Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, 12w^{2} + w + 7]$ |
| Dimension: | $26$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $104$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{26} + 6x^{25} - 19x^{24} - 174x^{23} + 53x^{22} + 2116x^{21} + 1491x^{20} - 13973x^{19} - 18102x^{18} + 53872x^{17} + 97395x^{16} - 118673x^{15} - 299051x^{14} + 120687x^{13} + 549081x^{12} + 37926x^{11} - 585026x^{10} - 231017x^{9} + 318109x^{8} + 221952x^{7} - 50767x^{6} - 76259x^{5} - 14182x^{4} + 3612x^{3} + 1078x^{2} - 39x - 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $...$ |
| 5 | $[5, 5, w]$ | $...$ |
| 11 | $[11, 11, 10w + 4]$ | $...$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $-1$ |
| 17 | $[17, 17, w + 1]$ | $...$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $...$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $...$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $...$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $...$ |
| 27 | $[27, 3, -3]$ | $...$ |
| 29 | $[29, 29, w + 7]$ | $...$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $...$ |
| 43 | $[43, 43, w^{2} - 11]$ | $...$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3]$ | $...$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $...$ |
| 79 | $[79, 79, w^{2} + 37]$ | $...$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, 12w^{2} + w + 7]$ | $1$ |