Base field \(\Q(\sqrt{317}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 79\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7,7,w - 9]$ |
| Dimension: | $26$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{26} + 7x^{25} - 33x^{24} - 309x^{23} + 372x^{22} + 5924x^{21} - 625x^{20} - 64880x^{19} - 23958x^{18} + 449615x^{17} + 258089x^{16} - 2065018x^{15} - 1290137x^{14} + 6402711x^{13} + 3671824x^{12} - 13378021x^{11} - 6080329x^{10} + 18396753x^{9} + 5538821x^{8} - 15749526x^{7} - 2356384x^{6} + 7529035x^{5} + 318154x^{4} - 1642445x^{3} - 65204x^{2} + 128054x + 16049\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w - 8]$ | $...$ |
| 7 | $[7, 7, -w + 9]$ | $-1$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w - 10]$ | $...$ |
| 11 | $[11, 11, -w - 9]$ | $...$ |
| 23 | $[23, 23, -w - 7]$ | $...$ |
| 23 | $[23, 23, -w + 8]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 31 | $[31, 31, -w - 10]$ | $...$ |
| 31 | $[31, 31, w - 11]$ | $...$ |
| 37 | $[37, 37, -w - 6]$ | $...$ |
| 37 | $[37, 37, w - 7]$ | $...$ |
| 43 | $[43, 43, 4w + 33]$ | $...$ |
| 43 | $[43, 43, 4w - 37]$ | $...$ |
| 53 | $[53, 53, -w - 11]$ | $...$ |
| 53 | $[53, 53, w - 12]$ | $...$ |
| 59 | $[59, 59, -w - 4]$ | $...$ |
| 59 | $[59, 59, w - 5]$ | $...$ |
| 61 | $[61, 61, 2w - 17]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,w - 9]$ | $1$ |