# Maass forms downloaded from the LMFDB on 18 June 2026. # Search link: https://www.lmfdb.org/ModularForm/GL2/Q/Maass/15/0/1/ # Query "{'level': 15, 'weight': 0}" returned 304 forms, sorted by level. # Each entry in the following data list has the form: # [Label, Level, Weight, Char, Spectral parameter, Symmetry, Fricke] # For more details, see the definitions at the bottom of the file. "15.0.1.1.1" 15 0 [15, 1] 1.51842933602416588036746726626 1 -1 "15.0.1.2.1" 15 0 [15, 1] 1.82147632892265862113987622066 0 1 "15.0.1.3.1" 15 0 [15, 1] 2.23047412064561808730126364629 1 -1 "15.0.1.4.1" 15 0 [15, 1] 2.36133422204256634651088038989 1 1 "15.0.1.5.1" 15 0 [15, 1] 2.91653733402465304220481312243 0 1 "15.0.1.6.1" 15 0 [15, 1] 3.10450058521073190818804678447 1 -1 "15.0.1.7.1" 15 0 [15, 1] 3.22026652842799542163572005631 0 1 "15.0.1.8.1" 15 0 [15, 1] 3.49290270259253829669762604106 0 -1 "15.0.1.9.1" 15 0 [15, 1] 3.61330792231513373629063083162 1 1 "15.0.1.10.1" 15 0 [15, 1] 3.85551540683416285366650206478 1 -1 "15.0.1.11.1" 15 0 [15, 1] 3.9277524689597685848188949845 0 -1 "15.0.1.12.1" 15 0 [15, 1] 4.22329657414339688238248729731 1 -1 "15.0.1.13.1" 15 0 [15, 1] 4.53086807747242567410336924024 0 1 "15.0.1.14.1" 15 0 [15, 1] 4.61137801143056251348731605181 0 1 "15.0.1.15.1" 15 0 [15, 1] 4.75479713394882413272958192519 0 1 "15.0.1.16.1" 15 0 [15, 1] 5.04639152421925115467652117489 1 1 "15.0.1.17.1" 15 0 [15, 1] 5.1172051641085013418147695668 1 -1 "15.0.1.18.1" 15 0 [15, 1] 5.23156860276545813953819318022 1 -1 "15.0.1.19.1" 15 0 [15, 1] 5.31220835198686664202485815516 0 -1 "15.0.1.20.1" 15 0 [15, 1] 5.31945091147029633606434503392 1 1 "15.0.1.21.1" 15 0 [15, 1] 5.59861573203898138782827219802 1 1 "15.0.1.22.1" 15 0 [15, 1] 5.85950414296348633115912355467 0 -1 "15.0.1.23.1" 15 0 [15, 1] 5.90447347444879828743011922607 1 -1 "15.0.1.24.1" 15 0 [15, 1] 5.98505799392075505386041870224 0 1 "15.0.1.25.1" 15 0 [15, 1] 6.0764219866034818733818106812 1 -1 "15.0.1.26.1" 15 0 [15, 1] 6.18043116287990243185791813716 0 1 "15.0.1.27.1" 15 0 [15, 1] 6.50436815346124173391115181578 0 1 "15.0.1.28.1" 15 0 [15, 1] 6.54089429078622357205063720462 0 -1 "15.0.1.29.1" 15 0 [15, 1] 6.71350181148883931633551252536 1 -1 "15.0.1.30.1" 15 0 [15, 1] 6.84293956587284457522059080612 1 1 "15.0.1.31.1" 15 0 [15, 1] 6.93465180361394280318775768972 0 -1 "15.0.1.32.1" 15 0 [15, 1] 6.99752889313935986194445805326 0 1 "15.0.1.33.1" 15 0 [15, 1] 7.05965411929993922610252179018 1 -1 "15.0.1.34.1" 15 0 [15, 1] 7.19520694814750650966937328408 0 -1 "15.0.1.35.1" 15 0 [15, 1] 7.19821130416664651903660524395 1 1 "15.0.1.36.1" 15 0 [15, 1] 7.33539452440829135761006733156 0 1 "15.0.1.37.1" 15 0 [15, 1] 7.358903069932244915646560768 0 1 "15.0.1.38.1" 15 0 [15, 1] 7.39439295725818142900734902354 1 -1 "15.0.1.39.1" 15 0 [15, 1] 7.55882759794222035420071702734 1 1 "15.0.1.40.1" 15 0 [15, 1] 7.56217196142289907783685343164 0 -1 "15.0.1.41.1" 15 0 [15, 1] 7.76333046177552089358528249615 0 1 "15.0.1.42.1" 15 0 [15, 1] 7.78622822281770437687453273928 1 -1 "15.0.1.43.1" 15 0 [15, 1] 7.91310981627936331988552529581 0 1 "15.0.1.44.1" 15 0 [15, 1] 8.15565536136961504908731501875 1 1 "15.0.1.45.1" 15 0 [15, 1] 8.39388640633562060543200192275 0 -1 "15.0.1.46.1" 15 0 [15, 1] 8.4854397033297492137005702893 1 1 "15.0.1.47.1" 15 0 [15, 1] 8.51721775113189780839886491205 1 -1 "15.0.1.48.1" 15 0 [15, 1] 8.66501125743234703233038713886 0 -1 "15.0.1.49.1" 15 0 [15, 1] 8.67808170374211862179525285776 0 -1 "15.0.1.50.1" 15 0 [15, 1] 8.68234129230134613141263994356 1 -1 "15.0.1.51.1" 15 0 [15, 1] 8.72098116223993428439213983559 1 -1 "15.0.1.52.1" 15 0 [15, 1] 8.90821836792061364958616442831 0 1 "15.0.1.53.1" 15 0 [15, 1] 8.92232953917331685190729411096 1 -1 "15.0.1.54.1" 15 0 [15, 1] 9.00979095878977776566996275947 1 1 "15.0.1.55.1" 15 0 [15, 1] 9.10018366858779944584008542418 0 1 "15.0.1.56.1" 15 0 [15, 1] 9.16197265961747581248960039913 0 1 "15.0.1.57.1" 15 0 [15, 1] 9.17881232884795972291041203319 0 1 "15.0.1.58.1" 15 0 [15, 1] 9.31426261097500412847942305256 1 -1 "15.0.1.59.1" 15 0 [15, 1] 9.34823014742830132598405023758 1 1 "15.0.1.60.1" 15 0 [15, 1] 9.61137343977827012882212537119 0 -1 "15.0.1.61.1" 15 0 [15, 1] 9.65190399311077087648104198976 1 -1 "15.0.1.62.1" 15 0 [15, 1] 9.67050751225751480553845124102 1 -1 "15.0.1.63.1" 15 0 [15, 1] 9.71661624186756721513501175116 1 1 "15.0.1.64.1" 15 0 [15, 1] 9.82317475633744643135098523957 1 1 "15.0.1.65.1" 15 0 [15, 1] 9.82417896066128541274978863687 0 1 "15.0.1.66.1" 15 0 [15, 1] 9.88449664131979310198264362833 0 -1 "15.0.1.67.1" 15 0 [15, 1] 9.95830408326171795136779903867 1 1 "15.0.1.68.1" 15 0 [15, 1] 10.0207163444650285234771424478 0 -1 "15.0.1.69.1" 15 0 [15, 1] 10.2345439612131553376813523652 1 -1 "15.0.1.70.1" 15 0 [15, 1] 10.2927392311175359110386622219 0 1 "15.0.1.71.1" 15 0 [15, 1] 10.3332479125874268331301501664 0 1 "15.0.1.72.1" 15 0 [15, 1] 10.4123667458329227004448749513 1 1 "15.0.1.73.1" 15 0 [15, 1] 10.484131488024725736860064474 1 -1 "15.0.1.74.1" 15 0 [15, 1] 10.4950859747829672648128951692 0 -1 "15.0.1.75.1" 15 0 [15, 1] 10.6884337126103035287243560486 1 -1 "15.0.1.76.1" 15 0 [15, 1] 10.699734460220935545870324584 0 1 "15.0.1.77.1" 15 0 [15, 1] 10.733004642739964006756104513 1 1 "15.0.1.78.1" 15 0 [15, 1] 10.7704482094491743466867333474 0 1 "15.0.1.79.1" 15 0 [15, 1] 10.7747112927792467914009053041 0 -1 "15.0.1.80.1" 15 0 [15, 1] 10.9271780664877098737750581705 1 -1 "15.0.1.81.1" 15 0 [15, 1] 10.9791052877594833320045672147 0 1 "15.0.1.82.1" 15 0 [15, 1] 11.041590811453463491486916231 0 -1 "15.0.1.83.1" 15 0 [15, 1] 11.1586298115048598838729509873 1 -1 "15.0.1.84.1" 15 0 [15, 1] 11.2065951033504189405841084873 0 1 "15.0.1.85.1" 15 0 [15, 1] 11.2911907467278288275712157182 0 -1 "15.0.1.86.1" 15 0 [15, 1] 11.3156361509643109940561235621 1 1 "15.0.1.87.1" 15 0 [15, 1] 11.4962916849561909491398325287 1 -1 "15.0.1.88.1" 15 0 [15, 1] 11.5221371450546348674254488522 0 -1 "15.0.1.89.1" 15 0 [15, 1] 11.5695018491603259401368794459 1 1 "15.0.1.90.1" 15 0 [15, 1] 11.6839515324564340790423775114 0 1 "15.0.1.91.1" 15 0 [15, 1] 11.7600983055055380288446453635 1 -1 "15.0.1.92.1" 15 0 [15, 1] 11.8225243579899381120593984074 1 1 "15.0.1.93.1" 15 0 [15, 1] 11.8739984964056757125574302859 0 -1 "15.0.1.94.1" 15 0 [15, 1] 11.9119697903966351501800894137 1 -1 "15.0.1.95.1" 15 0 [15, 1] 11.9275703294512012069554048761 0 1 "15.0.1.96.1" 15 0 [15, 1] 12.0305386587762883095573919254 0 1 "15.0.1.97.1" 15 0 [15, 1] 12.1105114325231370312060133548 1 -1 "15.0.1.98.1" 15 0 [15, 1] 12.1744371988437547465346445144 1 1 "15.0.1.99.1" 15 0 [15, 1] 12.2254089157236274658501505337 1 1 "15.0.1.100.1" 15 0 [15, 1] 12.2816628176168126994154122677 0 -1 "15.0.1.101.1" 15 0 [15, 1] 12.3164033346453280176322873543 0 -1 "15.0.1.102.1" 15 0 [15, 1] 12.3738745822056837622322721212 1 -1 "15.0.1.103.1" 15 0 [15, 1] 12.3841246799112190362029663107 0 1 "15.0.1.104.1" 15 0 [15, 1] 12.5225202833313374192635506594 0 1 "15.0.1.105.1" 15 0 [15, 1] 12.5653426648724845535056877253 1 1 "15.0.1.106.1" 15 0 [15, 1] 12.6337017811394169481344490744 0 1 "15.0.1.107.1" 15 0 [15, 1] 12.6398086516863788319532281862 1 -1 "15.0.1.108.1" 15 0 [15, 1] 12.7834819810044346143664029497 0 -1 "15.0.1.109.1" 15 0 [15, 1] 12.7992483012406712214843504984 1 1 "15.0.1.110.1" 15 0 [15, 1] 12.8154234545211056031907986898 1 1 "15.0.1.111.1" 15 0 [15, 1] 12.8261277577392505178292165033 1 -1 "15.0.1.112.1" 15 0 [15, 1] 12.8911300189501208117574041757 0 1 "15.0.1.113.1" 15 0 [15, 1] 12.9799547569079104898517572464 1 -1 "15.0.1.114.1" 15 0 [15, 1] 12.9875853925932969709280341514 1 1 "15.0.1.115.1" 15 0 [15, 1] 13.1223210201943070273245358548 0 1 "15.0.1.116.1" 15 0 [15, 1] 13.18245834911393876666360215 0 -1 "15.0.1.117.1" 15 0 [15, 1] 13.3100555736372809917130667015 0 -1 "15.0.1.118.1" 15 0 [15, 1] 13.3376605549051403900163032451 0 -1 "15.0.1.119.1" 15 0 [15, 1] 13.3515727286200086072960658547 0 -1 "15.0.1.120.1" 15 0 [15, 1] 13.411549449838130543827630634 1 -1 "15.0.1.121.1" 15 0 [15, 1] 13.4427786528988385535771942865 1 -1 "15.0.1.122.1" 15 0 [15, 1] 13.4772491398461775360637407852 0 1 "15.0.1.123.1" 15 0 [15, 1] 13.4874424443220803921000552585 1 -1 "15.0.1.124.1" 15 0 [15, 1] 13.7071453228109820857108502894 0 1 "15.0.1.125.1" 15 0 [15, 1] 13.7853115736658678675137565567 1 1 "15.0.1.126.1" 15 0 [15, 1] 13.8341628367615057061924200818 1 1 "15.0.1.127.1" 15 0 [15, 1] 13.8783567331800419516268127299 0 1 "15.0.1.128.1" 15 0 [15, 1] 13.937651787591620803037958992 0 1 "15.0.1.129.1" 15 0 [15, 1] 