Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[45, 45, -w^{3} + 4 w]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{4} + w^{3} + 4 w^{2} - 2 w - 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $-1$ |
| 19 | $[19, 19, w^{4} - 2 w^{3} - 4 w^{2} + 5 w + 4]$ | $-4$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3 w - 1]$ | $-2$ |
| 29 | $[29, 29, 2 w^{4} - 3 w^{3} - 8 w^{2} + 7 w + 4]$ | $-2$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}1$ |
| 37 | $[37, 37, w^{3} - 2 w^{2} - 2 w + 2]$ | $-10$ |
| 41 | $[41, 41, -2 w^{4} + 3 w^{3} + 9 w^{2} - 8 w - 6]$ | $\phantom{-}2$ |
| 43 | $[43, 43, -2 w^{4} + 3 w^{3} + 8 w^{2} - 8 w - 6]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w^{4} - 2 w^{3} - 5 w^{2} + 6 w + 5]$ | $-4$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4 w^{2} - w - 4]$ | $-6$ |
| 61 | $[61, 61, w^{2} - 2 w - 3]$ | $\phantom{-}6$ |
| 67 | $[67, 67, w^{4} - w^{3} - 4 w^{2} + 3 w]$ | $\phantom{-}4$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5 w^{2} - 2 w - 2]$ | $-8$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4 w^{2} + 5]$ | $\phantom{-}0$ |
| 71 | $[71, 71, w^{4} - 2 w^{3} - 3 w^{2} + 5 w + 3]$ | $\phantom{-}6$ |
| 71 | $[71, 71, 2 w^{4} - 2 w^{3} - 8 w^{2} + 5 w + 4]$ | $-12$ |
| 73 | $[73, 73, -2 w^{4} + 2 w^{3} + 9 w^{2} - 5 w - 6]$ | $-14$ |
| 81 | $[81, 3, -2 w^{4} + 3 w^{3} + 10 w^{2} - 9 w - 10]$ | $\phantom{-}8$ |
| 97 | $[97, 97, -2 w^{4} + 3 w^{3} + 7 w^{2} - 5 w - 4]$ | $-6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{4} + w^{3} + 4 w^{2} - 2 w - 2]$ | $1$ |
| $5$ | $[5, 5, w^{2} - w - 2]$ | $1$ |