Base field 5.5.173513.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 5x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^{4} + 2w^{3} + 4w^{2} - w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + x^{7} - 74x^{6} - 70x^{5} + 1678x^{4} + 1281x^{3} - 12756x^{2} - 6336x + 12048\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{4} + 2w^{3} + 4w^{2} - w - 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 7w^{2} + w - 5]$ | $\phantom{-}\frac{20157}{5284417702}e^{7} - \frac{5076965}{5284417702}e^{6} + \frac{9088190}{2642208851}e^{5} + \frac{175709919}{2642208851}e^{4} - \frac{442851100}{2642208851}e^{3} - \frac{6415720049}{5284417702}e^{2} + \frac{4464739833}{2642208851}e + \frac{14303197634}{2642208851}$ |
| 17 | $[17, 17, w^{4} - 2w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}\frac{38875479}{10568835404}e^{7} - \frac{94988773}{10568835404}e^{6} - \frac{1179233629}{5284417702}e^{5} + \frac{2694764735}{5284417702}e^{4} + \frac{17768630519}{5284417702}e^{3} - \frac{74317691041}{10568835404}e^{2} - \frac{24853980035}{2642208851}e + \frac{27805164822}{2642208851}$ |
| 19 | $[19, 19, w^{4} - w^{3} - 7w^{2} - w + 2]$ | $\phantom{-}\frac{18730263}{5284417702}e^{7} - \frac{55306111}{5284417702}e^{6} - \frac{578468224}{2642208851}e^{5} + \frac{1545315536}{2642208851}e^{4} + \frac{9268657303}{2642208851}e^{3} - \frac{39299544353}{5284417702}e^{2} - \frac{32711260580}{2642208851}e + \frac{20783926508}{2642208851}$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}\frac{29629723}{10568835404}e^{7} - \frac{6432423}{10568835404}e^{6} - \frac{436439736}{2642208851}e^{5} + \frac{213736501}{5284417702}e^{4} + \frac{12005219031}{5284417702}e^{3} - \frac{10073543937}{10568835404}e^{2} - \frac{22242088979}{5284417702}e + \frac{4355710580}{2642208851}$ |
| 23 | $[23, 23, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{11638719}{5284417702}e^{7} + \frac{52121317}{5284417702}e^{6} + \frac{315283504}{2642208851}e^{5} - \frac{1506147159}{2642208851}e^{4} - \frac{3484442258}{2642208851}e^{3} + \frac{40960660247}{5284417702}e^{2} - \frac{3214175025}{2642208851}e - \frac{24863716512}{2642208851}$ |
| 23 | $[23, 23, -w + 2]$ | $-\frac{5971964}{2642208851}e^{7} + \frac{22551251}{2642208851}e^{6} + \frac{363809534}{2642208851}e^{5} - \frac{1266104058}{2642208851}e^{4} - \frac{5580437293}{2642208851}e^{3} + \frac{15612222289}{2642208851}e^{2} + \frac{15520943620}{2642208851}e - \frac{2843175228}{2642208851}$ |
| 25 | $[25, 5, -w^{4} + 2w^{3} + 5w^{2} - 2w - 1]$ | $\phantom{-}\frac{22279271}{5284417702}e^{7} - \frac{119977253}{5284417702}e^{6} - \frac{653023032}{2642208851}e^{5} + \frac{3415599137}{2642208851}e^{4} + \frac{8922020759}{2642208851}e^{3} - \frac{89223271935}{5284417702}e^{2} - \frac{10359665958}{2642208851}e + \frac{50364233182}{2642208851}$ |
| 27 | $[27, 3, -2w^{4} + 4w^{3} + 9w^{2} - 4w - 3]$ | $\phantom{-}\frac{182840}{2642208851}e^{7} - \frac{4106040}{2642208851}e^{6} - \frac{21261460}{2642208851}e^{5} + \frac{287086656}{2642208851}e^{4} + \frac{767441735}{2642208851}e^{3} - \frac{4755472239}{2642208851}e^{2} - \frac{7983107997}{2642208851}e + \frac{15604633916}{2642208851}$ |
| 31 | $[31, 31, 2w^{4} - 4w^{3} - 9w^{2} + 4w + 4]$ | $\phantom{-}\frac{37074689}{10568835404}e^{7} - \frac{97323177}{10568835404}e^{6} - \frac{572381589}{2642208851}e^{5} + \frac{2627834497}{5284417702}e^{4} + \frac{18212723971}{5284417702}e^{3} - \frac{62672424179}{10568835404}e^{2} - \frac{64546361847}{5284417702}e + \frac{8472219584}{2642208851}$ |
| 32 | $[32, 2, -2]$ | $\phantom{-}\frac{62803649}{10568835404}e^{7} - \frac{195347707}{10568835404}e^{6} - \frac{1888676317}{5284417702}e^{5} + \frac{5578392689}{5284417702}e^{4} + \frac{28043802905}{5284417702}e^{3} - \frac{149598020295}{10568835404}e^{2} - \frac{38552392673}{2642208851}e + \frac{42309328833}{2642208851}$ |
| 41 | $[41, 41, w^{4} - 3w^{3} - 2w^{2} + 5w]$ | $\phantom{-}\frac{58476735}{10568835404}e^{7} - \frac{263496839}{10568835404}e^{6} - \frac{882856547}{2642208851}e^{5} + \frac{7500997967}{5284417702}e^{4} + \frac{26430774373}{5284417702}e^{3} - \frac{197691967849}{10568835404}e^{2} - \frac{64905604815}{5284417702}e + \frac{61029076050}{2642208851}$ |
| 43 | $[43, 43, w^{4} - w^{3} - 7w^{2} + 3]$ | $-\frac{26606185}{5284417702}e^{7} + \frac{51828121}{5284417702}e^{6} + \frac{775986255}{2642208851}e^{5} - \frac{1492993859}{2642208851}e^{4} - \frac{10535049291}{2642208851}e^{3} + \frac{41129324381}{5284417702}e^{2} + \frac{17274428787}{2642208851}e - \frac{12924738748}{2642208851}$ |
| 47 | $[47, 47, w^{2} - 2w - 1]$ | $\phantom{-}\frac{77783819}{10568835404}e^{7} - \frac{161813637}{10568835404}e^{6} - \frac{2259365839}{5284417702}e^{5} + \frac{4548156185}{5284417702}e^{4} + \frac{29927405611}{5284417702}e^{3} - \frac{121404251297}{10568835404}e^{2} - \frac{19597192716}{2642208851}e + \frac{23037771480}{2642208851}$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $-\frac{10747569}{5284417702}e^{7} - \frac{66157603}{5284417702}e^{6} + \frac{316360453}{2642208851}e^{5} + \frac{1930480456}{2642208851}e^{4} - \frac{4533806807}{2642208851}e^{3} - \frac{49529792257}{5284417702}e^{2} + \frac{16121971792}{2642208851}e + \frac{35103377070}{2642208851}$ |
| 67 | $[67, 67, -w^{4} + 2w^{3} + 5w^{2} - 4w - 2]$ | $-\frac{18118889}{2642208851}e^{7} + \frac{76836758}{2642208851}e^{6} + \frac{1094513682}{2642208851}e^{5} - \frac{4436818668}{2642208851}e^{4} - \frac{16623051414}{2642208851}e^{3} + \frac{60650068006}{2642208851}e^{2} + \frac{45616459191}{2642208851}e - \frac{95015896484}{2642208851}$ |
| 71 | $[71, 71, -2w^{4} + 4w^{3} + 10w^{2} - 5w - 4]$ | $-\frac{48771967}{10568835404}e^{7} + \frac{179661423}{10568835404}e^{6} + \frac{782231733}{2642208851}e^{5} - \frac{5047126605}{5284417702}e^{4} - \frac{26838329877}{5284417702}e^{3} + \frac{131920846905}{10568835404}e^{2} + \frac{100430171083}{5284417702}e - \frac{43537275414}{2642208851}$ |
| 73 | $[73, 73, w^{4} - w^{3} - 7w^{2} + 6]$ | $-\frac{26604273}{10568835404}e^{7} + \frac{66814155}{10568835404}e^{6} + \frac{907667609}{5284417702}e^{5} - \frac{1879009051}{5284417702}e^{4} - \frac{17004766239}{5284417702}e^{3} + \frac{44885509011}{10568835404}e^{2} + \frac{36204420699}{2642208851}e + \frac{5570273758}{2642208851}$ |
| 73 | $[73, 73, 2w^{4} - 3w^{3} - 11w^{2} - w + 6]$ | $-\frac{102756011}{10568835404}e^{7} + \frac{309895755}{10568835404}e^{6} + \frac{1570391258}{2642208851}e^{5} - \frac{8958707473}{5284417702}e^{4} - \frac{48557609729}{5284417702}e^{3} + \frac{246032824721}{10568835404}e^{2} + \frac{157869018091}{5284417702}e - \frac{81085428010}{2642208851}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, -w^{4} + 2w^{3} + 4w^{2} - w - 1]$ | $-1$ |