13.9846574472841839614102095332 1 -1 "15.0.1.130.1" 15 0 [15, 1] 14.0276462277580513679315689216 0 1 "15.0.1.131.1" 15 0 [15, 1] 14.0874463709043267531040202738 1 -1 "15.0.1.132.1" 15 0 [15, 1] 14.1483956486722671075964881791 1 -1 "15.0.1.133.1" 15 0 [15, 1] 14.1674813635536035973794244444 0 -1 "15.0.1.134.1" 15 0 [15, 1] 14.201049383857804485989835209 0 1 "15.0.1.135.1" 15 0 [15, 1] 14.2260209935805107038330982553 1 1 "15.0.1.136.1" 15 0 [15, 1] 14.3245075202138103886520294357 0 -1 "15.0.1.137.1" 15 0 [15, 1] 14.3365730955525218005121854331 0 -1 "15.0.1.138.1" 15 0 [15, 1] 14.3384468234102818012434559236 0 -1 "15.0.1.139.1" 15 0 [15, 1] 14.3430871812286678200720602035 1 -1 "15.0.1.140.1" 15 0 [15, 1] 14.3452711976464833009518971896 1 1 "15.0.1.141.1" 15 0 [15, 1] 14.4170963473149255924231128547 1 1 "15.0.1.142.1" 15 0 [15, 1] 14.5007913935921085810273201686 1 1 "15.0.1.143.1" 15 0 [15, 1] 14.6351891026060200502962470303 0 1 "15.0.1.144.1" 15 0 [15, 1] 14.6421005765394903969133240156 0 -1 "15.0.1.145.1" 15 0 [15, 1] 14.7264095664532946232536823122 0 -1 "15.0.1.146.1" 15 0 [15, 1] 14.7541736403196868396478905988 1 -1 "15.0.1.147.1" 15 0 [15, 1] 14.8310779474675114669951143305 0 1 "15.0.1.148.1" 15 0 [15, 1] 14.8772261447608003882438409577 1 1 "15.0.1.149.1" 15 0 [15, 1] 14.9021210942961061377190379909 0 1 "15.0.1.150.1" 15 0 [15, 1] 14.9457053184171948999404191106 1 -1 "15.0.1.151.1" 15 0 [15, 1] 15.0803055369229606321492755006 0 1 "15.0.1.152.1" 15 0 [15, 1] 15.1563999217977299508587962802 0 1 "15.0.1.153.1" 15 0 [15, 1] 15.230295888154499089683581646 1 0 "15.0.1.154.1" 15 0 [15, 1] 15.2335917355112958268501513405 1 1 "15.0.1.155.1" 15 0 [15, 1] 15.2373643386995385754383731508 0 -1 "15.0.1.156.1" 15 0 [15, 1] 15.3366884628158742878970212467 1 -1 "15.0.1.157.1" 15 0 [15, 1] 15.427541685900084659946734047 0 -1 "15.0.1.158.1" 15 0 [15, 1] 15.4323974123051758368718629049 1 -1 "15.0.1.159.1" 15 0 [15, 1] 15.4614210380933527639837047546 0 1 "15.0.1.160.1" 15 0 [15, 1] 15.4758898711831092080234771572 1 1 "15.0.1.161.1" 15 0 [15, 1] 15.5521886184757959257874078979 1 1 "15.0.1.162.1" 15 0 [15, 1] 15.5873841903253268913688773467 0 1 "15.0.1.163.1" 15 0 [15, 1] 15.7001784408189090002664956027 0 -1 "15.0.1.164.1" 15 0 [15, 1] 15.7335564327884238117410507365 1 -1 "15.0.1.165.1" 15 0 [15, 1] 15.8158273822656774545006565378 0 1 "15.0.1.166.1" 15 0 [15, 1] 15.843172161469076141974989512 1 -1 "15.0.1.167.1" 15 0 [15, 1] 15.9562995562489382688967235504 1 1 "15.0.1.168.1" 15 0 [15, 1] 15.9705944844205704151923179703 0 -1 "15.0.1.169.1" 15 0 [15, 1] 15.9799927909722504056061488007 1 0 "15.0.1.170.1" 15 0 [15, 1] 15.9968074063998459938290851915 1 -1 "15.0.1.171.1" 15 0 [15, 1] 16.003945812876984057676644376 1 -1 "15.0.1.172.1" 15 0 [15, 1] 16.0136345530727331940947273628 0 1 "15.0.1.173.1" 15 0 [15, 1] 16.0210132545673790593925185026 1 