Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[16, 4, 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 17x^{2} + 3x + 59\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -76w + 675]$ | $\phantom{-}e$ |
| 5 | $[5, 5, 76w + 599]$ | $\phantom{-}\frac{1}{3}e^{3} - e^{2} - \frac{11}{3}e + \frac{19}{3}$ |
| 7 | $[7, 7, -8w - 63]$ | $-\frac{1}{3}e^{3} + 2e^{2} + \frac{5}{3}e - \frac{40}{3}$ |
| 7 | $[7, 7, -8w + 71]$ | $\phantom{-}e^{3} - 4e^{2} - 7e + 27$ |
| 9 | $[9, 3, 3]$ | $-3$ |
| 17 | $[17, 17, 42w + 331]$ | $\phantom{-}\frac{5}{3}e^{3} - 6e^{2} - \frac{37}{3}e + \frac{116}{3}$ |
| 17 | $[17, 17, 42w - 373]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e - \frac{5}{3}$ |
| 29 | $[29, 29, -6w - 47]$ | $\phantom{-}2e^{3} - 7e^{2} - 14e + 47$ |
| 29 | $[29, 29, 6w - 53]$ | $\phantom{-}e^{3} - 2e^{2} - 10e + 13$ |
| 31 | $[31, 31, 10w + 79]$ | $\phantom{-}\frac{2}{3}e^{3} - 3e^{2} - \frac{16}{3}e + \frac{65}{3}$ |
| 31 | $[31, 31, -10w + 89]$ | $-e^{3} + 4e^{2} + 8e - 25$ |
| 43 | $[43, 43, 2w - 19]$ | $-\frac{1}{3}e^{3} + e^{2} + \frac{5}{3}e - \frac{4}{3}$ |
| 43 | $[43, 43, -2w - 17]$ | $-\frac{2}{3}e^{3} + 2e^{2} + \frac{19}{3}e - \frac{23}{3}$ |
| 53 | $[53, 53, 194w + 1529]$ | $-\frac{5}{3}e^{3} + 7e^{2} + \frac{37}{3}e - \frac{128}{3}$ |
| 53 | $[53, 53, -194w + 1723]$ | $\phantom{-}\frac{4}{3}e^{3} - 6e^{2} - \frac{29}{3}e + \frac{133}{3}$ |
| 59 | $[59, 59, -110w - 867]$ | $\phantom{-}\frac{5}{3}e^{3} - 6e^{2} - \frac{31}{3}e + \frac{110}{3}$ |
| 59 | $[59, 59, 110w - 977]$ | $\phantom{-}e^{3} - 2e^{2} - 11e + 9$ |
| 79 | $[79, 79, 650w - 5773]$ | $\phantom{-}\frac{4}{3}e^{3} - 3e^{2} - \frac{44}{3}e + \frac{58}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 8]$ | $-1$ |
| $2$ | $[2, 2, -w + 9]$ | $-1$ |