Base field 4.4.11661.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23, 23, -w^{3} + 4w + 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 14x^{6} + 32x^{4} - 11x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 2]$ | $-\frac{1}{3}e^{7} + \frac{13}{3}e^{5} - \frac{19}{3}e^{3} - \frac{11}{3}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{19}{3}e^{7} - \frac{262}{3}e^{5} + \frac{553}{3}e^{3} - \frac{94}{3}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{16}{3}e^{6} + \frac{220}{3}e^{4} - \frac{460}{3}e^{2} + \frac{88}{3}$ |
| 23 | $[23, 23, -w^{3} + 4w + 1]$ | $-1$ |
| 25 | $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{13}{3}e^{7} + \frac{178}{3}e^{5} - \frac{361}{3}e^{3} + \frac{28}{3}e$ |
| 25 | $[25, 5, w^{3} - w^{2} - 3w + 1]$ | $-\frac{8}{3}e^{7} + \frac{110}{3}e^{5} - \frac{230}{3}e^{3} + \frac{41}{3}e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $\phantom{-}\frac{5}{3}e^{7} - \frac{71}{3}e^{5} + \frac{173}{3}e^{3} - \frac{74}{3}e$ |
| 29 | $[29, 29, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}\frac{10}{3}e^{7} - \frac{139}{3}e^{5} + \frac{304}{3}e^{3} - \frac{61}{3}e$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{4}{3}e^{6} + \frac{58}{3}e^{4} - \frac{148}{3}e^{2} + \frac{52}{3}$ |
| 43 | $[43, 43, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}12e^{6} - 166e^{4} + 356e^{2} - 62$ |
| 61 | $[61, 61, -w^{2} + 2w + 4]$ | $-\frac{59}{3}e^{7} + \frac{815}{3}e^{5} - \frac{1736}{3}e^{3} + \frac{326}{3}e$ |
| 61 | $[61, 61, w^{2} - 5]$ | $\phantom{-}\frac{5}{3}e^{7} - \frac{68}{3}e^{5} + \frac{134}{3}e^{3} - \frac{20}{3}e$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ | $\phantom{-}\frac{52}{3}e^{7} - \frac{718}{3}e^{5} + \frac{1525}{3}e^{3} - \frac{277}{3}e$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 6w - 4]$ | $-12e^{7} + 165e^{5} - 343e^{3} + 51e$ |
| 101 | $[101, 101, -w^{3} + 3w^{2} + w - 7]$ | $\phantom{-}\frac{91}{3}e^{7} - \frac{1258}{3}e^{5} + \frac{2689}{3}e^{3} - \frac{517}{3}e$ |
| 101 | $[101, 101, w^{3} - 4w - 4]$ | $-\frac{23}{3}e^{7} + \frac{314}{3}e^{5} - \frac{629}{3}e^{3} + \frac{65}{3}e$ |
| 103 | $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ | $-\frac{11}{3}e^{6} + \frac{155}{3}e^{4} - \frac{365}{3}e^{2} + \frac{110}{3}$ |
| 103 | $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ | $-\frac{1}{3}e^{6} + \frac{10}{3}e^{4} + \frac{20}{3}e^{2} - \frac{35}{3}$ |
| 107 | $[107, 107, 2w^{2} - 3w - 4]$ | $\phantom{-}\frac{14}{3}e^{6} - \frac{191}{3}e^{4} + \frac{380}{3}e^{2} - \frac{38}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{3} + 4w + 1]$ | $1$ |