Base field 5.5.36497.1
Generator \(w\), with minimal polynomial \(x^{5} - 2 x^{4} - 3 x^{3} + 5 x^{2} + x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[23, 23, 2 w^{4} - 3 w^{3} - 6 w^{2} + 5 w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2 x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - 2 w^{3} - 3 w^{2} + 4 w + 1]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{3} - 2 w^{2} - 2 w + 2]$ | $-e - 4$ |
| 23 | $[23, 23, 2 w^{4} - 3 w^{3} - 6 w^{2} + 5 w + 1]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -w^{2} + 2 w + 2]$ | $\phantom{-}4$ |
| 29 | $[29, 29, -w^{4} + w^{3} + 4 w^{2} - 3 w - 1]$ | $\phantom{-}2 e$ |
| 31 | $[31, 31, w^{4} - w^{3} - 5 w^{2} + 2 w + 4]$ | $-2 e - 4$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}2 e + 3$ |
| 37 | $[37, 37, w^{4} - 2 w^{3} - 2 w^{2} + 4 w + 1]$ | $\phantom{-}2 e + 8$ |
| 47 | $[47, 47, w^{4} - w^{3} - 5 w^{2} + 2 w + 3]$ | $\phantom{-}4$ |
| 47 | $[47, 47, 2 w^{4} - 3 w^{3} - 6 w^{2} + 6 w + 2]$ | $\phantom{-}4$ |
| 49 | $[49, 7, -w^{4} + 2 w^{3} + 4 w^{2} - 6 w - 2]$ | $-4 e$ |
| 53 | $[53, 53, -2 w^{4} + 3 w^{3} + 7 w^{2} - 7 w - 2]$ | $-2 e - 4$ |
| 59 | $[59, 59, -2 w^{4} + 3 w^{3} + 6 w^{2} - 5 w - 2]$ | $-2 e + 2$ |
| 67 | $[67, 67, -w^{4} + 3 w^{3} + 2 w^{2} - 7 w]$ | $\phantom{-}4 e + 8$ |
| 67 | $[67, 67, -w^{4} + 3 w^{3} + w^{2} - 7 w + 1]$ | $-2 e - 12$ |
| 71 | $[71, 71, w^{4} - 2 w^{3} - 4 w^{2} + 3 w + 3]$ | $-4 e$ |
| 71 | $[71, 71, -w^{2} + 5]$ | $\phantom{-}4 e + 12$ |
| 79 | $[79, 79, 2 w^{4} - 3 w^{3} - 5 w^{2} + 3 w + 1]$ | $\phantom{-}2 e + 6$ |
| 81 | $[81, 3, -w^{4} + 3 w^{3} + 3 w^{2} - 8 w - 2]$ | $\phantom{-}3 e + 4$ |
| 83 | $[83, 83, -3 w^{4} + 3 w^{3} + 10 w^{2} - 2 w - 2]$ | $\phantom{-}8 e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, 2 w^{4} - 3 w^{3} - 6 w^{2} + 5 w + 1]$ | $-1$ |