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:
| \(x^{4} - 4x^{3} + 2x^{2} + 4x + 97\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{1}{40}e^{3} + \frac{3}{40}e^{2} - \frac{9}{40}e + \frac{7}{40}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{40}e^{3} - \frac{3}{40}e^{2} + \frac{9}{40}e - \frac{7}{40}$ |
| 7 | $[7, 7, -2w + 15]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{3}{20}e^{2} - \frac{11}{20}e - \frac{7}{20}$ |
| 7 | $[7, 7, -2w - 15]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{3}{20}e^{2} - \frac{11}{20}e - \frac{7}{20}$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}\frac{1}{20}e^{3} - \frac{3}{20}e^{2} + \frac{9}{20}e - \frac{7}{20}$ |
| 11 | $[11, 11, w + 6]$ | $-\frac{1}{20}e^{3} + \frac{3}{20}e^{2} - \frac{9}{20}e + \frac{7}{20}$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{3}{40}e^{3} - \frac{29}{40}e^{2} + \frac{67}{40}e - \frac{1}{40}$ |
| 19 | $[19, 19, w + 18]$ | $-\frac{3}{40}e^{3} + \frac{29}{40}e^{2} - \frac{67}{40}e + \frac{1}{40}$ |
| 23 | $[23, 23, w + 9]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{3}{10}e^{2} - \frac{11}{10}e + \frac{33}{10}$ |
| 23 | $[23, 23, -w + 9]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{3}{10}e^{2} - \frac{11}{10}e + \frac{33}{10}$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}7$ |
| 29 | $[29, 29, w]$ | $\phantom{-}0$ |
| 37 | $[37, 37, w + 13]$ | $-\frac{3}{40}e^{3} - \frac{1}{40}e^{2} - \frac{7}{40}e + \frac{31}{40}$ |
| 37 | $[37, 37, w + 24]$ | $\phantom{-}\frac{3}{40}e^{3} + \frac{1}{40}e^{2} + \frac{7}{40}e - \frac{31}{40}$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}\frac{1}{40}e^{3} - \frac{3}{40}e^{2} + \frac{9}{40}e - \frac{7}{40}$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{1}{40}e^{3} + \frac{3}{40}e^{2} - \frac{9}{40}e + \frac{7}{40}$ |
| 61 | $[61, 61, w + 27]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{1}{2}$ |
| 61 | $[61, 61, w + 34]$ | $-\frac{1}{2}e^{2} + e + \frac{1}{2}$ |
| 71 | $[71, 71, 12w - 91]$ | $-\frac{1}{10}e^{3} + \frac{3}{10}e^{2} + \frac{11}{10}e - \frac{73}{10}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $\frac{1}{40}e^{3} - \frac{3}{40}e^{2} + \frac{9}{40}e - \frac{7}{40}$ |
| $3$ | $[3, 3, w + 2]$ | $-\frac{1}{40}e^{3} + \frac{3}{40}e^{2} - \frac{9}{40}e + \frac{7}{40}$ |