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: | $[36, 6, 6]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} - 2x^{2} - 18x - 14\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}e^{3} + 2e^{2} - 7e - 8$ |
| 5 | $[5, 5, -w - 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $-1$ |
| 13 | $[13, 13, w + 3]$ | $-2e^{3} - 5e^{2} + 13e + 22$ |
| 13 | $[13, 13, w - 4]$ | $\phantom{-}e^{3} + 3e^{2} - 7e - 16$ |
| 17 | $[17, 17, w + 6]$ | $-2e^{3} - 5e^{2} + 13e + 23$ |
| 17 | $[17, 17, -w + 7]$ | $\phantom{-}e^{2} + e - 7$ |
| 19 | $[19, 19, w + 2]$ | $-6e^{3} - 15e^{2} + 35e + 59$ |
| 19 | $[19, 19, w - 3]$ | $\phantom{-}3e^{3} + 7e^{2} - 17e - 27$ |
| 23 | $[23, 23, w + 1]$ | $-2e^{3} - 5e^{2} + 11e + 18$ |
| 23 | $[23, 23, -w + 2]$ | $-e^{3} - 3e^{2} + 3e + 10$ |
| 31 | $[31, 31, -w - 7]$ | $-3e^{3} - 8e^{2} + 17e + 30$ |
| 31 | $[31, 31, w - 8]$ | $\phantom{-}6e^{3} + 14e^{2} - 35e - 56$ |
| 37 | $[37, 37, 2w - 9]$ | $\phantom{-}8e^{3} + 21e^{2} - 47e - 82$ |
| 37 | $[37, 37, 2w + 7]$ | $-5e^{3} - 13e^{2} + 27e + 48$ |
| 43 | $[43, 43, 4w + 17]$ | $\phantom{-}4e^{3} + 12e^{2} - 21e - 47$ |
| 43 | $[43, 43, 4w - 21]$ | $-7e^{3} - 18e^{2} + 37e + 67$ |
| 47 | $[47, 47, -w - 8]$ | $\phantom{-}6e^{3} + 17e^{2} - 35e - 68$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}e^{3} + 3e^{2} - 5e - 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |
| $9$ | $[9, 3, 3]$ | $1$ |