Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,w - 8]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 8x^{3} - 3x^{2} + 8x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - 13e^{2} + \frac{7}{2}e + 11$ |
| 7 | $[7, 7, -2w - 15]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 4e^{2} - \frac{1}{2}e + 4$ |
| 11 | $[11, 11, w + 5]$ | $-3e^{4} - 2e^{3} + 23e^{2} - 3e - 15$ |
| 11 | $[11, 11, w + 6]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - 12e^{2} + \frac{11}{2}e + 9$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}e - 2$ |
| 19 | $[19, 19, w + 18]$ | $-\frac{3}{2}e^{4} + \frac{1}{2}e^{3} + 13e^{2} - \frac{17}{2}e - 9$ |
| 23 | $[23, 23, w + 9]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{3}{2}e^{3} - 11e^{2} - \frac{9}{2}e + 8$ |
| 23 | $[23, 23, -w + 9]$ | $-e^{4} + 8e^{2} - 2e - 2$ |
| 25 | $[25, 5, 5]$ | $-2e^{4} + 17e^{2} - 9e - 13$ |
| 29 | $[29, 29, w]$ | $-\frac{5}{2}e^{4} - \frac{1}{2}e^{3} + 21e^{2} - \frac{11}{2}e - 17$ |
| 37 | $[37, 37, w + 13]$ | $\phantom{-}5e^{4} + 2e^{3} - 39e^{2} + 11e + 29$ |
| 37 | $[37, 37, w + 24]$ | $\phantom{-}e^{4} - e^{3} - 11e^{2} + 11e + 14$ |
| 43 | $[43, 43, w + 12]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 2e^{2} - \frac{5}{2}e + 2$ |
| 43 | $[43, 43, w + 31]$ | $\phantom{-}e^{4} - e^{3} - 10e^{2} + 9e + 12$ |
| 61 | $[61, 61, w + 27]$ | $-2e^{4} - 2e^{3} + 16e^{2} + 7e - 14$ |
| 61 | $[61, 61, w + 34]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{1}{2}e^{3} - 14e^{2} + \frac{15}{2}e + 12$ |
| 71 | $[71, 71, 12w - 91]$ | $-\frac{7}{2}e^{4} - \frac{1}{2}e^{3} + 31e^{2} - \frac{19}{2}e - 25$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w]$ | $-1$ |
| $3$ | $[3,3,-w + 2]$ | $-1$ |