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: | $[16, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 23x^{6} + 176x^{4} - 482x^{2} + 289\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 2]$ | $-\frac{6}{17}e^{7} + \frac{87}{17}e^{5} - \frac{325}{17}e^{3} + \frac{223}{17}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{2}{17}e^{7} - \frac{29}{17}e^{5} + \frac{114}{17}e^{3} - \frac{131}{17}e$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 23 | $[23, 23, -w^{3} + 4w + 1]$ | $-2e^{6} + 28e^{4} - 98e^{2} + 60$ |
| 25 | $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{7}{17}e^{7} + \frac{93}{17}e^{5} - \frac{280}{17}e^{3} + \frac{25}{17}e$ |
| 25 | $[25, 5, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{15}{17}e^{7} - \frac{209}{17}e^{5} + \frac{719}{17}e^{3} - \frac{362}{17}e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $-\frac{4}{17}e^{7} + \frac{58}{17}e^{5} - \frac{228}{17}e^{3} + \frac{228}{17}e$ |
| 29 | $[29, 29, w^{3} - w^{2} - 5w + 1]$ | $-\frac{4}{17}e^{7} + \frac{58}{17}e^{5} - \frac{228}{17}e^{3} + \frac{228}{17}e$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e^{6} - 15e^{4} + 59e^{2} - 44$ |
| 43 | $[43, 43, w^{3} - w^{2} - 4w + 2]$ | $-4e^{6} + 57e^{4} - 206e^{2} + 130$ |
| 61 | $[61, 61, -w^{2} + 2w + 4]$ | $-\frac{4}{17}e^{7} + \frac{58}{17}e^{5} - \frac{194}{17}e^{3} + \frac{24}{17}e$ |
| 61 | $[61, 61, w^{2} - 5]$ | $\phantom{-}2e^{3} - 16e$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ | $\phantom{-}\frac{16}{17}e^{7} - \frac{232}{17}e^{5} + \frac{878}{17}e^{3} - \frac{640}{17}e$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 6w - 4]$ | $\phantom{-}\frac{20}{17}e^{7} - \frac{290}{17}e^{5} + \frac{1106}{17}e^{3} - \frac{936}{17}e$ |
| 101 | $[101, 101, -w^{3} + 3w^{2} + w - 7]$ | $\phantom{-}\frac{50}{17}e^{7} - \frac{708}{17}e^{5} + \frac{2544}{17}e^{3} - \frac{1694}{17}e$ |
| 101 | $[101, 101, w^{3} - 4w - 4]$ | $-\frac{2}{17}e^{7} + \frac{12}{17}e^{5} + \frac{90}{17}e^{3} - \frac{328}{17}e$ |
| 103 | $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ | $-2e^{6} + 30e^{4} - 120e^{2} + 96$ |
| 103 | $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ | $\phantom{-}10e^{6} - 142e^{4} + 512e^{2} - 334$ |
| 107 | $[107, 107, 2w^{2} - 3w - 4]$ | $-9e^{6} + 128e^{4} - 463e^{2} + 308$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |