Base field 6.6.1997632.1
Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[27,3,-w^{5} + 6w^{3} + w^{2} - 8w - 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 43x^{8} + 594x^{6} - 3053x^{4} + 5948x^{2} - 3721\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{4} - 5w^{2} - w + 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w]$ | $-\frac{2355}{282479}e^{8} + \frac{97489}{282479}e^{6} - \frac{1231881}{282479}e^{4} + \frac{4994395}{282479}e^{2} - \frac{5817220}{282479}$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}\frac{19421}{17231219}e^{9} - \frac{823635}{17231219}e^{7} + \frac{11266210}{17231219}e^{5} - \frac{58100678}{17231219}e^{3} + \frac{88305045}{17231219}e$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $-\frac{62587}{17231219}e^{9} + \frac{2572657}{17231219}e^{7} - \frac{32553061}{17231219}e^{5} + \frac{135128118}{17231219}e^{3} - \frac{140754054}{17231219}e$ |
| 27 | $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ | $\phantom{-}\frac{1756}{282479}e^{8} - \frac{71373}{282479}e^{6} + \frac{897678}{282479}e^{4} - \frac{3914177}{282479}e^{2} + \frac{4610479}{282479}$ |
| 27 | $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{4} - 6w^{2} + w + 8]$ | $-\frac{96588}{17231219}e^{9} + \frac{4106009}{17231219}e^{7} - \frac{54794314}{17231219}e^{5} + \frac{252483772}{17231219}e^{3} - \frac{361786163}{17231219}e$ |
| 29 | $[29, 29, -w^{4} + 6w^{2} + w - 8]$ | $\phantom{-}\frac{274516}{17231219}e^{9} - \frac{11225969}{17231219}e^{7} + \frac{139923740}{17231219}e^{5} - \frac{562349654}{17231219}e^{3} + \frac{634696041}{17231219}e$ |
| 41 | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $\phantom{-}\frac{6284}{282479}e^{8} - \frac{256058}{282479}e^{6} + \frac{3171238}{282479}e^{4} - \frac{12476434}{282479}e^{2} + \frac{11050183}{282479}$ |
| 41 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $\phantom{-}\frac{17635}{17231219}e^{9} - \frac{781607}{17231219}e^{7} + \frac{10656909}{17231219}e^{5} - \frac{45812238}{17231219}e^{3} + \frac{65045218}{17231219}e$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ | $-\frac{85909}{17231219}e^{9} + \frac{3488090}{17231219}e^{7} - \frac{42882847}{17231219}e^{5} + \frac{168375679}{17231219}e^{3} - \frac{204136785}{17231219}e$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ | $-\frac{3747}{282479}e^{8} + \frac{148276}{282479}e^{6} - \frac{1749155}{282479}e^{4} + \frac{6337985}{282479}e^{2} - \frac{7382681}{282479}$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $-\frac{92865}{17231219}e^{9} + \frac{3651778}{17231219}e^{7} - \frac{41628289}{17231219}e^{5} + \frac{130079824}{17231219}e^{3} - \frac{94301406}{17231219}e$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $\phantom{-}\frac{329630}{17231219}e^{9} - \frac{13622772}{17231219}e^{7} + \frac{172194623}{17231219}e^{5} - \frac{697754009}{17231219}e^{3} + \frac{702159098}{17231219}e$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 7]$ | $-\frac{1333}{282479}e^{8} + \frac{61419}{282479}e^{6} - \frac{924344}{282479}e^{4} + \frac{4958463}{282479}e^{2} - \frac{6958949}{282479}$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ | $-\frac{380420}{17231219}e^{9} + \frac{15917823}{17231219}e^{7} - \frac{205711075}{17231219}e^{5} + \frac{872332280}{17231219}e^{3} - \frac{945476893}{17231219}e$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ | $-\frac{634518}{17231219}e^{9} + \frac{25930074}{17231219}e^{7} - \frac{323039472}{17231219}e^{5} + \frac{1290164567}{17231219}e^{3} - \frac{1348761787}{17231219}e$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{367109}{17231219}e^{9} - \frac{15237968}{17231219}e^{7} + \frac{193808597}{17231219}e^{5} - \frac{787346126}{17231219}e^{3} + \frac{721808156}{17231219}e$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $-\frac{47245}{17231219}e^{9} + \frac{1478387}{17231219}e^{7} - \frac{6247978}{17231219}e^{5} - \frac{95082742}{17231219}e^{3} + \frac{316574033}{17231219}e$ |
| 113 | $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ | $-\frac{81914}{17231219}e^{9} + \frac{3394080}{17231219}e^{7} - \frac{41973390}{17231219}e^{5} + \frac{140888379}{17231219}e^{3} + \frac{18843606}{17231219}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27,3,-w^{5} + 6w^{3} + w^{2} - 8w - 2]$ | $-1$ |