Base field \(\Q(\zeta_{15})^+\)
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 4 x^2 + 4 x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[145,145,w^3 - 4 w - 3]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^2 + 1]$ | $-1$ |
| 9 | $[9, 3, w^3 + w^2 - 4 w - 3]$ | $\phantom{-}4$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}3$ |
| 29 | $[29, 29, -w^3 - w^2 + 2 w + 3]$ | $-2$ |
| 29 | $[29, 29, -w^2 + w + 3]$ | $-1$ |
| 29 | $[29, 29, w^3 - w^2 - 4 w + 2]$ | $-2$ |
| 29 | $[29, 29, 2 w^3 + w^2 - 7 w]$ | $-2$ |
| 31 | $[31, 31, -2 w + 1]$ | $\phantom{-}4$ |
| 31 | $[31, 31, 2 w^2 - 5]$ | $-10$ |
| 31 | $[31, 31, 2 w^3 + 2 w^2 - 6 w - 3]$ | $\phantom{-}4$ |
| 31 | $[31, 31, 2 w^3 - 8 w + 1]$ | $\phantom{-}4$ |
| 59 | $[59, 59, w^3 + w^2 - 2 w - 5]$ | $-4$ |
| 59 | $[59, 59, -w^3 + 2 w^2 + 4 w - 5]$ | $\phantom{-}10$ |
| 59 | $[59, 59, -3 w^3 + 10 w - 4]$ | $-4$ |
| 59 | $[59, 59, -2 w^3 - w^2 + 7 w - 2]$ | $-4$ |
| 61 | $[61, 61, 4 w^3 + w^2 - 13 w - 1]$ | $\phantom{-}6$ |
| 61 | $[61, 61, 2 w^3 - w^2 - 5 w + 2]$ | $\phantom{-}6$ |
| 61 | $[61, 61, -3 w^3 - w^2 + 8 w]$ | $-8$ |
| 61 | $[61, 61, 3 w^3 - w^2 - 10 w + 5]$ | $\phantom{-}6$ |
| 89 | $[89, 89, w^3 + w^2 - w - 4]$ | $-6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w^3 + 4 w - 2]$ | $1$ |
| $29$ | $[29,29,-w^2 + w + 3]$ | $1$ |