^33 - 64225028202769958763*x^32 - 144977179415410931059*x^31 + 37146678383037357599*x^30 + 82083768841397212916*x^29 - 18503273667823749981*x^28 - 39401070358328128357*x^27 + 7909310141793977360*x^26 + 15884383865881513203*x^25 - 2888606293700585114*x^24 - 5318999201236822750*x^23 + 895770431655491856*x^22 + 1460005714690483881*x^21 - 233633572623104933*x^20 - 323311425884005921*x^19 + 50522681841636315*x^18 + 56634941785632275*x^17 - 8876446981591498*x^16 - 7653222807256428*x^15 + 1233305630827894*x^14 + 771379033170536*x^13 - 130877441199681*x^12 - 55218075845520*x^11 + 10130195693182*x^10 + 2589061913743*x^9 - 534907655205*x^8 - 67172741213*x^7 + 17192160614*x^6 + 493652535*x^5 - 260868161*x^4 + 9858343*x^3 + 525815*x^2 - 16874*x - 507 p = 2, dimension = 90. Computing complement of Modular symbols space of level 2549, weight 2, and dimension 90 J0( N: 2549 ) NewformDecomposition( M: Modular symbols space of level 2549, weight 2, and dimension... ) In file "/home/was/modsym/decomp.m", line 326, column 7: >> assert Dimension(M) eq &+[Integers()|Dimension(d) : d in D]; ^ Runtime error in assert: Assertion failed >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2549, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 335.600 seconds Magma V2.7-1 Mon Jan 29 2001 12:08:18 on modular [Seed = 3953429671] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2551 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.791 s) III. 3-term relations. Computing quotient by 852 relations. Form quot and then images (0.52 s) (total time to create space = 1.341 s) Computing cuspidal part of Full Modular symbols space of level 2551, weight 2, and dimension 213 Computing new part of Modular symbols space of level 2551, weight 2, and dimension 212. Computing 2551-new part of Modular symbols space of level 2551, weight 2, and dimension 212. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2551, weight 2, and dimension 212. Computing 2551-new part of Modular symbols space of level 2551, weight 2, and dimension 212. Computing cuspidal part of Modular symbols space of level 2551, weight 2, and dimension 212 Decomposing space of level 2551 and dimension 212 using T_2. (will stop at 426) Computing T_2 on dual space of dimension 212. Computing DualVectorSpace of Modular symbols space of level 2551, weight 2, and dimension 212. Computing complement of Modular symbols space of level 2551, weight 2, and dimension 212 Computing representation of Modular symbols space of level 2551, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 213. (0.509 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2551, weight 2, and dimension 1 T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). 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(0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). Computing characteristic polynomial of T_2. x^212 - x^211 - 316*x^210 + 314*x^209 + 49141*x^208 - 48517*x^207 - 5013419*x^206 + 4917625*x^205 + 377426723*x^204 - 367780577*x^203 - 22360940292*x^202 + 21644292040*x^201 + 1085812407907*x^200 - 1043919123051*x^199 - 44440549311601*x^198 + 42433690759229*x^197 + 1564714570802753*x^196 - 1483697810047277*x^195 - 48136657452345097*x^194 + 45323531811315907*x^193 + 1309813910897567237*x^192 - 1224481770237016735*x^191 - 31835507372720539058*x^190 + 29546473484309461966*x^189 + 696779659979313418995*x^188 - 641941548640441820825*x^187 - 13825917961176236149770*x^186 + 12643107014435853030796*x^185 + 250143660353264510245218*x^184 - 227018599847581289272446*x^183 - 4146733380628265209079956*x^182 + 3734573210324609222463680*x^181 + 63252646150261233249729389*x^180 - 56523074069624091091513905*x^179 - 891056269038505957457355517*x^178 + 789972703629575674604836973*x^177 + 11630180910514066331866911132*x^176 - 10228201665609059434154227378*x^175 - 141045247695007579208288362472*x^174 + 123032918853679263236638565874*x^173 + 1593369504103701947921373083492*x^172 - 1378388910386985812778683407851*x^171 - 16804893735082571423344388533872*x^170 + 14415305133930224393153501335591*x^169 + 165801147310941555462940204471225*x^168 - 141008980066971490689957814678204*x^167 - 1533036674644991660194473266889403*x^166 + 1292466250966984281748305273798181*x^165 + 13305529632980280985790017937651639*x^164 - 11118349338686582398862610382172207*x^163 - 108556945146734577146964996454781023*x^162 + 89895719002387381997980624745625032*x^161 + 833676863125695189922184946688923891*x^160 - 684040449672390932816212309376304968*x^159 - 6033449350889626405652704143065272234*x^158 + 4904325349700066835056827052070543278*x^157 + 41193085440993830745708851390344631379*x^156 - 33165906633156113637226893678938261525*x^155 - 265577502416999571558144064322090271089*x^154 + 211755420164707914827768517419460445367*x^153 + 1618239836460462394563099931737326180384*x^152 - 1277558766365360279839119104828625818056*x^151 - 9326480579394364115318129194811663253923*x^150 + 7288980524721179705137656254842431952262*x^149 + 50876828197294399867333444332175714079942*x^148 - 39354411777432108061619357726757844607517*x^147 - 262858304133524881468384851641630084421389*x^146 + 201200920903344317323434070699181779056826*x^145 + 1286960721531133522716745163914706018536827*x^144 - 974576415693761562585966391562288151541229*x^143 - 5974006486139076622018951393390273839832139*x^142 + 4474691186418510843328453323050411160776225*x^141 + 26303404072089168955266127198519854331091814*x^140 - 19483072473267218902434589644744506360468421*x^139 - 109892706164243654329586758216693063345437196*x^138 + 80474942067780117188614354539964578347405112*x^137 + 435790998352230717248879806024579210791636879*x^136 - 315436117334324289316722537415731967559355046*x^135 - 1640817091600320481912336016052319084010695424*x^134 + 1173617452397686804766835143187191718804239032*x^133 + 5866970507480466166076729506580297652891944500*x^132 - 4145741343510062539452763838024462364720038084*x^131 - 19925941693864620777371806725245390630863837982*x^130 + 13906395508279427485394676939605272497078348519*x^129 + 64288793892218473223118338325168671745418155650*x^128 - 44301741146213856763338535684063569979016156952*x^127 - 197062924843427569733975888850470271496768072025*x^126 + 134047743903966001538967552200947396800882585192*x^125 + 573920278259291020399821135110805619649902580598*x^124 - 385257816546997717401097175411188092333987491104*x^123 - 1588113188286170113644903638336246573430936550399*x^122 + 1051719513867369676482270728026229808638244365391*x^121 + 4175260894400329285356608137811272803324878896368*x^120 - 2727037630106010113588219192042396617414768520525*x^119 - 10428700254780338837027758683823702174931718148394*x^118 + 6715749076970439303728538123346148919676307996748*x^117 + 24744377247805909624272368814943447701992363102511*x^116 - 15705896883365273373248865591301091003678363697592*x^115 - 55764958930319769513950693890182585084667542562679*x^114 + 34876455435355028114132343439413297042585786597767*x^113 + 119345733820767876890203659530410768173311861838671*x^112 - 73523002760749477647008090844337794463768778734254*x^111 - 242503810633300637849853635389659960109633934989487*x^110 + 147108921773445081191046708761983002280775151970208*x^109 + 467719146918820046705973354323537711997893146867183*x^108 - 279297328525833648548432760533535816796988002357431*x^107 - 856009293414757585969251581229814921448412509447982*x^106 + 503010483490617899543692285349656284210577736472700*x^105 + 1486117765704359205759575397574343937622875906252375*x^104 - 859059871177217465352685090029352278829058773059736*x^103 - 2446507571614447561046657569373456906497832493549467*x^102 + 1390728960450047220281172543452350454358465808536225*x^101 + 3817488943245853920303750837141304992917955498779041*x^100 - 2133306568147373066456198513242745222585188487293122*x^99 - 5643491020581927982367453984914317518148849548219294*x^98 + 3099251703725121393719505324910578669670511270658699*x^97 + 7900212206333256177557642462975789439521077667367053*x^96 - 4262220074680914897975296156659283233871272245650348*x^95 - 10466778997088508571813641825075672573761090035593033*x^94 + 5545668376184737875933037042325564468951272241577233*x^93 + 13116349871098406944027402985532747757702139713387216*x^92 - 6822675250671229474251638314260934401220798605353808*x^91 - 15536735655516845760509460319320373886912202266242238*x^90 + 7931612008600908920849107434686902822336419175449758*x^89 + 17384117316851937780800513363932975470704351687292955*x^88 - 8707146313280962967768229625736043015267307481074468*x^87 - 18359796092384123439435796571001071225981764141903727*x^86 + 9019385399498055055024467655778664066369772642902992*x^85 + 18287635475977895460465649281896107178038012293218905*x^84 - 8808868729706557647650960942355985753518174664264297*x^83 - 17165187390994033504486429771141573812771420083728474*x^82 + 8104677477775271582639306029909258157361056005460055*x^81 + 15168439031338917976095883245659243045340481935936702*x^80 - 7018228723811766859260012886388898669939404128636061*x^79 - 12606843969571956157484686326959745415495344252895544*x^78 + 5714405502063946888062698186529993085169702118901375*x^77 + 9844345909822023239608054682014978519303783069019451*x^76 - 4370306110776615936185478075399777796280212037444696*x^75 - 7214270339908879914418248905011337654487837682374453*x^74 + 3135907727772708962167327335472220209909973130332752*x^73 + 4955634237759933734513745429214731181314444305412792*x^72 - 2108648350944629194907689724530768272746261088016886*x^71 - 3186746462298838179254927697851715335909304025131944*x^70 + 1327016246164937852874399261831847579119634148519389*x^69 + 1915749956778121314698992316451142111446514671405415*x^68 - 780514849081719654360493480073997663579143259802722*x^67 - 1075062065311499077153791250685452539252705928584484*x^66 + 428427395641951394304322335243898488234974023258579*x^65 + 562273706317930934376388118749795210884467644982442*x^64 - 219116777640317765177266771170206481384293309320043*x^63 - 273621455180474796638068858980979776701220662938514*x^62 + 104240459482255869165273245816896391409659257800015*x^61 + 123668231764021723663769622745027822637039580136936*x^60 - 46042967451985535123393954799613842687312268896070*x^59 - 51812457435142131749259418702751307151739273852576*x^58 + 18845142116767039818921952580225620098195435570596*x^57 + 20080809501712750560206770265658242719067966406732*x^56 - 7132147841070298857436834967064702567505268794466*x^55 - 7183529708129472052413417716467555703559599944623*x^54 + 2490163961494668893411008752224967648033568001060*x^53 + 2366318888848349636984038399829208162655102387221*x^52 - 800097244573216710910272405191665479941039660442*x^51 - 715947004440437406179125020994358582271995402543*x^50 + 235936717495282284289905738176970542950900651905*x^49 + 198413914441447673062218075842733479927299849043*x^48 - 63667454259234064291248031640960098757849572340*x^47 - 50219102268537067994157681555898601016270786580*x^46 + 15672186749939841950958333727291362212501086429*x^45 + 11571653877286945223309839956031095912752404290*x^44 - 3506955194417177926729227932588677495140111217*x^43 - 2419180808762828395094541735458126186693159091*x^42 + 710691377525718096677063269569210287572666864*x^41 + 457178626716689603799842055646362365194878265*x^40 - 129894611583636476362868972365722921563442232*x^39 - 77788421770564125514933747073234156024166006*x^38 + 21315645986548674104881513690340834158272053*x^37 + 11865194115145710203451419419877380614040383*x^36 - 3124991759828067210750116129216397142879963*x^35 - 1614797472095103434618336628037096395290295*x^34 + 407071803570011158669873309074685882413666*x^33 + 195076726882126021552486665058306946871136*x^32 - 46832539211830927051449197537585956842432*x^31 - 20800533307320407128253465124097776610616*x^30 + 4726954656335465331895394087394903816668*x^29 + 1945348961776826443527630714185015648092*x^28 - 415483355455214481679059679098749755502*x^27 - 