Base field \(\Q(\sqrt{51}) \)
Generator \(w\), with minimal polynomial \(x^2 - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[34, 34, w + 17]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $220$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 7]$ | $-1$ |
| 3 | $[3, 3, w]$ | $\phantom{-}2$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}4$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}4$ |
| 13 | $[13, 13, w - 8]$ | $\phantom{-}2$ |
| 13 | $[13, 13, w + 8]$ | $\phantom{-}2$ |
| 17 | $[17, 17, w]$ | $-1$ |
| 29 | $[29, 29, w + 14]$ | $\phantom{-}0$ |
| 29 | $[29, 29, w + 15]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w + 12]$ | $\phantom{-}4$ |
| 31 | $[31, 31, w + 19]$ | $\phantom{-}4$ |
| 41 | $[41, 41, w + 16]$ | $\phantom{-}6$ |
| 41 | $[41, 41, w + 25]$ | $\phantom{-}6$ |
| 47 | $[47, 47, -w - 2]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w - 2]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 3 w - 20]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 10 w - 71]$ | $\phantom{-}0$ |
| 79 | $[79, 79, w + 29]$ | $-8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 7]$ | $1$ |
| $17$ | $[17, 17, w]$ | $1$ |