Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, 46w - 312]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 5x^{2} + 13x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w - 7]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{7}{2}e + 4$ |
| 3 | $[3, 3, w - 7]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -9w + 61]$ | $-e + 1$ |
| 5 | $[5, 5, -9w - 61]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{7}{2}e + 3$ |
| 7 | $[7, 7, 4w - 27]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{7}{2}e + 5$ |
| 7 | $[7, 7, 4w + 27]$ | $-e - 1$ |
| 23 | $[23, 23, 78w - 529]$ | $\phantom{-}2e^{2} - 2e - 8$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}e^{2} + e - 8$ |
| 37 | $[37, 37, w - 3]$ | $-e^{3} + 3e^{2} + 6e - 8$ |
| 41 | $[41, 41, -2w + 15]$ | $\phantom{-}e^{3} - 9e + 1$ |
| 41 | $[41, 41, 2w + 15]$ | $-2e^{2} + 4e + 9$ |
| 53 | $[53, 53, -3w - 19]$ | $\phantom{-}\frac{3}{2}e^{3} - 2e^{2} - \frac{23}{2}e + 11$ |
| 53 | $[53, 53, 3w - 19]$ | $\phantom{-}e^{2} - 4e - 7$ |
| 59 | $[59, 59, 11w - 75]$ | $-\frac{1}{2}e^{3} + \frac{13}{2}e - 3$ |
| 59 | $[59, 59, -11w - 75]$ | $\phantom{-}e^{3} - e^{2} - 9e + 1$ |
| 61 | $[61, 61, -5w + 33]$ | $-\frac{1}{2}e^{3} + 2e^{2} - \frac{3}{2}e - 9$ |
| 61 | $[61, 61, 5w + 33]$ | $\phantom{-}2e^{3} - 3e^{2} - 14e + 13$ |
| 73 | $[73, 73, -24w - 163]$ | $\phantom{-}\frac{3}{2}e^{3} - 3e^{2} - \frac{19}{2}e + 9$ |
| 73 | $[73, 73, -24w + 163]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{1}{2}e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, 23w - 156]$ | $1$ |