158462787575177576064306198758402370316*x^26 + 31541020343188199371785621829554687310*x^25 + 11153842015427345807714646709638665128*x^24 - 2048946211905211255550414745192548111*x^23 - 672299342875656052033450015360539559*x^22 + 112720152736204260297674307103096614*x^21 + 34340266006900380614900629521414908*x^20 - 5190236527924995866152233737242313*x^19 - 1468365437482112210272424071923579*x^18 + 197375538335182985882561841450033*x^17 + 51802451138087604443894599501813*x^16 - 6105045078730460516224523882795*x^15 - 1481711570579984289161146700737*x^14 + 150896329102497834946712887174*x^13 + 33633615167100830627825022798*x^12 - 2917958295211888937340785583*x^11 - 589764074682970292725545039*x^10 + 42984077560170378524005452*x^9 + 7711234326865353211369734*x^8 - 464846491128185302498172*x^7 - 71541244260871712857512*x^6 + 3480494250014762986482*x^5 + 435961488604288960048*x^4 - 16151544745989836835*x^3 - 1516455062666736439*x^2 + 35073482854661907*x + 2144530091555787 time = 5.799 Factoring characteristic polynomial. [ , ] time = 1.25 Cutting out subspace using f(T_2), where f=x^86 + 15*x^85 - 7*x^84 - 1196*x^83 - 3966*x^82 + 41891*x^81 + 244455*x^80 - 784962*x^79 - 7779242*x^78 + 5850318*x^77 + 164061576*x^76 + 99114707*x^75 - 2509970301*x^74 - 4008404813*x^73 + 29038818696*x^72 + 73105174266*x^71 - 257699124093*x^70 - 926584775596*x^69 + 1727696976065*x^68 + 9040422357976*x^67 - 8052826105332*x^66 - 70933176599173*x^65 + 15902944308246*x^64 + 458105091007639*x^63 + 130962786376248*x^62 - 2467763866420200*x^61 - 1766272957811309*x^60 + 11166555089717164*x^59 + 12442438686816687*x^58 - 42526945235441816*x^57 - 64797879782582779*x^56 + 135828240679293405*x^55 + 271130510965495582*x^54 - 359566201618892832*x^53 - 942624140445287271*x^52 + 766905694740830920*x^51 + 2768566364924835255*x^50 - 1223081873623042585*x^49 - 6930843909274862639*x^48 + 1072114515391030326*x^47 + 14857067922799465570*x^46 + 1166389270995936782*x^45 - 27320647526765886571*x^44 - 7561775930158299237*x^43 + 43087254731666146652*x^42 + 19526368986503117249*x^41 - 58158219075282921283*x^40 - 35940479805870704149*x^39 + 66926972497990907629*x^38 + 52249155884911541095*x^37 - 65275790186489728938*x^36 - 62145149310638232857*x^35 + 53498302338922987015*x^34 + 61346645472719474551*x^33 - 36385168048859394865*x^32 - 50526874783204641503*x^31 + 20142899693854528390*x^30 + 34734462294144385898*x^29 - 8780503872274321362*x^28 - 19873039688137411139*x^27 + 2810288149784276127*x^26 + 9412480061544331374*x^25 - 526973964255538385*x^24 - 3662396262159145955*x^23 - 32488587604875693*x^22 + 1159099223615432507*x^21 + 65656229417693443*x^20 - 294634687541913721*x^19 - 26413787601576072*x^18 + 59199625273344371*x^17 + 6484706059107192*x^16 - 9211583593523052*x^15 - 1084540492461822*x^14 + 1080591970539724*x^13 + 125200798798673*x^12 - 92177386420069*x^11 - 9788245128699*x^10 + 5444469268886*x^9 + 500642991000*x^8 - 208703187113*x^7 - 16071469811*x^6 + 4793283311*x^5 + 303826158*x^4 - 58701176*x^3 - 3021139*x^2 + 290622*x + 11973. Cutting out subspace using f(T_2), where f=x^126 - 16*x^125 - 69*x^124 + 2433*x^123 - 3007*x^122 - 174252*x^121 + 641327*x^120 + 7717583*x^119 - 44012445*x^118 - 230900507*x^117 + 1905467425*x^116 + 4642027880*x^115 - 60254111253*x^114 - 50315314140*x^113 + 1485368918514*x^112 - 385165697742*x^111 - 29607564535523*x^110 + 33035460231121*x^109 + 487984169157376*x^108 - 912942026283572*x^107 - 6740755710375574*x^106 + 17648082854483053*x^105 + 78538634877386579*x^104 - 271037845322015020*x^103 - 770735704893773804*x^102 + 3473473443258174862*x^101 + 6283675990536690501*x^100 - 38104154456855391715*x^99 - 40828018910000184394*x^98 + 363383331524847418266*x^97 + 183719733274377226585*x^96 - 3043478715330084696870*x^95 - 136535579531781501814*x^94 + 22543981573367472026872*x^93 - 7900563008114399344159*x^92 - 148399954045134746000311*x^91 + 104938619381205618350558*x^90 + 870809826640326079528557*x^89 - 910717597279869419637260*x^88 - 4562258991365924555367048*x^87 + 6320173832956013486197820*x^86 + 21340187406628657622737039*x^85 - 37265024573850228588790437*x^84 - 88948733762320761225935853*x^83 + 191766801287398138996152477*x^82 + 328835849144385444756028842*x^81 - 873774832874583225368416826*x^80 - 1068349438719334581017108446*x^79 + 3555598668211582410787823147*x^78 + 2995390146332302294305793522*x^77 - 12992087083469369168256955144*x^76 - 6965127907464618963086445711*x^75 + 42779122668841251823997300891*x^74 + 12006742278392111419409064803*x^73 - 127217665366253891332462376165*x^72 - 7780588215623829622240145846*x^71 + 342131395506382164934341446564*x^70 - 45444335190624896908462496213*x^69 - 832549804475493233376231832551*x^68 + 257284731381173685817454301511*x^67 + 1832983837344498999549564846506*x^66 - 868238664999663420751296972422*x^65 - 3648633235507271528953763910618*x^64 + 2306804697384578624570430005349*x^63 + 6557541488361504791488502183189*x^62 - 5181187898226334693746501713714*x^61 - 10619316717300661196693746041569*x^60 + 10123040811624058485937728351939*x^59 + 15449743241999050924228817773409*x^58 - 17445206982590143472173853575383*x^57 - 20110883633967352791033046714179*x^56 + 26710994174010186269363534692192*x^55 + 23286383658522639270942989454339*x^54 - 36476639350705766003169282872047*x^53 - 23780763978214952939271002419658*x^52 + 44505710208024191101547076770910*x^51 + 21133944247654962309437456746617*x^50 - 48536008988840670004830250447368*x^49 - 15966146753897575558268916570699*x^48 + 47282344931291850709972231547129*x^47 + 9767242055546569916555944042220*x^46 - 41088269354437399020445668406849*x^45 - 4208987515453108558037168393403*x^44 + 31785298861595786792498522962820*x^43 + 406676892271760659935553741624*x^42 - 21830582487930261691410748554866*x^41 + 1421194492765718885009503464642*x^40 + 13268543705009026638043776252203*x^39 - 1768631106481381517780646077432*x^38 - 7109489407414879015258865188527*x^37 + 1374492508787638491020902336052*x^36 + 3343455667917073805807844343066*x^35 - 823761373008684571196962365831*x^34 - 1373153574025025758302094818180*x^33 + 402755068645256367873109647831*x^32 + 489739638201399136006612647794*x^31 - 163924397346828111361905550605*x^30 - 150735731591327483663413029063*x^29 + 55917862932772129489650188783*x^28 + 39763010257289764023323118141*x^27 - 15990001653244979593843459462*x^26 - 8922635731895546806647470747*x^25 + 3818619229872422739881365199*x^24 + 1689434865615761039282672162*x^23 - 756571531714252317914942053*x^22 - 267585543979449435318062258*x^21 + 123236650110599407122009665*x^20 + 35125848568273016840821952*x^19 - 16314499962133215814399681*x^18 - 3782754372900984840476517*x^17 + 1730382603741992066973414*x^16 + 330236205739422616398122*x^15 - 144449171307815021638374*x^14 - 23012154944134033754168*x^13 + 9279140348053845165208*x^12 + 1251792481417171303781*x^11 - 445505860312903451316*x^10 - 51364015234157954559*x^9 + 15381909304971471763*x^8 + 1505846542778406655*x^7 - 362714676686509510*x^6 - 28900971565573473*x^5 + 5448385612152278*x^4 + 312969866876924*x^3 - 47034735925728*x^2 - 1418269575107*x + 179113847119. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 3953429671 Time to this point: 169.77 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2551, a, ^ User error: Identifier 'a' has not been declared or assigned Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 3953429671 Time to this point: 170.11 Segmentation fault Magma V2.7-1 Mon Jan 29 2001 12:13:51 on modular [Seed = 3886580710] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2553 and weight 2.... I. Manin symbols list. (0.05 s) II. 2-term relations. (1.131 s) III. 3-term relations. Computing quotient by 1216 relations. Form quot and then images (0.919 s) (total time to create space = 2.13 s) Computing cuspidal part of Full Modular symbols space of level 2553, weight 2, and dimension 308 Computing new part of Modular symbols space of level 2553, weight 2, and dimension 301. Computing 3-new part of Modular symbols space of level 2553, weight 2, and dimension 301. Computing space of modular symbols of level 851 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.27 s) III. 3-term relations. Computing quotient by 304 relations. Form quot and then images (0.121 s) (total time to create space = 0.4 s) Computing index-1 degeneracy map from level 2553 to 851. (0.66 s) Computing index-3 degeneracy map from level 2553 to 851. (0.63 s) Computing index-1 degeneracy map from level 851 to 2553. (0.869 s) Computing index-3 degeneracy map from level 851 to 2553. (0.76 s) Computing DualVectorSpace of Modular symbols space of level 2553, weight 2, and dimension 301. Computing complement of Modular symbols space of level 2553, weight 2, and dimension 301 Computing representation of Modular symbols space of level 2553, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 308. (0.25 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^7 - 21*x^6 + 189*x^5 - 945*x^4 + 2835*x^3 - 5103*x^2 + 5103*x - 2187 p = %o, dimension = %o. 2 7 Computing complement of Modular symbols space of level 2553, weight 2, and dimension 7 Computing 23-new part of Modular symbols space of level 2553, weight 2, and dimension 301. Computing space of modular symbols of level 111 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.04 s) III. 3-term relations. Computing quotient by 52 relations. Form quot and then images (0.009 s) (total time to create space = 0.05 s) Computing index-1 degeneracy map from level 2553 to 111. (0.081 s) Computing index-23 degeneracy map from level 2553 to 111. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 3886580710 Time to this point: 99.83 Segmentation fault Magma V2.7-1 Mon Jan 29 2001 12:17:08 on modular [Seed = 3853156575] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2554 and weight 2.... I. Manin symbols list. (0.05 s) II. 2-term relations. (1.2 s) III. 3-term relations. Computing quotient by 1278 relations. Form quot and then images (0.98 s) (total time to create space = 2.261 s) Computing cuspidal part of Full Modular symbols space of level 2554, weight 2, and dimension 321 Computing new part of Modular symbols space of level 2554, weight 2, and dimension 318. Computing 2-new part of Modular symbols space of level 2554, weight 2, and dimension 318. Computing space of modular symbols of level 1277 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.37 s) III. 3-term relations. Computing quotient by 426 relations. Form quot and then images (0.19 s) (total time to create space = 0.58 s) Computing index-1 degeneracy map from level 2554 to 1277. (1.661 s) Computing index-2 degeneracy map from level 2554 to 1277. (1.559 s) Computing index-1 degeneracy map from level 1277 to 2554. (1.299 s) Computing index-2 degeneracy map from level 1277 to 2554. (0.931 s) Computing DualVectorSpace of Modular symbols space of level 2554, weight 2, and dimension 318. Computing complement of Modular symbols space of level 2554, weight 2, and dimension 318 Computing representation of Modular symbols space of level 2554, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 321. (0.299 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^3 - 4*x^2 + 5*x - 2 p = %o, dimension = %o. 2 56 Computing T_3 on space of dimension 321. (0.15 s) Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). %o x^3 - 12*x^2 + 48*x - 64 p = %o, dimension = %o. 3 3 Computing complement of Modular symbols space of level 2554, weight 2, and dimension 3 Computing 1277-new part of Modular symbols space of level 2554, weight 2, and dimension 318. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0.001 s) II. 2-term relations. (0.011 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0 s) (total time to create space = 0.011 s) Computing index-1 degeneracy map from level 2554 to 2. (0.06 s) Computing index-1277 degeneracy map from level 2554 to 2. (458.149 s) Computing index-1 degeneracy map from level 2 to 2554. (35.78 s) Computing index-1277 degeneracy map from level 2 to 2554. (23.521 s) Finding newform decomposition of Modular symbols space of level 2554, weight 2, and dimension 318. Computing cuspidal part of Modular symbols space of level 2554, weight 2, and dimension 318 Decomposing space of level 2554 and dimension 106 using T_3. (will stop at 639) Computing T_3 on dual space of dimension 106. