Base field 3.3.1396.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w^{2} + w - 3]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 2x^{15} - 22x^{14} - 44x^{13} + 189x^{12} + 378x^{11} - 806x^{10} - 1605x^{9} + 1817x^{8} + 3534x^{7} - 2220x^{6} - 3925x^{5} + 1578x^{4} + 2026x^{3} - 675x^{2} - 375x + 125\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $...$ |
| 5 | $[5, 5, -w^{2} + 6]$ | $...$ |
| 5 | $[5, 5, -w + 2]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $...$ |
| 11 | $[11, 11, 2w - 1]$ | $...$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $\phantom{-}1$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $...$ |
| 41 | $[41, 41, 3w^{2} - w - 23]$ | $...$ |
| 41 | $[41, 41, w^{2} - 2]$ | $...$ |
| 43 | $[43, 43, w^{2} - w - 3]$ | $...$ |
| 47 | $[47, 47, -w - 4]$ | $...$ |
| 49 | $[49, 7, 3w^{2} - 2w - 24]$ | $...$ |
| 53 | $[53, 53, 2w^{2} - w - 12]$ | $...$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $...$ |
| 61 | $[61, 61, -w^{2} + 3w - 3]$ | $...$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $...$ |
| 79 | $[79, 79, 2w + 3]$ | $...$ |
| 89 | $[89, 89, 2w - 7]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{2} + w - 3]$ | $-1$ |