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: | $[4, 2, 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 2x^{5} - 20x^{4} - 30x^{3} + 93x^{2} + 45x - 54\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $-1$ |
| 2 | $[2, 2, -w + 9]$ | $-1$ |
| 5 | $[5, 5, -76w + 675]$ | $\phantom{-}e$ |
| 5 | $[5, 5, 76w + 599]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -8w - 63]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{1}{9}e^{4} - \frac{17}{9}e^{3} + \frac{4}{3}e^{2} + \frac{16}{3}e$ |
| 7 | $[7, 7, -8w + 71]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{1}{9}e^{4} - \frac{17}{9}e^{3} + \frac{4}{3}e^{2} + \frac{16}{3}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{3}e^{4} + \frac{1}{3}e^{3} + \frac{14}{3}e^{2} - 4e - 2$ |
| 17 | $[17, 17, 42w + 331]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{14}{3}e^{2} + 4e + 6$ |
| 17 | $[17, 17, 42w - 373]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{14}{3}e^{2} + 4e + 6$ |
| 29 | $[29, 29, -6w - 47]$ | $\phantom{-}\frac{1}{3}e^{5} - 5e^{3} - \frac{2}{3}e^{2} + 8e + 6$ |
| 29 | $[29, 29, 6w - 53]$ | $\phantom{-}\frac{1}{3}e^{5} - 5e^{3} - \frac{2}{3}e^{2} + 8e + 6$ |
| 31 | $[31, 31, 10w + 79]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{4}{9}e^{4} - \frac{14}{9}e^{3} + 7e^{2} + \frac{4}{3}e - 12$ |
| 31 | $[31, 31, -10w + 89]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{4}{9}e^{4} - \frac{14}{9}e^{3} + 7e^{2} + \frac{4}{3}e - 12$ |
| 43 | $[43, 43, 2w - 19]$ | $-\frac{2}{9}e^{5} - \frac{1}{9}e^{4} + \frac{28}{9}e^{3} + 2e^{2} - \frac{11}{3}e - 6$ |
| 43 | $[43, 43, -2w - 17]$ | $-\frac{2}{9}e^{5} - \frac{1}{9}e^{4} + \frac{28}{9}e^{3} + 2e^{2} - \frac{11}{3}e - 6$ |
| 53 | $[53, 53, 194w + 1529]$ | $-\frac{1}{3}e^{4} + \frac{1}{3}e^{3} + \frac{14}{3}e^{2} - 4e - 6$ |
| 53 | $[53, 53, -194w + 1723]$ | $-\frac{1}{3}e^{4} + \frac{1}{3}e^{3} + \frac{14}{3}e^{2} - 4e - 6$ |
| 59 | $[59, 59, -110w - 867]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{14}{3}e^{3} + 5e^{2} + 5e - 6$ |
| 59 | $[59, 59, 110w - 977]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{14}{3}e^{3} + 5e^{2} + 5e - 6$ |
| 79 | $[79, 79, 650w - 5773]$ | $\phantom{-}\frac{1}{9}e^{5} + \frac{2}{9}e^{4} - \frac{20}{9}e^{3} - \frac{13}{3}e^{2} + \frac{28}{3}e + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 8]$ | $1$ |
| $2$ | $[2, 2, -w + 9]$ | $1$ |