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing characteristic polynomial of T_3. x^105 + 638736368/229033047*x^104 - 18461030115/76344349*x^103 - 130047171205/229033047*x^102 + 2124415921553/76344349*x^101 + 12743077713985/229033047*x^100 - 155503524160592/76344349*x^99 - 266836264911251/76344349*x^98 + 24473240618990798/229033047*x^97 + 36230969192702356/229033047*x^96 - 982343995710628019/229033047*x^95 - 419599967126373212/76344349*x^94 + 31441111101216353801/229033047*x^93 + 11643153199132117105/76344349*x^92 - 825427784892238995001/229033047*x^91 - 795120548793056714869/229033047*x^90 + 18142824264570143720761/229033047*x^89 + 5045007994396341975946/76344349*x^88 - 339056876484808295095162/229033047*x^87 - 244314837403388383666958/229033047*x^86 + 5452115567919227145399869/229033047*x^85 + 3379830110160461000496700/229033047*x^84 - 76151009324078581745135149/229033047*x^83 - 13461584688486051894226471/76344349*x^82 + 930860548487320809360187537/229033047*x^81 + 139719459958539982995827272/76344349*x^80 - 10019519668157609742938885480/229033047*x^79 - 1264416193716690846493758767/76344349*x^78 + 95438560773391329697238668961/229033047*x^77 + 29987429930163121029306823261/229033047*x^76 - 269250742600394395796732555860/76344349*x^75 - 207047437092470113210837353089/229033047*x^74 + 6094572611907957957646157593192/229033047*x^73 + 1244819626114051465640949985424/229033047*x^72 - 41103198332248303764744878328442/229033047*x^71 - 2156533426893299914693930903772/76344349*x^70 + 248309876506668868345484993740378/229033047*x^69 + 28624067660243640966069984645637/229033047*x^68 - 448629744368213218945349736400135/76344349*x^67 - 104248821510089605302306104742205/229033047*x^66 + 6553109726926780789805999163833702/229033047*x^65 + 285585876969926888295267617644363/229033047*x^64 - 28685753523746493871815305917681144/229033047*x^63 - 127471051229538069243679376719662/76344349*x^62 + 112945360998118376650207398040372150/229033047*x^61 - 1531636766098618716522953639425013/229033047*x^60 - 400046149050466349103119344859173651/229033047*x^59 + 14933638668730487626755475783757492/229033047*x^58 + 424801189276870069743901994097443506/76344349*x^57 - 74141879851380897694323415197744874/229033047*x^56 - 1216510058563243637851258250380569749/76344349*x^55 + 278380990723687910939899812113107258/229033047*x^54 + 9387295386909558954694050940509180433/229033047*x^53 - 861580857102452435287402744969870613/229033047*x^52 - 21662982247454826961762006410106297333/229033047*x^51 + 2270583875759183424383648899011993235/229033047*x^50 + 14928116651200557418417512626687709007/76344349*x^49 - 5171871312734989075712149405764252976/229033047*x^48 - 27596059216705196862026987744935818740/76344349*x^47 + 10256023740706717485758647033716655360/229033047*x^46 + 136547956005252441646241961688479852005/229033047*x^45 - 5921079246579537376328663086506385026/76344349*x^44 - 200419858976348757078816423154666323137/229033047*x^43 + 26889507414665291845776239309233590643/229033047*x^42 + 260977936278599590958826926270603467321/229033047*x^41 - 35538731053659717663435304620087430942/229033047*x^40 - 100139188939822912370512195667255232634/76344349*x^39 + 13636013717660446221626729980597435493/76344349*x^38 + 304445693322771740891283108853146175853/229033047*x^37 - 40858854999863435299155324733358850719/229033047*x^36 - 270320649875757225739786902186271159126/229033047*x^35 + 11745194861258897706366880513213197833/76344349*x^34 + 209135243575052314083131976623583435886/229033047*x^33 - 8690688854107873115322346383090500538/76344349*x^32 - 140075243556807154754707185446440850488/229033047*x^31 + 5475143666636202550775744896020638834/76344349*x^30 + 26872434650892186666322938822669976832/76344349*x^29 - 2909357036940069408741271850921337937/76344349*x^28 - 39519888606699768772356600603189229589/229033047*x^27 + 1289108808273407279531575551649465145/76344349*x^26 + 16331373694033005087141647598143071169/229033047*x^25 - 1409124309508042359069999722349420401/229033047*x^24 - 5619307130152151640240474863135943313/229033047*x^23 + 415122320212174768432619495724975601/229033047*x^22 + 528685099318620001998054844758083279/76344349*x^21 - 96871248832011734055417920988715750/229033047*x^20 - 360571324209029280717813589929191591/229033047*x^19 + 79823861411169091857590307189657/1045813*x^18 + 64534463886595892617626717741383566/229033047*x^17 - 2378866805033880181737422367354056/229033047*x^16 - 8832273720890992242787040979822812/229033047*x^15 + 240089705702894775157899261312704/229033047*x^14 + 889745025343365547308371937630512/229033047*x^13 - 6098129759523996182081405572992/76344349*x^12 - 62659686183263548328645341995712/229033047*x^11 + 1125635222343767098555875745280/229033047*x^10 + 2869555038913265491862499878656/229033047*x^9 - 55078019627030504261471493632/229033047*x^8 - 76732934471099687805497643008/229033047*x^7 + 1553082508526517400992419840/229033047*x^6 + 1004062772939637077686398976/229033047*x^5 - 11560947204271000577081344/229033047*x^4 - 1759286862991985741512704/76344349*x^3 + 1507216163220434485248/76344349*x^2 + 2596359343800741986304/76344349*x - 3113800935995473920/76344349 time = 9.299 Factoring characteristic polynomial. [ , ] time = 0.48 Cutting out subspace using f(T_3), where f=x - 1. Cutting out subspace using f(T_3), where f=x^104 + 867769415/229033047*x^103 - 54515320930/229033047*x^102 - 184562492135/229033047*x^101 + 6188685272524/229033047*x^100 + 18931762986509/229033047*x^99 - 447578809495267/229033047*x^98 - 1248087604229020/229033047*x^97 + 23225153014761778/229033047*x^96 + 