Base field \(\Q(\sqrt{101}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 9x^{6} + 13x^{5} + 83x^{4} - 227x^{3} - 120x^{2} + 684x - 364\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 5]$ | $-\frac{1}{2}e^{6} + \frac{5}{2}e^{5} + \frac{9}{2}e^{4} - \frac{61}{2}e^{3} - \frac{3}{2}e^{2} + 89e - 51$ |
| 5 | $[5, 5, -w - 4]$ | $-\frac{1}{2}e^{6} + \frac{5}{2}e^{5} + \frac{9}{2}e^{4} - \frac{61}{2}e^{3} - \frac{3}{2}e^{2} + 89e - 51$ |
| 9 | $[9, 3, 3]$ | $-1$ |
| 13 | $[13, 13, w + 3]$ | $-17e^{6} + 94e^{5} + 105e^{4} - 1044e^{3} + 228e^{2} + 2826e - 1769$ |
| 13 | $[13, 13, w - 4]$ | $-17e^{6} + 94e^{5} + 105e^{4} - 1044e^{3} + 228e^{2} + 2826e - 1769$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{49}{2}e^{6} - \frac{271}{2}e^{5} - \frac{303}{2}e^{4} + \frac{3015}{2}e^{3} - \frac{667}{2}e^{2} - 4088e + 2577$ |
| 17 | $[17, 17, -w + 7]$ | $\phantom{-}\frac{49}{2}e^{6} - \frac{271}{2}e^{5} - \frac{303}{2}e^{4} + \frac{3015}{2}e^{3} - \frac{667}{2}e^{2} - 4088e + 2577$ |
| 19 | $[19, 19, w + 2]$ | $-2e^{6} + 11e^{5} + 13e^{4} - 124e^{3} + 24e^{2} + 339e - 213$ |
| 19 | $[19, 19, w - 3]$ | $-2e^{6} + 11e^{5} + 13e^{4} - 124e^{3} + 24e^{2} + 339e - 213$ |
| 23 | $[23, 23, w + 1]$ | $\phantom{-}\frac{45}{2}e^{6} - \frac{249}{2}e^{5} - \frac{277}{2}e^{4} + \frac{2765}{2}e^{3} - \frac{613}{2}e^{2} - 3743e + 2349$ |
| 23 | $[23, 23, -w + 2]$ | $\phantom{-}\frac{45}{2}e^{6} - \frac{249}{2}e^{5} - \frac{277}{2}e^{4} + \frac{2765}{2}e^{3} - \frac{613}{2}e^{2} - 3743e + 2349$ |
| 31 | $[31, 31, -w - 7]$ | $-27e^{6} + 149e^{5} + 170e^{4} - 1667e^{3} + 353e^{2} + 4547e - 2853$ |
| 31 | $[31, 31, w - 8]$ | $-27e^{6} + 149e^{5} + 170e^{4} - 1667e^{3} + 353e^{2} + 4547e - 2853$ |
| 37 | $[37, 37, 2w - 9]$ | $\phantom{-}33e^{6} - 183e^{5} - 200e^{4} + 2023e^{3} - 463e^{2} - 5455e + 3430$ |
| 37 | $[37, 37, 2w + 7]$ | $\phantom{-}33e^{6} - 183e^{5} - 200e^{4} + 2023e^{3} - 463e^{2} - 5455e + 3430$ |
| 43 | $[43, 43, 4w + 17]$ | $-17e^{6} + 94e^{5} + 106e^{4} - 1051e^{3} + 233e^{2} + 2865e - 1816$ |
| 43 | $[43, 43, 4w - 21]$ | $-17e^{6} + 94e^{5} + 106e^{4} - 1051e^{3} + 233e^{2} + 2865e - 1816$ |
| 47 | $[47, 47, -w - 8]$ | $\phantom{-}\frac{27}{2}e^{6} - \frac{149}{2}e^{5} - \frac{169}{2}e^{4} + \frac{1665}{2}e^{3} - \frac{361}{2}e^{2} - 2272e + 1433$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}\frac{27}{2}e^{6} - \frac{149}{2}e^{5} - \frac{169}{2}e^{4} + \frac{1665}{2}e^{3} - \frac{361}{2}e^{2} - 2272e + 1433$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $1$ |