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: | $[4, 2, 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 22x^{8} + 160x^{6} + 430x^{4} + 391x^{2} + 28\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $-e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}\frac{1}{6}e^{8} + 3e^{6} + \frac{97}{6}e^{4} + 24e^{2} + \frac{8}{3}$ |
| 7 | $[7, 7, -2w - 15]$ | $\phantom{-}\frac{1}{6}e^{8} + 3e^{6} + \frac{97}{6}e^{4} + 24e^{2} + \frac{8}{3}$ |
| 11 | $[11, 11, w + 5]$ | $-e^{5} - 11e^{3} - 19e$ |
| 11 | $[11, 11, w + 6]$ | $\phantom{-}e^{5} + 11e^{3} + 19e$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{6}e^{9} + \frac{7}{2}e^{7} + \frac{139}{6}e^{5} + \frac{99}{2}e^{3} + \frac{83}{3}e$ |
| 19 | $[19, 19, w + 18]$ | $-\frac{1}{6}e^{9} - \frac{7}{2}e^{7} - \frac{139}{6}e^{5} - \frac{99}{2}e^{3} - \frac{83}{3}e$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{1}{2}e^{6} - 5e^{4} - \frac{9}{2}e^{2} + 6$ |
| 23 | $[23, 23, -w + 9]$ | $-\frac{1}{2}e^{6} - 5e^{4} - \frac{9}{2}e^{2} + 6$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{1}{6}e^{8} + \frac{5}{2}e^{6} + \frac{61}{6}e^{4} + \frac{19}{2}e^{2} + \frac{8}{3}$ |
| 29 | $[29, 29, w]$ | $\phantom{-}0$ |
| 37 | $[37, 37, w + 13]$ | $\phantom{-}\frac{1}{6}e^{9} + \frac{7}{2}e^{7} + \frac{139}{6}e^{5} + \frac{101}{2}e^{3} + \frac{104}{3}e$ |
| 37 | $[37, 37, w + 24]$ | $-\frac{1}{6}e^{9} - \frac{7}{2}e^{7} - \frac{139}{6}e^{5} - \frac{101}{2}e^{3} - \frac{104}{3}e$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}\frac{1}{6}e^{9} + \frac{7}{2}e^{7} + \frac{133}{6}e^{5} + \frac{79}{2}e^{3} + \frac{47}{3}e$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{1}{6}e^{9} - \frac{7}{2}e^{7} - \frac{133}{6}e^{5} - \frac{79}{2}e^{3} - \frac{47}{3}e$ |
| 61 | $[61, 61, w + 27]$ | $-\frac{1}{2}e^{7} - 7e^{5} - \frac{53}{2}e^{3} - 30e$ |
| 61 | $[61, 61, w + 34]$ | $\phantom{-}\frac{1}{2}e^{7} + 7e^{5} + \frac{53}{2}e^{3} + 30e$ |
| 71 | $[71, 71, 12w - 91]$ | $-2e^{2} - 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |