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: | $[5, 5, 42w + 305]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $47$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 2x^{15} - 20x^{14} + 40x^{13} + 150x^{12} - 304x^{11} - 518x^{10} + 1090x^{9} + 804x^{8} - 1865x^{7} - 448x^{6} + 1394x^{5} + 50x^{4} - 442x^{3} + 30x^{2} + 47x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -393w - 2854]$ | $...$ |
| 2 | $[2, 2, -393w + 3247]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 4w - 33]$ | $...$ |
| 3 | $[3, 3, 4w + 29]$ | $...$ |
| 5 | $[5, 5, 42w + 305]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -42w + 347]$ | $...$ |
| 29 | $[29, 29, 1820w + 13217]$ | $...$ |
| 29 | $[29, 29, 1820w - 15037]$ | $...$ |
| 41 | $[41, 41, -80w - 581]$ | $...$ |
| 41 | $[41, 41, 80w - 661]$ | $...$ |
| 47 | $[47, 47, 34w - 281]$ | $...$ |
| 47 | $[47, 47, 34w + 247]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, 6w + 43]$ | $...$ |
| 53 | $[53, 53, 6w - 49]$ | $...$ |
| 59 | $[59, 59, 10w + 73]$ | $...$ |
| 59 | $[59, 59, 10w - 83]$ | $...$ |
| 61 | $[61, 61, 4178w + 30341]$ | $...$ |
| 61 | $[61, 61, 4178w - 34519]$ | $...$ |
| 67 | $[67, 67, -332w + 2743]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, 42w + 305]$ | $-1$ |