Base field \(\Q(\zeta_{15})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 4x^{2} + 4x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[151,151,4w^{3} + w^{2} - 12w - 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 18x^{4} + 80x^{2} - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{2} + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} + w^{2} - 4w - 3]$ | $-\frac{1}{16}e^{5} + \frac{5}{8}e^{3}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{2}e^{2} + 9$ |
| 29 | $[29, 29, -w^{3} - w^{2} + 2w + 3]$ | $-\frac{1}{8}e^{5} + \frac{9}{4}e^{3} - 9e$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $\phantom{-}\frac{3}{16}e^{5} - \frac{23}{8}e^{3} + 8e$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{3}{16}e^{5} - \frac{23}{8}e^{3} + 8e$ |
| 29 | $[29, 29, 2w^{3} + w^{2} - 7w]$ | $-\frac{1}{8}e^{5} + \frac{9}{4}e^{3} - 9e$ |
| 31 | $[31, 31, -2w + 1]$ | $\phantom{-}e^{2} - 4$ |
| 31 | $[31, 31, 2w^{2} - 5]$ | $-\frac{1}{4}e^{4} + \frac{5}{2}e^{2}$ |
| 31 | $[31, 31, 2w^{3} + 2w^{2} - 6w - 3]$ | $-\frac{1}{4}e^{4} + \frac{5}{2}e^{2}$ |
| 31 | $[31, 31, 2w^{3} - 8w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 16$ |
| 59 | $[59, 59, w^{3} + w^{2} - 2w - 5]$ | $-\frac{1}{4}e^{5} + \frac{9}{2}e^{3} - 18e$ |
| 59 | $[59, 59, -w^{3} + 2w^{2} + 4w - 5]$ | $\phantom{-}\frac{1}{16}e^{5} - \frac{5}{8}e^{3} - e$ |
| 59 | $[59, 59, -3w^{3} + 10w - 4]$ | $-\frac{1}{4}e^{5} + \frac{9}{2}e^{3} - 18e$ |
| 59 | $[59, 59, -2w^{3} - w^{2} + 7w - 2]$ | $\phantom{-}\frac{3}{8}e^{5} - \frac{23}{4}e^{3} + 16e$ |
| 61 | $[61, 61, 4w^{3} + w^{2} - 13w - 1]$ | $-\frac{1}{2}e^{4} + 5e^{2} - 2$ |
| 61 | $[61, 61, 2w^{3} - w^{2} - 5w + 2]$ | $\phantom{-}2e^{2} - 10$ |
| 61 | $[61, 61, -3w^{3} - w^{2} + 8w]$ | $\phantom{-}2e^{2} - 10$ |
| 61 | $[61, 61, 3w^{3} - w^{2} - 10w + 5]$ | $-\frac{1}{4}e^{4} + \frac{7}{2}e^{2} - 6$ |
| 89 | $[89, 89, w^{3} + w^{2} - w - 4]$ | $\phantom{-}\frac{3}{16}e^{5} - \frac{31}{8}e^{3} + 16e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $151$ | $[151,151,4w^{3} + w^{2} - 12w - 1]$ | $1$ |