Base field 3.3.1593.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w^{2} - 3w - 2]$ |
| Dimension: | $14$ |
| 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:
| \(x^{14} + 2x^{13} - 18x^{12} - 36x^{11} + 113x^{10} + 231x^{9} - 310x^{8} - 669x^{7} + 379x^{6} + 937x^{5} - 144x^{4} - 610x^{3} - 68x^{2} + 149x + 44\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 2w - 4]$ | $...$ |
| 7 | $[7, 7, w]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 7 | $[7, 7, -w^{2} + 2w + 3]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w - 2]$ | $\phantom{-}6e^{13} + 9e^{12} - 113e^{11} - 159e^{10} + 767e^{9} + 993e^{8} - 2420e^{7} - 2743e^{6} + 3834e^{5} + 3536e^{4} - 2886e^{3} - 2016e^{2} + 749e + 446$ |
| 25 | $[25, 5, -w^{2} - w + 3]$ | $...$ |
| 29 | $[29, 29, w^{2} - 2w - 6]$ | $...$ |
| 31 | $[31, 31, w^{2} - 5]$ | $...$ |
| 37 | $[37, 37, -w^{2} - 2w + 2]$ | $...$ |
| 41 | $[41, 41, w^{2} - 8]$ | $...$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $...$ |
| 53 | $[53, 53, 2w^{2} - 5w - 4]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $...$ |
| 61 | $[61, 61, -w^{2} + 2w + 12]$ | $...$ |
| 67 | $[67, 67, -2w^{2} + 6w + 3]$ | $...$ |
| 71 | $[71, 71, w^{2} - w - 11]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{2} - 3w - 2]$ | $-1$ |