1 "15.0.1.174.1" 15 0 [15, 1] 16.0303973543649264211210140103 0 -1 "15.0.1.175.1" 15 0 [15, 1] 16.2890708221608030664157089731 0 1 "15.0.1.176.1" 15 0 [15, 1] 16.3284095971595751769052517186 0 -1 "15.0.1.177.1" 15 0 [15, 1] 16.3720372546830004897757316396 0 1 "15.0.1.178.1" 15 0 [15, 1] 16.4118564154251888356250176049 1 0 "15.0.1.179.1" 15 0 [15, 1] 16.4340139266412300138778774477 0 -1 "15.0.1.180.1" 15 0 [15, 1] 16.4418282501136229276153237769 1 0 "15.0.1.181.1" 15 0 [15, 1] 16.44233628848787264413087761 1 0 "15.0.1.182.1" 15 0 [15, 1] 16.4860164559922146974245351117 0 -1 "15.0.1.183.1" 15 0 [15, 1] 16.5784500632701440846682473071 1 0 "15.0.1.184.1" 15 0 [15, 1] 16.5856414862723883915254327539 1 0 "15.0.1.185.1" 15 0 [15, 1] 16.591925839125858922953595214 1 0 "15.0.1.186.1" 15 0 [15, 1] 16.6519586488576441948576671136 1 1 "15.0.1.187.1" 15 0 [15, 1] 16.6909587658095205852644183873 0 -1 "15.0.1.188.1" 15 0 [15, 1] 16.7073008093040435912786735123 1 1 "15.0.1.189.1" 15 0 [15, 1] 16.7421068737425537837966250802 0 1 "15.0.1.190.1" 15 0 [15, 1] 16.7716937609212790012052090825 0 1 "15.0.1.191.1" 15 0 [15, 1] 16.9084419702310594678430412282 1 -1 "15.0.1.192.1" 15 0 [15, 1] 16.9573854470924023527475909678 1 0 "15.0.1.193.1" 15 0 [15, 1] 17.0236332341743183870458285746 0 1 "15.0.1.194.1" 15 0 [15, 1] 17.1423354350245969110252499101 0 -1 "15.0.1.195.1" 15 0 [15, 1] 17.1509315065294968789124276465 0 1 "15.0.1.196.1" 15 0 [15, 1] 17.2011366504125960797273554208 1 1 "15.0.1.197.1" 15 0 [15, 1] 17.2150114362716819831657581424 0 1 "15.0.1.198.1" 15 0 [15, 1] 17.2561412863906617027379421735 1 0 "15.0.1.199.1" 15 0 [15, 1] 17.3135186089487208674431537841 1 0 "15.0.1.200.1" 15 0 [15, 1] 17.3272292877641452299264010301 0 -1 "15.0.1.201.1" 15 0 [15, 1] 17.3506737128578344952648004118 0 1 "15.0.1.202.1" 15 0 [15, 1] 17.35587683614996834924693573 1 0 "15.0.1.203.1" 15 0 [15, 1] 17.4053414878989441561954450467 0 1 "15.0.1.204.1" 15 0 [15, 1] 17.4818935984384403044191211885 1 0 "15.0.1.205.1" 15 0 [15, 1] 17.4920562100076460286088156534 1 0 "15.0.1.206.1" 15 0 [15, 1] 17.5319574240122120958984609535 0 -1 "15.0.1.207.1" 15 0 [15, 1] 17.6333011804383086675187978075 1 0 "15.0.1.208.1" 15 0 [15, 1] 17.699639459780360660384953773 0 -1 "15.0.1.209.1" 15 0 [15, 1] 17.7339208563220661615189194703 0 -1 "15.0.1.210.1" 15 0 [15, 1] 17.7464152866679530821924698075 1 0 "15.0.1.211.1" 15 0 [15, 1] 17.7629086344071575353588329086 0 0 "15.0.1.212.1" 15 0 [15, 1] 17.8974323286274674094930718698 1 0 "15.0.1.213.1" 15 0 [15, 1] 17.9099044400932334320406865313 1 0 "15.0.1.214.1" 15 0 [15, 1] 17.9462483988620039705068640414 1 0 "15.0.1.215.1" 15 0 [15, 1] 17.9653462019761914463674788706 1 0 "15.0.1.216.1" 15 0 [15, 1] 18.0160153362662966227634781561 0 1 "15.0.1.217.1" 15 0 [15, 1] 18.030516827139286494143185624 0 1 "15.0.1.218.1" 15 0 [15, 1] 