Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, 3w - 19]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 9x^{2} + 11\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $-e$ |
| 3 | $[3, 3, -w - 5]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-e^{2} + 4$ |
| 7 | $[7, 7, 3w - 19]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -2w - 11]$ | $\phantom{-}e^{2} - 6$ |
| 11 | $[11, 11, -2w + 13]$ | $\phantom{-}e^{2} - 6$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}e^{3} - 6e$ |
| 13 | $[13, 13, -w + 5]$ | $-e^{3} + 6e$ |
| 19 | $[19, 19, 5w - 31]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -w - 7]$ | $-2e^{2} + 7$ |
| 23 | $[23, 23, w - 8]$ | $-2e^{2} + 7$ |
| 25 | $[25, 5, -5]$ | $-9$ |
| 31 | $[31, 31, -w - 1]$ | $\phantom{-}e^{3} - 5e$ |
| 31 | $[31, 31, w - 2]$ | $-e^{3} + 5e$ |
| 41 | $[41, 41, 6w + 31]$ | $-e^{3} + 7e$ |
| 41 | $[41, 41, 6w - 37]$ | $\phantom{-}e^{3} - 7e$ |
| 43 | $[43, 43, -3w - 17]$ | $\phantom{-}2e^{2} - 12$ |
| 43 | $[43, 43, -3w + 20]$ | $\phantom{-}2e^{2} - 12$ |
| 59 | $[59, 59, 3w - 17]$ | $-e^{3} + 8e$ |
| 59 | $[59, 59, 3w + 14]$ | $\phantom{-}e^{3} - 8e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, 3w - 19]$ | $-1$ |