Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2 x^{3} - 5 x^{2} + 2 x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[81, 3, 3]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $98$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -w^{3} + 3 w^{2} + w - 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{3} + 3 w^{2} + 2 w - 5]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w^{3} - 2 w^{2} - 4 w + 2]$ | $\phantom{-}2$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}2$ |
| 17 | $[17, 17, w^{3} - 3 w^{2} - 2 w + 2]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $-2$ |
| 19 | $[19, 19, w^{3} - 2 w^{2} - 3 w + 2]$ | $\phantom{-}4$ |
| 23 | $[23, 23, w^{2} - 2 w - 1]$ | $\phantom{-}8$ |
| 27 | $[27, 3, w^{3} - 2 w^{2} - 5 w - 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{3} + 2 w^{2} + 5 w - 1]$ | $-8$ |
| 37 | $[37, 37, -w^{3} + 2 w^{2} + 5 w - 4]$ | $\phantom{-}2$ |
| 41 | $[41, 41, 2 w^{3} - 5 w^{2} - 6 w + 4]$ | $-4$ |
| 53 | $[53, 53, w^{3} - 2 w^{2} - 3 w - 2]$ | $-2$ |
| 59 | $[59, 59, w - 4]$ | $-8$ |
| 67 | $[67, 67, 2 w^{2} - 3 w - 8]$ | $\phantom{-}2$ |
| 73 | $[73, 73, 2 w^{3} - 5 w^{2} - 6 w + 5]$ | $\phantom{-}2$ |
| 89 | $[89, 89, -2 w^{3} + 6 w^{2} + 5 w - 7]$ | $\phantom{-}0$ |
| 97 | $[97, 97, -2 w^{3} + 6 w^{2} + 3 w - 7]$ | $-18$ |
| 97 | $[97, 97, -w^{3} + 3 w^{2} + 3 w - 1]$ | $-2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |
| $27$ | $[27, 3, w^{3} - 2 w^{2} - 5 w - 1]$ | $-1$ |