18.0411270301769691313090623406 0 1 "15.0.1.219.1" 15 0 [15, 1] 18.0475671854822194626447948953 0 -1 "15.0.1.220.1" 15 0 [15, 1] 18.1209881056864452002690897728 0 1 "15.0.1.221.1" 15 0 [15, 1] 18.1788831447505110464644238387 0 1 "15.0.1.222.1" 15 0 [15, 1] 18.2051298538350144761860153695 0 0 "15.0.1.223.1" 15 0 [15, 1] 18.2784000557844644093564572346 0 -1 "15.0.1.224.1" 15 0 [15, 1] 18.4242828133012245375623527205 1 0 "15.0.1.225.1" 15 0 [15, 1] 18.4293556102192869123950761947 1 0 "15.0.1.226.1" 15 0 [15, 1] 18.4515068853851381156426206957 1 0 "15.0.1.227.1" 15 0 [15, 1] 18.4905295996519722103241437823 1 0 "15.0.1.228.1" 15 0 [15, 1] 18.5149182483828933097314340519 1 0 "15.0.1.229.1" 15 0 [15, 1] 18.5423741599404934042766588308 0 -1 "15.0.1.230.1" 15 0 [15, 1] 18.6067138351548174934357976411 1 0 "15.0.1.231.1" 15 0 [15, 1] 18.6265165240337801355683267369 1 0 "15.0.1.232.1" 15 0 [15, 1] 18.6296396631616645091600447753 0 0 "15.0.1.233.1" 15 0 [15, 1] 18.7112584094562126454609435154 1 0 "15.0.1.234.1" 15 0 [15, 1] 18.7207651434870612611464938102 0 1 "15.0.1.235.1" 15 0 [15, 1] 18.768725868184916849373912346 1 0 "15.0.1.236.1" 15 0 [15, 1] 18.8462228558305222663489411189 0 0 "15.0.1.237.1" 15 0 [15, 1] 18.8678334960027141989275263653 0 1 "15.0.1.238.1" 15 0 [15, 1] 18.9213875149328359261206937777 0 -1 "15.0.1.239.1" 15 0 [15, 1] 18.9848533912357635013544886368 1 0 "15.0.1.240.1" 15 0 [15, 1] 19.0259718489916469815608322173 1 0 "15.0.1.241.1" 15 0 [15, 1] 19.0656416197186066683490333931 1 0 "15.0.1.242.1" 15 0 [15, 1] 19.1520602479381772456800197945 0 0 "15.0.1.243.1" 15 0 [15, 1] 19.1540294208929375037564786877 1 0 "15.0.1.244.1" 15 0 [15, 1] 19.1744717076927709724326661806 0 0 "15.0.1.245.1" 15 0 [15, 1] 19.1874878277644104481815862382 0 -1 "15.0.1.246.1" 15 0 [15, 1] 19.2426016515647409560444464772 1 0 "15.0.1.247.1" 15 0 [15, 1] 19.270820964792782880749404476 0 1 "15.0.1.248.1" 15 0 [15, 1] 19.3113013127820834676014095918 0 0 "15.0.1.249.1" 15 0 [15, 1] 19.3181919416176701635901663747 1 0 "15.0.1.250.1" 15 0 [15, 1] 19.3450757904734613797107629283 0 0 "15.0.1.251.1" 15 0 [15, 1] 19.4300783265801281365419528556 0 0 "15.0.1.252.1" 15 0 [15, 1] 19.4730514474154931851915946646 1 0 "15.0.1.253.1" 15 0 [15, 1] 19.4876982877444649050065092985 1 0 "15.0.1.254.1" 15 0 [15, 1] 19.4995572845859651640243184712 0 -1 "15.0.1.255.1" 15 0 [15, 1] 19.5275224537367848575727898401 0 0 "15.0.1.256.1" 15 0 [15, 1] 19.5501030700094385256694244569 1 0 "15.0.1.257.1" 15 0 [15, 1] 19.6342747964120544956737383161 0 -1 "15.0.1.258.1" 15 0 [15, 1] 19.6480428857383977026660490942 1 0 "15.0.1.259.1" 15 0 [15, 1] 19.7109281035859468157691840388 1 0 "15.0.1.260.1" 15 0 [15, 1] 19.7204289375053924451520860966 0 0 "15.0.1.261.1" 15 0 [15, 1] 19.7339648525393873801509517181 1 0 "15.0.1.262.1" 15 0 [15, 1] 19.7910568755626157683002710196 1 0 "15.0.1.263.1" 15 0 [15, 1] 19.8893172057455004438416512685 0 0 "15.0.1.264.1" 15 0 [15, 1] 19.9501574425340816389457636436 0 0 "15.0.1.265.1" 15 0 [15, 1] 19.9619971736462129071978480395 1 0 "15.0.1.266.1" 15 0 [15, 1] 19.9762669882243477528379780504 1 0 "15.0.1.267.1" 15 0 [15, 1] 19.9791608760440441296256792215 1 0 "15.0.1.268.1" 15 0 [15, 1] 19.9914964562134285325785213491 0 0 "15.0.1.269.1" 15 0 [15, 1] 20.0125664462171042898790081912 0 0 "15.0.1.270.1" 15 0 [15, 1] 20.0540993027645565627929777833 0 0 "15.0.1.271.1" 15 0 [15, 1] 20.118270186971168444873718131 1 0 "15.0.1.272.1" 15 0 [15, 1] 20.1796174830606388144775884766 0 0 "15.0.1.273.1" 15 0 [15, 1] 20.2452201797862146817739194344 0 0 "15.0.1.274.1" 15 0 [15, 1] 20.2904635269052555590630483348 1 0 "15.0.1.275.1" 15 0 [15, 1] 20.2995964880860255117331529585 0 0 "15.0.1.276.1" 15 0 [15, 1] 20.2999659814839154618216200437 1 0 "15.0.1.277.1" 15 0 [15, 1] 20.3411616055749970013459006737 1 0 "15.0.1.278.1" 15 0 [15, 1] 20.35241498916903214914090362 1 0 "15.0.1.279.1" 15 0 [15, 1] 20.4402630410387324031624594124 1 0 "15.0.1.280.1" 15 0 [15, 1] 20.507007918466813131509632672 0 0 "15.0.1.281.1" 15 0 [15, 1] 20.530165201892437002099465328 1 0 "15.0.1.282.1" 15 0 [15, 1] 20.5578542779913907388112085192 0 0 "15.0.1.283.1" 15 0 [15, 1] 20.5858238979001997440772936584 1 0 "15.0.1.284.1" 15 0 [15, 1] 20.6460664477497999984641601563 1 0 "15.0.1.285.1" 15 0 [15, 1] 20.6631833287598594945256822833 0 0 "15.0.1.286.1" 15 0 [15, 1] 20.671301798993651498332148856 1 0 "15.0.1.287.1" 15 0 [15, 1] 20.7182830523669501668411272669 0 0 "15.0.1.288.1" 15 0 [15, 1] 20.7295681724332825812549130599 0 0 "15.0.1.289.1" 15 0 [15, 1] 20.8723337984213239703540473086 0 0 "15.0.1.290.1" 15 0 [15, 1] 20.9645247157827270235242978624 0 0 "15.0.1.291.1" 15 0 [15, 1] 20.9991251145500047736932478917 0 0 "15.0.1.292.1" 15 0 [15, 1] 21.0076899639346705912392369891 0 0 "15.0.1.293.1" 15 0 [15, 1] 21.0782125661595692758064784084 0 0 "15.0.1.294.1" 15 0 [15, 1] 21.0907445823156507437271105787 1 0 "15.0.1.295.1" 15 0 [15, 1] 21.1164405457947474633655265516 1 0 "15.0.1.296.1" 15 0 [15, 1] 21.1627467543451966377910364953 1 0 "15.0.1.297.1" 15 0 [15, 1] 21.2202831216332748851739598204 1 0 "15.0.1.298.1" 15 0 [15, 1] 21.2365472084673991433176604686 0 0 "15.0.1.299.1" 15 0 [15, 1] 21.3056893793339154120295025569 0 0 "15.0.1.300.1" 15 0 [15, 1] 21.3717646887768475897122332273 1 0 "15.0.1.301.1" 15 0 [15, 1] 21.491253192976772292970793756 0 0 "15.0.1.302.1" 15 0 [15, 1] 21.5024332806041062935317923976 0 0 "15.0.1.303.1" 15 0 [15, 1] 21.7192987455846393603439819907 0 0 "15.0.1.304.1" 15 0 [15, 1] 21.8123864089885897677280853151 1 0 #Label (maass_label) -- # The **label** of a Maass newform $f \in M_k(\Gamma_0(N), \chi)$ either has the format $N.k.a.m.d$ or $N.m$, where # - $N$ is the level; # - $k$ is the