Base field 4.4.19821.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 8 x^2 + 6 x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[27, 9, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 2 w - 1]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, \frac{1}{3} w^3 - \frac{2}{3} w^2 - 2 w + 2]$ | $\phantom{-}4$ |
| 9 | $[9, 3, w + 1]$ | $-1$ |
| 13 | $[13, 13, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 5 w]$ | $-5$ |
| 16 | $[16, 2, 2]$ | $-5$ |
| 17 | $[17, 17, \frac{1}{3} w^3 - \frac{2}{3} w^2 - 3 w + 5]$ | $-6$ |
| 19 | $[19, 19, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 2 w - 5]$ | $-2$ |
| 23 | $[23, 23, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 3 w - 2]$ | $\phantom{-}0$ |
| 25 | $[25, 5, \frac{1}{3} w^3 + \frac{1}{3} w^2 - 3 w]$ | $-2$ |
| 25 | $[25, 5, -\frac{2}{3} w^3 + \frac{1}{3} w^2 + 5 w - 3]$ | $\phantom{-}2$ |
| 29 | $[29, 29, -\frac{2}{3} w^3 + \frac{1}{3} w^2 + 4 w - 3]$ | $-6$ |
| 29 | $[29, 29, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 2 w]$ | $\phantom{-}9$ |
| 37 | $[37, 37, \frac{1}{3} w^3 + \frac{1}{3} w^2 - 2 w - 3]$ | $\phantom{-}2$ |
| 41 | $[41, 41, -\frac{2}{3} w^3 + \frac{1}{3} w^2 + 5 w - 4]$ | $\phantom{-}12$ |
| 43 | $[43, 43, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 6 w]$ | $-1$ |
| 47 | $[47, 47, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 4 w]$ | $\phantom{-}3$ |
| 59 | $[59, 59, \frac{1}{3} w^3 + \frac{1}{3} w^2 - 2 w - 4]$ | $\phantom{-}0$ |
| 59 | $[59, 59, \frac{4}{3} w^3 - \frac{5}{3} w^2 - 10 w + 9]$ | $-3$ |
| 67 | $[67, 67, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 3 w]$ | $-4$ |
| 71 | $[71, 71, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 4 w + 1]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $1$ |