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: | $[12,6,-2w + 20]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $78$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 9]$ | $\phantom{-}2$ |
3 | $[3, 3, -w + 10]$ | $-1$ |
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, -6w + 59]$ | $-4$ |
5 | $[5, 5, -6w - 53]$ | $-1$ |
17 | $[17, 17, -13w - 115]$ | $\phantom{-}0$ |
17 | $[17, 17, 13w - 128]$ | $\phantom{-}3$ |
19 | $[19, 19, -5w - 44]$ | $-2$ |
19 | $[19, 19, 5w - 49]$ | $\phantom{-}4$ |
23 | $[23, 23, -w - 10]$ | $-8$ |
23 | $[23, 23, w - 11]$ | $\phantom{-}7$ |
29 | $[29, 29, -3w + 29]$ | $-8$ |
29 | $[29, 29, 3w + 26]$ | $-5$ |
31 | $[31, 31, -w - 7]$ | $-2$ |
31 | $[31, 31, w - 8]$ | $-8$ |
37 | $[37, 37, 63w - 620]$ | $\phantom{-}3$ |
37 | $[37, 37, -63w - 557]$ | $-3$ |
41 | $[41, 41, 8w + 71]$ | $\phantom{-}10$ |
41 | $[41, 41, 8w - 79]$ | $-2$ |
49 | $[49, 7, -7]$ | $-3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,-w + 10]$ | $1$ |
$4$ | $[4,2,2]$ | $1$ |