weight; # - $N.a$ is the Conrey label of the Dirichlet character $\chi$; # - $m$ is the spectral index, which uniquely identifies the eigenvalue $\lambda$ of $f$; # - $d$ indicates which form among those of level $N$, Dirichlet character $N.a$, and eigenvalue $\lambda$ this is. # The shorter form is used when $k=0$ and $a=1$ and $d=1$. # For squarefree level, it is conjectured that there is only one Maass form per eigenvalue $\lambda$, hence $d$ is (currently) always $1$. Generally, there are only finitely many Maass newforms in $M_k(\Gamma_0(N), \chi)$ with the same eigenvalue $\lambda$. Then $d$ denotes the index among these finitely many forms, where the ordering is lexicographical in the sequence $\{ \bigl(\mathrm{Re}(a(n)), \mathrm{Im}(a(n))\bigr) \}_{n \geq 1}$. # Level -- # A Maass form \( f \) is said to have **level** $N$ if \( f\) is invariant under the principal congruence subgroup $\Gamma(N)$. # Weight -- # A Maass form is of **weight** $k$ if it is an eigenfunction of the weight $k$ Laplacian # \( \Delta_k = y^2\left( \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\right) - iky\frac{\partial}{\partial x} \). #Char (character) -- # Maass forms of weight $0$ # ------------------ # The character column refers to the character under which the corresponding Maass form is invariant. The actual labels are explained in more details on the corresponding pages for Dirichlet characters. # Maass forms of weight $k$ # ------------------ # The column character denotes the multiplier. For example "eta" means that # the corresponding Maass form transform according to the canonical eta multiplier of weight $k$: # \( v(A) = v_{\eta}^{2k}:=\eta(Az)^{2k}/\eta(z)^{2k} \) #Spectral parameter (spectral_parameter) -- # If \(f\) is a Maass form with Laplace eigenvalue \(\lambda = \frac{1}{4}+R^{2}\), the number $R$ is said to be the **spectral parameter** of \(f\). # Symmetry -- # The modular group and its congruence subgroups has an outer automorphism of order two, which is given by the reflection in the imaginary axis: \( z=x+iy \mapsto -\bar{z}=-x+iy \). # This map belongs to $\mathrm{PGL}(2,\mathbb{Z})$ and can be represented by the matrix # $\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$. # A Maass form $f$ is said to be **even** if $f(-\bar{z})=f(z)$ and **odd** if $f(-\bar{z})=-f(z)$. #Fricke (fricke_eigenvalue) -- # The **Fricke involution** is the Atkin-Lehner involution $w_N$ on the space $S_k(\Gamma_0(N))$ (induced by the corresponding involution on the modular curve $X_0(N)$). # For a newform $f \in S_k^{\textup{new}}(\Gamma_0(N))$, the sign of the functional equation satisfied by the L-function attached to $f$ is $i^{-k}$ times the eigenvalue of $\omega_N$ on $f$. So, for example when $k=2$, the signs swap, and the analytic rank of $f$ is even when $w_N f = -f$ and odd when $w_N f = +f$.