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: | $[9, 3, 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $74$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 8x^{4} + 12x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{2}e^{5} - \frac{7}{2}e^{3} - 3e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{1}{2}e^{5} - \frac{7}{2}e^{3} - 3e$ |
| 7 | $[7, 7, -2w + 15]$ | $-\frac{1}{2}e^{4} - 2e^{2} + 3$ |
| 7 | $[7, 7, -2w - 15]$ | $-\frac{1}{2}e^{4} - 4e^{2} - 5$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{1}{2}e^{3} - 2e$ |
| 11 | $[11, 11, w + 6]$ | $-2e^{5} - \frac{29}{2}e^{3} - 16e$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}e^{3} + 7e$ |
| 19 | $[19, 19, w + 18]$ | $-2e^{5} - 15e^{3} - 15e$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{1}{2}e^{4} - 5e^{2} - 8$ |
| 23 | $[23, 23, -w + 9]$ | $-\frac{7}{2}e^{4} - 25e^{2} - 20$ |
| 25 | $[25, 5, 5]$ | $-e^{4} - 7e^{2} - 6$ |
| 29 | $[29, 29, w]$ | $\phantom{-}2e^{5} + 15e^{3} + 16e$ |
| 37 | $[37, 37, w + 13]$ | $-\frac{1}{2}e^{5} - 5e^{3} - 11e$ |
| 37 | $[37, 37, w + 24]$ | $-\frac{3}{2}e^{5} - 9e^{3} - e$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}3e^{5} + 23e^{3} + 26e$ |
| 43 | $[43, 43, w + 31]$ | $-3e^{5} - 21e^{3} - 14e$ |
| 61 | $[61, 61, w + 27]$ | $\phantom{-}\frac{7}{2}e^{5} + 25e^{3} + 19e$ |
| 61 | $[61, 61, w + 34]$ | $-\frac{3}{2}e^{5} - 13e^{3} - 23e$ |
| 71 | $[71, 71, 12w - 91]$ | $\phantom{-}\frac{1}{2}e^{4} + 5e^{2} + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $\frac{1}{2}e^{5} + \frac{7}{2}e^{3} + 3e$ |
| $3$ | $[3, 3, w + 2]$ | $\frac{1}{2}e^{5} + \frac{7}{2}e^{3} + 3e$ |