Base field 6.6.1683101.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29,29,w^{4} - 2w^{3} - 4w^{2} + 6w + 5]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + 9x^{10} + 3x^{9} - 162x^{8} - 293x^{7} + 900x^{6} + 2148x^{5} - 1609x^{4} - 4562x^{3} + 194x^{2} + 716x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ | $\phantom{-}\frac{310106946}{22756947667}e^{10} + \frac{2064710427}{22756947667}e^{9} - \frac{3959530100}{22756947667}e^{8} - \frac{40770396153}{22756947667}e^{7} + \frac{9933601082}{22756947667}e^{6} + \frac{265911896525}{22756947667}e^{5} - \frac{15080154162}{22756947667}e^{4} - \frac{627907469838}{22756947667}e^{3} + \frac{157124794172}{22756947667}e^{2} + \frac{204784891779}{22756947667}e - \frac{25909868799}{22756947667}$ |
| 13 | $[13, 13, w^{2} - 3]$ | $-\frac{1081629690}{22756947667}e^{10} - \frac{7083972416}{22756947667}e^{9} + \frac{13992104598}{22756947667}e^{8} + \frac{140308905053}{22756947667}e^{7} - \frac{23110047384}{22756947667}e^{6} - \frac{894455681340}{22756947667}e^{5} - \frac{155002295649}{22756947667}e^{4} + \frac{1895128757383}{22756947667}e^{3} + \frac{221783568004}{22756947667}e^{2} - \frac{102238376257}{22756947667}e - \frac{73276382223}{22756947667}$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{469211446}{22756947667}e^{10} + \frac{2960840275}{22756947667}e^{9} - \frac{6672908322}{22756947667}e^{8} - \frac{58836922835}{22756947667}e^{7} + \frac{21628338590}{22756947667}e^{6} + \frac{375483030624}{22756947667}e^{5} + \frac{1500725439}{22756947667}e^{4} - \frac{789788414827}{22756947667}e^{3} + \frac{10538040148}{22756947667}e^{2} - \frac{2478631136}{22756947667}e - \frac{36933797635}{22756947667}$ |
| 29 | $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ | $-\frac{1259731817}{22756947667}e^{10} - \frac{9229983495}{22756947667}e^{9} + \frac{9782054149}{22756947667}e^{8} + \frac{175354151229}{22756947667}e^{7} + \frac{98828601948}{22756947667}e^{6} - \frac{1062497411621}{22756947667}e^{5} - \frac{965188299699}{22756947667}e^{4} + \frac{2190472680409}{22756947667}e^{3} + \frac{1925631520849}{22756947667}e^{2} - \frac{500745502233}{22756947667}e - \frac{158925506473}{22756947667}$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w^{2} + 4]$ | $-\frac{3085170407}{22756947667}e^{10} - \frac{20504967389}{22756947667}e^{9} + \frac{37805277661}{22756947667}e^{8} + \frac{404719800426}{22756947667}e^{7} - \frac{19969401245}{22756947667}e^{6} - \frac{2581169225969}{22756947667}e^{5} - \frac{784805860968}{22756947667}e^{4} + \frac{5644617250507}{22756947667}e^{3} + \frac{1508058747403}{22756947667}e^{2} - \frac{1188252041997}{22756947667}e - \frac{170049290878}{22756947667}$ |
| 41 | $[41, 41, -w^{2} + 2w + 3]$ | $-\frac{2157613865}{22756947667}e^{10} - \frac{13792680253}{22756947667}e^{9} + \frac{30467358002}{22756947667}e^{8} + \frac{276258535949}{22756947667}e^{7} - \frac{103349594951}{22756947667}e^{6} - \frac{1808723104755}{22756947667}e^{5} + \frac{107173002069}{22756947667}e^{4} + \frac{4143868349989}{22756947667}e^{3} - \frac{549285041777}{22756947667}e^{2} - \frac{1039975312925}{22756947667}e - \frac{377864723}{22756947667}$ |
| 43 | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $\phantom{-}\frac{292729473}{22756947667}e^{10} + \frac{2134726712}{22756947667}e^{9} - \frac{2352006828}{22756947667}e^{8} - \frac{42120390740}{22756947667}e^{7} - \frac{29603637372}{22756947667}e^{6} + \frac{266803364905}{22756947667}e^{5} + \frac{339822638511}{22756947667}e^{4} - \frac{605102563252}{22756947667}e^{3} - \frac{913218921955}{22756947667}e^{2} + \frac{375080567266}{22756947667}e + \frac{220454400916}{22756947667}$ |
| 43 | $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $-\frac{1478052903}{22756947667}e^{10} - \frac{10660201985}{22756947667}e^{9} + \frac{12886665273}{22756947667}e^{8} + \frac{204919553416}{22756947667}e^{7} + \frac{88690234169}{22756947667}e^{6} - \frac{1262181297364}{22756947667}e^{5} - \frac{949605207861}{22756947667}e^{4} + \frac{2652231788098}{22756947667}e^{3} + \frac{1816852054195}{22756947667}e^{2} - \frac{529031107160}{22756947667}e - \frac{225895694166}{22756947667}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{3454440947}{22756947667}e^{10} + \frac{22147538448}{22756947667}e^{9} - \frac{47919901180}{22756947667}e^{8} - \frac{442818454406}{22756947667}e^{7} + \frac{137353630629}{22756947667}e^{6} + \frac{2868902931761}{22756947667}e^{5} + \frac{93570484205}{22756947667}e^{4} - \frac{6305908942406}{22756947667}e^{3} + \frac{159837618771}{22756947667}e^{2} + \frac{837975933574}{22756947667}e - \frac{32315733808}{22756947667}$ |
