Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 16x^{2} - 60x - 35\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 10]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w - 11]$ | $-1$ |
| 5 | $[5, 5, -116w - 1171]$ | $\phantom{-}e$ |
| 5 | $[5, 5, 116w - 1287]$ | $-\frac{2}{3}e^{3} + \frac{31}{3}e + 10$ |
| 7 | $[7, 7, -1002w - 10115]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{17}{3}e - \frac{23}{3}$ |
| 7 | $[7, 7, 1002w - 11117]$ | $-e^{3} + \frac{1}{3}e^{2} + 15e + \frac{25}{3}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{3}e^{2} - e - \frac{17}{3}$ |
| 11 | $[11, 11, 10w - 111]$ | $-\frac{2}{3}e^{3} + \frac{31}{3}e + 9$ |
| 11 | $[11, 11, -10w - 101]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{2}{3}e^{2} - \frac{31}{3}e - \frac{5}{3}$ |
| 23 | $[23, 23, -32w + 355]$ | $\phantom{-}\frac{4}{3}e^{3} - \frac{1}{3}e^{2} - \frac{59}{3}e - \frac{49}{3}$ |
| 23 | $[23, 23, 32w + 323]$ | $\phantom{-}\frac{4}{3}e^{3} - e^{2} - \frac{59}{3}e - 7$ |
| 41 | $[41, 41, -8w - 81]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{14}{3}e + \frac{1}{3}$ |
| 41 | $[41, 41, -8w + 89]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{2}{3}e^{2} - \frac{14}{3}e - \frac{43}{3}$ |
| 53 | $[53, 53, 4w - 45]$ | $-\frac{5}{3}e^{3} + \frac{73}{3}e + 20$ |
| 53 | $[53, 53, 4w + 41]$ | $-\frac{5}{3}e^{3} - \frac{2}{3}e^{2} + \frac{79}{3}e + \frac{88}{3}$ |
| 59 | $[59, 59, -3892w + 43181]$ | $\phantom{-}2e^{3} - \frac{2}{3}e^{2} - 31e - \frac{53}{3}$ |
| 59 | $[59, 59, 3892w + 39289]$ | $-2e^{3} + 31e + 29$ |
| 61 | $[61, 61, 770w - 8543]$ | $\phantom{-}\frac{11}{3}e^{3} - \frac{166}{3}e - 50$ |
| 61 | $[61, 61, -770w - 7773]$ | $-e^{3} + \frac{2}{3}e^{2} + 12e + \frac{8}{3}$ |
| 67 | $[67, 67, 158w + 1595]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{1}{3}e^{2} - \frac{31}{3}e - \frac{50}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 10]$ | $-1$ |
| $2$ | $[2, 2, w - 11]$ | $1$ |