Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15, 15, -2w + 15]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $41$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 2x^{2} + 6x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $-1$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e^{3} - 2e^{2} - 2e + 2$ |
| 5 | $[5, 5, 4w + 25]$ | $-1$ |
| 5 | $[5, 5, -4w + 29]$ | $\phantom{-}e^{2} - e - 1$ |
| 11 | $[11, 11, w - 8]$ | $\phantom{-}e^{3} - 5e^{2} + 3e + 6$ |
| 11 | $[11, 11, -w - 7]$ | $-e^{3} + 3e^{2} + e - 3$ |
| 13 | $[13, 13, 3w + 19]$ | $-e^{3} + 2e^{2} + 4e - 4$ |
| 13 | $[13, 13, 3w - 22]$ | $-e + 2$ |
| 29 | $[29, 29, 6w + 37]$ | $-e^{3} + e^{2} + 6e$ |
| 29 | $[29, 29, 6w - 43]$ | $-e^{3} + 3e^{2} - e - 5$ |
| 37 | $[37, 37, 2w - 13]$ | $-e^{3} - 2e^{2} + 11e + 4$ |
| 37 | $[37, 37, 2w + 11]$ | $-2e^{2} + 2e + 7$ |
| 43 | $[43, 43, -w - 1]$ | $\phantom{-}4e^{3} - 12e^{2} + 14$ |
| 43 | $[43, 43, w - 2]$ | $-2e^{3} + 6e^{2} + e - 9$ |
| 49 | $[49, 7, -7]$ | $-e^{2} + 10$ |
| 59 | $[59, 59, 5w - 37]$ | $\phantom{-}3e^{3} - 7e^{2} - 6e + 9$ |
| 59 | $[59, 59, 5w + 32]$ | $\phantom{-}2e^{3} - 9e^{2} + 3e + 13$ |
| 67 | $[67, 67, 21w + 131]$ | $\phantom{-}2e^{3} - 5e^{2} - 6e + 2$ |
| 67 | $[67, 67, 21w - 152]$ | $-3e^{3} + 7e^{2} + 5e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 6]$ | $1$ |
| $5$ | $[5, 5, 4w + 25]$ | $1$ |