Base field \(\Q(\sqrt{349}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 87\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 9]$ | $-1$ |
| 3 | $[3, 3, -w + 10]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}4$ |
| 5 | $[5, 5, -6w + 59]$ | $\phantom{-}2$ |
| 5 | $[5, 5, -6w - 53]$ | $\phantom{-}2$ |
| 17 | $[17, 17, -13w - 115]$ | $\phantom{-}3$ |
| 17 | $[17, 17, 13w - 128]$ | $\phantom{-}3$ |
| 19 | $[19, 19, -5w - 44]$ | $-5$ |
| 19 | $[19, 19, 5w - 49]$ | $-5$ |
| 23 | $[23, 23, -w - 10]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w - 11]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -3w + 29]$ | $\phantom{-}1$ |
| 29 | $[29, 29, 3w + 26]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -w - 7]$ | $\phantom{-}7$ |
| 31 | $[31, 31, w - 8]$ | $\phantom{-}7$ |
| 37 | $[37, 37, 63w - 620]$ | $-3$ |
| 37 | $[37, 37, -63w - 557]$ | $-3$ |
| 41 | $[41, 41, 8w + 71]$ | $\phantom{-}10$ |
| 41 | $[41, 41, 8w - 79]$ | $\phantom{-}10$ |
| 49 | $[49, 7, -7]$ | $-6$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).