59456122207464134/229033047*x^95 - 307629291167721295/76344349*x^94 - 727229258294094507/76344349*x^93 + 29259423326334070280/229033047*x^92 + 64188882923730421595/229033047*x^91 - 761238901968508573406/229033047*x^90 - 518786483587188429425/76344349*x^89 + 16586464813808578432486/229033047*x^88 + 31721488796997604360324/229033047*x^87 - 102445129229270230244946/76344349*x^86 - 551650225091199074401796/229033047*x^85 + 1633488447609342690332691/76344349*x^84 + 8280295452988489071494773/229033047*x^83 - 22623571290363364224546792/76344349*x^82 - 36085155978849416118773263/76344349*x^81 + 822605080550772561003867748/229033047*x^80 + 1241763460426392509991349564/229033047*x^79 - 8777756207731217232947535916/229033047*x^78 - 12571004788881289772428812217/229033047*x^77 + 82867555984510039924809856744/229033047*x^76 + 112854985914673160954116680005/229033047*x^75 - 694897241886510026436080987575/229033047*x^74 - 300648226326326713215639446888/76344349*x^73 + 5192627932928977817999239252528/229033047*x^72 + 2145815853014343094546729745984/76344349*x^71 - 34665750773205274481104689090490/229033047*x^70 - 41135351053885174225186481801806/229033047*x^69 + 69058175150927898040099503979524/76344349*x^68 + 235798593113027335086368496584209/229033047*x^67 - 1110090639991612321749680712616196/229033047*x^66 - 404779820500567309017328939119467/76344349*x^65 + 5338770265425078862754012346475301/229033047*x^64 + 1874785380798335250349759988039888/76344349*x^63 - 23061397381351488120766025953561480/229033047*x^62 - 23443810535040102328497064083720466/229033047*x^61 + 29833850154359424773903444652217228/76344349*x^60 + 87969913696979655605187380317226671/229033047*x^59 - 104025411784495564499310654847315660/76344349*x^58 - 297142596684756205871176488758189488/229033047*x^57 + 977260971145854003360529493534141030/229033047*x^56 + 903119091294473105666206078336396156/229033047*x^55 - 2746411084395257807887568672805313091/229033047*x^54 - 2468030093671569896947668860692205833/229033047*x^53 + 2306421764412663019248794026605658200/76344349*x^52 + 6057684436135536622458979334847103987/229033047*x^51 - 5201765937106430113101009025086397782/76344349*x^50 - 13334713935560106914919378176247200111/229033047*x^49 + 31449636018041565340333159703815926910/229033047*x^48 + 8759254901768858754873670099350557978/76344349*x^47 - 18836804314936338107153317645585260762/76344349*x^46 - 46254389204102296835701305903039126926/229033047*x^45 + 30097855600383381603513551928480241693/76344349*x^44 + 24176776353803844227184888841973856667/76344349*x^43 - 1751911368697770197222763789434859632/3137439*x^42 - 101000022500271932551485517319511162493/229033047*x^41 + 53325971259442552802447136317030768276/76344349*x^40 + 124439182724667940743906104331004873886/229033047*x^39 - 175978384094800796367630482670760824016/229033047*x^38 - 135070342941819457702750292728968517537/229033047*x^37 + 169375350380952283188532816124177658316/229033047*x^36 + 128516495381088847889377491390818807597/229033047*x^35 - 141804154494668377850409410795452351529/229033047*x^34 - 106568569910891684731308769255812758030/229033047*x^33 + 102566673664160629351823207367770677856/229033047*x^32 + 76494607101837010005856168218499176242/229033047*x^31 - 63580636454970144748851017227941674246/229033047*x^30 - 47155205455061537096523782539879757744/229033047*x^29 + 458384910926233190444452519563427024/3137439*x^28 + 24734027386794814676221218375366158941/229033047*x^27 - 14785861219904954096135382227823070648/229033047*x^26 - 10918534795084732257540655572874675213/229033047*x^25 + 5412838898948272829600992025268395956/229033047*x^24 + 4003714589440230470530992302918975555/229033047*x^23 - 1615592540711921169709482560216967758/229033047*x^22 - 1200470220499746401276863064491992157/229033047*x^21 + 385585077456113604717301469782257680/229033047*x^20 + 288713828624101870661883548793541930/229033047*x^19 - 71857495584927410055930041135649661/229033047*x^18 - 54376069935881378939117763861114778/229033047*x^17 + 3386131316904837892836317960089596/76344349*x^16 + 7779527145680633496771531512914732/229033047*x^15 - 1052746575210358746015509466908080/229033047*x^14 - 812656869507463970857610205595376/229033047*x^13 + 25696051945300525483587244011712/76344349*x^12 + 19597922185776529301505838438720/76344349*x^11 - 3865919625933960424127826679552/229033047*x^10 - 2740284403590193325571950934272/229033047*x^9 + 129270635323072166290548944384/229033047*x^8 + 24730871898680554009692483584/76344349*x^7 - 2540318775058025776420192256/229033047*x^6 - 329078755510502791809257472/76344349*x^5 + 16826506408128702258626560/229033047*x^4 + 1755186401285900560515072/76344349*x^3 - 4100461706085180997632/76344349*x^2 - 2593245542864746512384/76344349*x + 3113800935995473920/76344349. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 3853156575 Time to this point: 751.63 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2554, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 752.019 seconds Magma V2.7-1 Mon Jan 29 2001 12:41:55 on modular [Seed = 3717366448] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2555 and weight 2.... I. Manin symbols list. (0.04 s) II. 2-term relations. (1.11 s) III. 3-term relations. Computing quotient by 1184 relations. Form quot and then images (0.881 s) (total time to create space = 2.06 s) Computing cuspidal part of Full Modular symbols space of level 2555, weight 2, and dimension 300 Computing new part of Modular symbols space of level 2555, weight 2, and dimension 293. Computing 5-new part of Modular symbols space of level 2555, weight 2, and dimension 293. Computing space of modular symbols of level 511 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.171 s) III. 3-term relations. Computing quotient by 200 relations. Form quot and then images (0.069 s) (total time to create space = 0.251 s) Computing index-1 degeneracy map from level 2555 to 511. (0.309 s) Computing index-5 degeneracy map from level 2555 to 