| 71 | $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ | $\phantom{-}\frac{5149309131}{22756947667}e^{10} + \frac{34174971299}{22756947667}e^{9} - \frac{63561621354}{22756947667}e^{8} - \frac{672765963979}{22756947667}e^{7} + \frac{56715363109}{22756947667}e^{6} + \frac{4276087386703}{22756947667}e^{5} + \frac{1033002661118}{22756947667}e^{4} - \frac{9231064770704}{22756947667}e^{3} - \frac{1617695398302}{22756947667}e^{2} + \frac{1295871869489}{22756947667}e + \frac{157035998052}{22756947667}$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ | $\phantom{-}\frac{3013407193}{22756947667}e^{10} + \frac{19294564131}{22756947667}e^{9} - \frac{40813226753}{22756947667}e^{8} - \frac{380908167934}{22756947667}e^{7} + \frac{98615631770}{22756947667}e^{6} + \frac{2409369276805}{22756947667}e^{5} + \frac{242148341570}{22756947667}e^{4} - \frac{5050811838088}{22756947667}e^{3} - \frac{283566609772}{22756947667}e^{2} + \frac{362035309774}{22756947667}e - \frac{16403241762}{22756947667}$ |
| 71 | $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-\frac{4335472889}{22756947667}e^{10} - \frac{27940396593}{22756947667}e^{9} + \frac{57906382045}{22756947667}e^{8} + \frac{548665682194}{22756947667}e^{7} - \frac{146048007053}{22756947667}e^{6} - \frac{3466877649641}{22756947667}e^{5} - \frac{150461592246}{22756947667}e^{4} + \frac{7370547964051}{22756947667}e^{3} - \frac{420747843405}{22756947667}e^{2} - \frac{739071534819}{22756947667}e + \frac{130772045538}{22756947667}$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ | $-\frac{365915330}{22756947667}e^{10} - \frac{2531027736}{22756947667}e^{9} + \frac{4098478690}{22756947667}e^{8} + \frac{52121813739}{22756947667}e^{7} + \frac{13302634890}{22756947667}e^{6} - \frac{354360911449}{22756947667}e^{5} - \frac{260041422818}{22756947667}e^{4} + \frac{870830748509}{22756947667}e^{3} + \frac{690200157125}{22756947667}e^{2} - \frac{383275684185}{22756947667}e - \frac{109484326553}{22756947667}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ | $-\frac{974035601}{22756947667}e^{10} - \frac{5204688459}{22756947667}e^{9} + \frac{20648933173}{22756947667}e^{8} + \frac{110355638660}{22756947667}e^{7} - \frac{194163049753}{22756947667}e^{6} - \frac{778511206438}{22756947667}e^{5} + \frac{1101112628888}{22756947667}e^{4} + \frac{1924738107100}{22756947667}e^{3} - \frac{2829771775755}{22756947667}e^{2} - \frac{332671015543}{22756947667}e + \frac{380290432961}{22756947667}$ |
| 83 | $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ | $-\frac{1986057973}{22756947667}e^{10} - \frac{13310044805}{22756947667}e^{9} + \frac{22840342452}{22756947667}e^{8} + \frac{256515178468}{22756947667}e^{7} + \frac{4916808088}{22756947667}e^{6} - \frac{1586581129419}{22756947667}e^{5} - \frac{536629641495}{22756947667}e^{4} + \frac{3376541692833}{22756947667}e^{3} + \frac{899286365468}{22756947667}e^{2} - \frac{751865927650}{22756947667}e - \frac{40262261138}{22756947667}$ |
| 97 | $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $-\frac{457556460}{22756947667}e^{10} - \frac{2496693272}{22756947667}e^{9} + \frac{8963988628}{22756947667}e^{8} + \frac{52921223827}{22756947667}e^{7} - \frac{63138597117}{22756947667}e^{6} - \frac{355849877317}{22756947667}e^{5} + \frac{219594024999}{22756947667}e^{4} + \frac{714780365276}{22756947667}e^{3} - \frac{434020344572}{22756947667}e^{2} + \frac{274591022374}{22756947667}e + \frac{11654057706}{22756947667}$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ | $\phantom{-}\frac{5000527469}{22756947667}e^{10} + \frac{33708740185}{22756947667}e^{9} - \frac{57630137660}{22756947667}e^{8} - \frac{653520451348}{22756947667}e^{7} - \frac{6906046528}{22756947667}e^{6} + \frac{4067159591738}{22756947667}e^{5} + \frac{1242105228548}{22756947667}e^{4} - \frac{8551175095665}{22756947667}e^{3} - \frac{1763555723159}{22756947667}e^{2} + \frac{1048338636993}{22756947667}e + \frac{297023607899}{22756947667}$ |
| 113 | $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ | $\phantom{-}\frac{5972012631}{22756947667}e^{10} + \frac{38268697790}{22756947667}e^{9} - \frac{82114856506}{22756947667}e^{8} - \frac{759110414253}{22756947667}e^{7} + \frac{237409032647}{22756947667}e^{6} + \frac{4873335143406}{22756947667}e^{5} + \frac{53969653659}{22756947667}e^{4} - \frac{10672995887676}{22756947667}e^{3} + \frac{745317882161}{22756947667}e^{2} + \frac{1706330626218}{22756947667}e - \frac{203672207172}{22756947667}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29,29,w^{4} - 2w^{3} - 4w^{2} + 6w + 5]$ | $-1$ |