Base field \(\Q(\sqrt{119}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 119\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| 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:
| \(x^{4} + 4x^{3} - 24x^{2} - 56x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 11]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{1}{10}e^{3} - \frac{3}{10}e^{2} + \frac{11}{5}e + \frac{7}{5}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{11}{5}e - \frac{17}{5}$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{16}{5}e - \frac{17}{5}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{1}{10}e^{3} - \frac{1}{5}e^{2} + \frac{17}{5}e + 2$ |
| 11 | $[11, 11, w + 8]$ | $-\frac{1}{10}e^{3} - \frac{2}{5}e^{2} + 3e + \frac{24}{5}$ |
| 17 | $[17, 17, w]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w - 10]$ | $\phantom{-}\frac{3}{10}e^{2} + \frac{3}{5}e - \frac{21}{5}$ |
| 19 | $[19, 19, -w - 10]$ | $-\frac{3}{10}e^{2} - \frac{3}{5}e + \frac{21}{5}$ |
| 23 | $[23, 23, w + 2]$ | $\phantom{-}\frac{3}{10}e^{2} + \frac{3}{5}e - \frac{21}{5}$ |
| 23 | $[23, 23, w + 21]$ | $-\frac{3}{10}e^{2} - \frac{3}{5}e + \frac{21}{5}$ |
| 41 | $[41, 41, w + 18]$ | $-\frac{1}{5}e^{3} - \frac{3}{5}e^{2} + \frac{22}{5}e + \frac{54}{5}$ |
| 41 | $[41, 41, w + 23]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{22}{5}e + \frac{6}{5}$ |
| 47 | $[47, 47, -3w + 32]$ | $\phantom{-}\frac{1}{5}e^{3} + e^{2} - \frac{28}{5}e - \frac{62}{5}$ |
| 47 | $[47, 47, 8w - 87]$ | $\phantom{-}\frac{1}{5}e^{3} + \frac{1}{5}e^{2} - \frac{36}{5}e - \frac{6}{5}$ |
| 53 | $[53, 53, -2w + 23]$ | $-6$ |
| 53 | $[53, 53, -13w + 142]$ | $-6$ |
| 59 | $[59, 59, -5w + 54]$ | $-\frac{1}{10}e^{3} - \frac{1}{10}e^{2} + \frac{18}{5}e + \frac{3}{5}$ |
| 59 | $[59, 59, 6w - 65]$ | $-\frac{1}{10}e^{3} - \frac{1}{2}e^{2} + \frac{14}{5}e + \frac{31}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 11]$ | $-1$ |