Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7,7,-w + 3]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 6x^{4} + 8x^{2} - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-e^{5} + 6e^{3} - 7e$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}e^{3} - 3e$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e^{2} + 1$ |
| 7 | $[7, 7, w + 4]$ | $-1$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}e^{4} - 5e^{2} + 6$ |
| 13 | $[13, 13, w + 11]$ | $-2e^{4} + 8e^{2} - 2$ |
| 17 | $[17, 17, w + 8]$ | $-e^{5} + 4e^{3} - 3e$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}2e^{5} - 9e^{3} + 5e$ |
| 19 | $[19, 19, w + 7]$ | $-e^{4} + e^{2} + 6$ |
| 19 | $[19, 19, -w + 7]$ | $-2e^{4} + 11e^{2} - 7$ |
| 29 | $[29, 29, -w - 1]$ | $-3e^{5} + 15e^{3} - 10e$ |
| 29 | $[29, 29, w - 1]$ | $-4e^{5} + 24e^{3} - 32e$ |
| 37 | $[37, 37, w + 17]$ | $\phantom{-}2e^{4} - 9e^{2} + 9$ |
| 37 | $[37, 37, w + 20]$ | $-4e^{4} + 17e^{2} - 7$ |
| 71 | $[71, 71, 2w - 7]$ | $\phantom{-}e^{5} - 4e^{3} + 3e$ |
| 71 | $[71, 71, -2w - 7]$ | $\phantom{-}3e^{5} - 23e^{3} + 38e$ |
| 83 | $[83, 83, w + 14]$ | $-9e^{5} + 51e^{3} - 54e$ |
| 83 | $[83, 83, w + 69]$ | $\phantom{-}6e^{5} - 30e^{3} + 26e$ |
| 101 | $[101, 101, -7w + 37]$ | $\phantom{-}7e^{5} - 42e^{3} + 59e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-w + 3]$ | $1$ |