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: | $4$ |
| 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:
| \(x^{4} - 4x^{3} + 6x^{2} - 4x + 145\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{24}e^{3} - \frac{1}{8}e^{2} + \frac{5}{8}e - \frac{13}{24}$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{12}e^{2} + \frac{1}{6}e - \frac{1}{12}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{12}e^{2} - \frac{1}{6}e + \frac{1}{12}$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}\frac{1}{24}e^{3} - \frac{1}{8}e^{2} - \frac{3}{8}e - \frac{13}{24}$ |
| 7 | $[7, 7, -2w - 15]$ | $-\frac{1}{24}e^{3} + \frac{1}{8}e^{2} + \frac{3}{8}e - \frac{35}{24}$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{1}{12}e^{2} + \frac{1}{6}e - \frac{1}{12}$ |
| 11 | $[11, 11, w + 6]$ | $\phantom{-}\frac{1}{12}e^{2} - \frac{1}{6}e + \frac{1}{12}$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{4}e^{2} + \frac{5}{4}e - \frac{13}{12}$ |
| 19 | $[19, 19, w + 18]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{4}e^{2} + \frac{5}{4}e - \frac{13}{12}$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{1}{12}e^{3} + \frac{1}{4}e^{2} + \frac{3}{4}e - \frac{59}{12}$ |
| 23 | $[23, 23, -w + 9]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{4}e^{2} - \frac{3}{4}e - \frac{37}{12}$ |
| 25 | $[25, 5, 5]$ | $-2$ |
| 29 | $[29, 29, w]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{4}e^{2} + \frac{5}{4}e - \frac{13}{12}$ |
| 37 | $[37, 37, w + 13]$ | $-\frac{1}{2}e^{2} + e - \frac{1}{2}$ |
| 37 | $[37, 37, w + 24]$ | $\phantom{-}\frac{1}{2}e^{2} - e + \frac{1}{2}$ |
| 43 | $[43, 43, w + 12]$ | $-\frac{1}{6}e^{2} + \frac{1}{3}e - \frac{1}{6}$ |
| 43 | $[43, 43, w + 31]$ | $\phantom{-}\frac{1}{6}e^{2} - \frac{1}{3}e + \frac{1}{6}$ |
| 61 | $[61, 61, w + 27]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{4}e^{2} + \frac{5}{4}e - \frac{13}{12}$ |
| 61 | $[61, 61, w + 34]$ | $\phantom{-}\frac{1}{12}e^{3} - \frac{1}{4}e^{2} + \frac{5}{4}e - \frac{13}{12}$ |
| 71 | $[71, 71, 12w - 91]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $\frac{1}{12}e^{2} - \frac{1}{6}e + \frac{1}{12}$ |
| $3$ | $[3, 3, w + 2]$ | $-\frac{1}{12}e^{2} + \frac{1}{6}e - \frac{1}{12}$ |