Base field \(\Q(\sqrt{241}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 18x^{2} - 19x + 86\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -393w - 2854]$ | $-1$ |
| 2 | $[2, 2, -393w + 3247]$ | $-1$ |
| 3 | $[3, 3, 4w - 33]$ | $-e^{2} - e + 10$ |
| 3 | $[3, 3, 4w + 29]$ | $-e^{2} - e + 10$ |
| 5 | $[5, 5, 42w + 305]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -42w + 347]$ | $\phantom{-}e$ |
| 29 | $[29, 29, 1820w + 13217]$ | $-e^{2} - 2e + 6$ |
| 29 | $[29, 29, 1820w - 15037]$ | $-e^{2} - 2e + 6$ |
| 41 | $[41, 41, -80w - 581]$ | $\phantom{-}e^{3} + 2e^{2} - 10e - 10$ |
| 41 | $[41, 41, 80w - 661]$ | $\phantom{-}e^{3} + 2e^{2} - 10e - 10$ |
| 47 | $[47, 47, 34w - 281]$ | $-e^{3} + 11e - 6$ |
| 47 | $[47, 47, 34w + 247]$ | $-e^{3} + 11e - 6$ |
| 49 | $[49, 7, -7]$ | $-e^{3} + 12e - 2$ |
| 53 | $[53, 53, 6w + 43]$ | $-e$ |
| 53 | $[53, 53, 6w - 49]$ | $-e$ |
| 59 | $[59, 59, 10w + 73]$ | $\phantom{-}e^{3} + e^{2} - 10e + 4$ |
| 59 | $[59, 59, 10w - 83]$ | $\phantom{-}e^{3} + e^{2} - 10e + 4$ |
| 61 | $[61, 61, 4178w + 30341]$ | $\phantom{-}e^{3} - 10e + 14$ |
| 61 | $[61, 61, 4178w - 34519]$ | $\phantom{-}e^{3} - 10e + 14$ |
| 67 | $[67, 67, -332w + 2743]$ | $-e^{3} - 2e^{2} + 9e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -393w - 2854]$ | $1$ |
| $2$ | $[2, 2, -393w + 3247]$ | $1$ |