511. (0.361 s) Computing index-1 degeneracy map from level 511 to 2555. (1.019 s) Computing index-5 degeneracy map from level 511 to 2555. (0.839 s) Computing DualVectorSpace of Modular symbols space of level 2555, weight 2, and dimension 293. Computing complement of Modular symbols space of level 2555, weight 2, and dimension 293 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 300. (0.24 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^7 - 21*x^6 + 189*x^5 - 945*x^4 + 2835*x^3 - 5103*x^2 + 5103*x - 2187 p = %o, dimension = %o. 2 7 Computing complement of Modular symbols space of level 2555, weight 2, and dimension 7 Computing 7-new part of Modular symbols space of level 2555, weight 2, and dimension 293. Computing space of modular symbols of level 365 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.119 s) III. 3-term relations. Computing quotient by 148 relations. Form quot and then images (0.05 s) (total time to create space = 0.169 s) Computing index-1 degeneracy map from level 2555 to 365. (0.2 s) Computing index-7 degeneracy map from level 2555 to 365. (0.34 s) Computing index-1 degeneracy map from level 365 to 2555. (0.85 s) Computing index-7 degeneracy map from level 365 to 2555. (0.969 s) Computing 73-new part of Modular symbols space of level 2555, weight 2, and dimension 293. Computing space of modular symbols of level 35 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 16 relations. Form quot and then images (0.01 s) (total time to create space = 0.019 s) Computing index-1 degeneracy map from level 2555 to 35. (0.071 s) Computing index-73 degeneracy map from level 2555 to 35. (4.049 s) Computing index-1 degeneracy map from level 35 to 2555. (1.701 s) Computing index-73 degeneracy map from level 35 to 2555. (1.909 s) Finding newform decomposition of Modular symbols space of level 2555, weight 2, and dimension 293. Computing cuspidal part of Modular symbols space of level 2555, weight 2, and dimension 293 Decomposing space of level 2555 and dimension 143 using T_2. (will stop at 592) Computing T_2 on dual space of dimension 143. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing characteristic polynomial of T_2. x^143 - x^142 - 217*x^141 + 217*x^140 + 22994*x^139 - 22986*x^138 - 1585758*x^137 + 1584102*x^136 + 80040225*x^135 - 79872945*x^134 - 3152689489*x^133 + 3141699265*x^132 + 100902706342*x^131 - 100374599382*x^130 - 2697866626946*x^129 + 2678077132394*x^128 + 61488808149340*x^127 - 60886687045284*x^126 - 1213025701740964*x^125 + 1197732169616676*x^124 + 20961960255020416*x^123 - 20631089024130408*x^122 - 320357203358289244*x^121 + 314166103835134100*x^120 + 4363780487147385011*x^119 - 4262386316188173563*x^118 - 53323323792134992275*x^117 + 51855966727335126795*x^116 + 587679927540374791130*x^115 - 568769170282631279802*x^114 - 5868312552339403889562*x^113 + 5649879134690403590514*x^112 + 53298911971590008203863*x^111 - 51025410152667750969407*x^110 - 441770355881629661970847*x^109 + 420351244142494349688327*x^108 + 3351077927944028424221874*x^107 - 3167717876983007335496074*x^106 - 23320943076933775202728362*x^105 + 21889983706697677235986346*x^104 + 149209692348318763815514169*x^103 - 139000624142448433813004553*x^102 - 879274453287661538007813541*x^101 + 812528698293354154845254229*x^100 + 4779723223676109372792541176*x^99 - 4379011117003736164005619536*x^98 - 23999729726933999046187955624*x^97 + 21786764880291589727926472696*x^96 + 111434642047566261858439993786*x^95 - 100175719509702457927941038682*x^94 - 478903960594303992996847916918*x^93 + 426066232816666433256621480702*x^92 + 1906431378659764024483379725384*x^91 - 1677466378799559160397980474808*x^90 - 7033971199459126718753482699704*x^89 + 6117031598296350988539928312104*x^88 + 24064973277508593446309672683712*x^87 - 20669102603781428625844725358600*x^86 - 76368580684525346363738266934632*x^85 + 64732114676748582230838868566464*x^84 + 224838761458739705215469400106792*x^83 - 187932124247516807741269886893400*x^82 - 614162312030472565700977032849876*x^81 + 505796638439900456014457337849740*x^80 + 1556419171994109290544900565004396*x^79 - 1261832748886192215109967219450092*x^78 - 3658693737563810885428945718331888*x^77 + 2917317417407141159770110667439648*x^76 + 7975458778198395176515681222427534*x^75 - 6248492787112560505310680754078422*x^74 - 16115326088620561375253969904587102*x^73 + 12393074156983822184802592247395566*x^72 + 30168197183439956722644808608329744*x^71 - 22748152526792353046686118893635936*x^70 - 52288734881390678182742893895341056*x^69 + 38616741514174910844010175664585840*x^68 + 83846431819697975778094673075087258*x^67 - 60577801881885725190466141101631946*x^66 - 124277846790647453099830322067768650*x^65 + 87730593053617067178149059404850842*x^64 + 170096072550491425943592373974238300*x^63 - 117171710721973464325521964970390084*x^62 - 214726751825437120030157906871707096*x^61 + 144146354278384586692775107198212480*x^60 + 249693461083010031218064419305159652*x^59 - 163119565866498558194946406539658012*x^58 - 267072650569087086072296848774995344*x^57 + 169541321280594658916314140900040048*x^56 + 262334173908283279674905339957103400*x^55 - 161579505849349396974568578956254640*x^54 - 236216560599136475605086272746999544*x^53 + 140940232655561806706725511392727584*x^52 + 194599484635255723592956818329874880*x^51 - 112288227071468260712758124759924624*x^50 - 146354856141703546773346462829994804*x^49 + 81527460928568922397375478581209708*x^48 + 100246613300438884876752390146080189*x^47 - 53809787486385590225735966460669357*x^46 - 62371832637736858035963642260540985*x^45 + 32196495834771074355327669355958457*x^44 + 35148660687479981875987544253147118*x^43 - 17410788899318203565402175967488326*x^42 - 17883419750740385193518626192567050*x^41 + 8480382679216377032720016331225274*x^40 + 8186449290650283673439999998053363*x^39 - 3706415339080646862534408782015659*x^38 - 3358705939105564400389799761186591*x^37 + 1447408626103690634294798487634679*x^36 + 1229806070964222785462384973083170*x^35 - 502633707493950717040321711782570*x^34 - 399994278830546139415699446407542*x^33 + 154378093673301388835583100073862*x^32 + 114965923762936351442041753827509*x^31 - 41678737517737736008895502489101*x^30 - 29032013225489306787303069814213*x^29 + 9821109603378889499688755560605*x^28 + 6399973433767215683615521845336*x^27 - 2003342734880941068894801586232*x^26 - 1222699285163956321957313331200*x^25 + 350360675961410474136183952720*x^24 + 200776181865241491427117051456*x^23 - 51936005591283463485339679808*x^22 - 28067564043779499142239792384*x^21 + 6435727165778052189141323520*x^20 + 3302893589140161958446334976*x^19 - 655304571590926999116340224*x^18 - 322725894275463396048519168*x^17 + 53634580476303750353821696*x^16 + 25737832181128945094017024*x^15 - 3425761245122288238608384*x^14 - 1638469082531129465241600*x^13 + 163634014355174409830400*x^12 + 80796032098128823320576*x^11 - 5457420211525641568256*x^10 - 2958534018296192172032*x^9 + 110905987625924952064*x^8 + 75561380526879145984*x^7 - 861177706673340416*x^6 - 1217911275380539392*x^5 - 10261465466404864*x^4 + 10323046506168320*x^3 + 184615142686720*x^2 - 29071559884800*x time = 64.54 Factoring characteristic polynomial. [ , , , , , , , , , , , , , , , ] time = 0.839 Cutting out subspace using f(T_2), where f=x - 2. Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). Charpoly = x^2 + 8*x + 16. Decomposing space of level 2555 and dimension 2 using T_2. (will stop at 592) Computing characteristic polynomial of T_2. x^2 + 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Charpoly = x^2 - 4*x + 4. Decomposing space of level 2555 and dimension 2 using T_3. (will stop at 592) Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing characteristic polynomial of T_3. x^2 - 2*x - 3 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_3), where f=x - 3. Cutting out subspace using f(T_3), where f=x + 1. Cutting out subspace using f(T_2), where f=x^2 - 5. Cutting out subspace using f(T_2), where f=x^3 + x^2 - 6*x - 4. Cutting out subspace using f(T_2), where f=x^4 - 4*x^2 - x + 1. Cutting out subspace using f(T_2), where f=x^9 + 6*x^8 + 5*x^7 - 28*x^6 - 44*x^5 + 35*x^4 + 73*x^3 - 9*x^2 - 34*x - 4. Cutting out subspace using f(T_2), where f=x^13 - 18*x^11 - x^10 + 116*x^9 + 11*x^8 - 333*x^7 - 33*x^6 + 441*x^5 + 43*x^4 - 239*x^3 - 25*x^2 + 28*x + 5. Cutting out subspace using f(T_2), where f=x^13 - 17*x^11 + x^10 + 109*x^9 - 12*x^8 - 328*x^7 + 51*x^6 + 469*x^5 - 94*x^4 - 278*x^3 + 67*x^2 + 40*x - 8. Cutting out subspace using f(T_2), where f=x^15 + 3*x^14 - 15*x^13 - 46*x^12 + 86*x^11 + 265*x^10 - 250*x^9 - 733*x^8 + 408*x^7 + 1017*x^6 - 378*x^5 - 667*x^4 + 183*x^3 + 172*x^2 - 36*x - 8. Cutting out subspace using f(T_2), where f=x^17 - 5*x^16 - 13*x^15 + 92*x^14 + 42*x^13 - 673*x^12 + 94*x^11 + 2549*x^10 - 816*x^9 - 5401*x^8 + 1696*x^7 + 6363*x^6 - 1427*x^5 - 3804*x^4 + 524*x^3 + 952*x^2 - 96*x - 64. Cutting out subspace using f(T_2), where f=x^17 + 4*x^16 - 17*x^15 - 81*x^14 + 94*x^13 + 638*x^12 - 105*x^11 - 2472*x^10 - 746*x^9 + 4900*x^8 + 2682*x^7 - 4642*x^6 - 3061*x^5 + 1724*x^4 + 1084*x^3 - 195*x^2 - 68*x + 4. Cutting out subspace using f(T_2), where f=x^21 - 5*x^20 - 26*x^19 + 167*x^18 + 198*x^17 - 2258*x^16 + 422*x^15 + 15721*x^14 - 14717*x^13 - 58749*x^12 + 89430*x^11 + 107772*x^10 - 250189*x^9 - 56005*x^8 + 340849*x^7 - 76632*x^6 - 212293*x^5 + 94677*x^4 + 53793*x^3 - 31224*x^2 - 3948*x + 2888. Cutting out subspace using f(T_2), where f=x^23 - 7*x^22 - 14*x^21 + 197*x^20 - 98*x^19 - 2254*x^18 + 3300*x^17 + 13327*x^16 - 28957*x^15 - 41827*x^14 + 129662*x^13 + 57288*x^12 - 327005*x^11 + 21351*x^10 + 460267*x^9 - 156754*x^8 - 335861*x^7 + 156253*x^6 + 114109*x^5 - 53286*x^4 - 15804*x^3 + 6032*x^2 + 784*x - 192. Computing representation of Modular symbols space of level 2555, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 2 2 Computing T_3 on space of dimension 300. (0.141 s) Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x - 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 2 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^2 - 5 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^3 + x^2 - 6*x - 4 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 2555, weight 2, and dimension 4. Goal dimension = 4. J0( N: 2555 ) NewformDecomposition( M: Modular symbols space of level 2555, weight 2, and dimension... ) !!( M: Full Modular symbols space of level 2555, weight 2, and dime..., x: Modular symbols space of level 2555, weight 2, and dimension... ) subset( M1: Modular symbols space of level 2555, weight 2, and dimension..., M2: Full Modular symbols space of level 2555, weight 2, and dime... ) Representation( M: Modular symbols space of level 2555, weight 2, and dimension... ) VectorSpace( M: Modular symbols space of level 2555, weight 2, and dimension... ) Restrict( A: [3 0 -2 2 0 -2 2 0 -2 0 2 -2 0 0 0 0 2 0 0 -2 0 0 0 2 -2 0 2..., x: Vector space of degree 300, dimension 143 over Rational Fiel... ) In file "/home/was/modsym/linalg.m", line 264, column 21: >> v := [Coordinates(S, S.i*A) : i in [1..#B]]; ^ Runtime error in 'Coordinates': Argument 2 is not in argument 1 >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2555, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 1553.200 seconds Magma V2.7-1 Mon Jan 29 2001 13:32:52 on modular [Seed = 3136680384] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2557 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.781 s) III. 3-term relations. Computing quotient by 854 relations. Form quot and then images (0.52 s) (total time to create space = 1.34 s) Computing cuspidal part of Full Modular symbols space of level 2557, weight 2, and dimension 213 Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 3136680384 Time to this point: 2.78 Segmentation fault >> -2750.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2557, a, ^ User error: Identifier 'a' has not been declared or assigned