Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); 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: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 6]$ | $-2$ |
3 | $[3, 3, -w + 7]$ | $-2$ |
4 | $[4, 2, 2]$ | $\phantom{-}3$ |
11 | $[11, 11, -3w - 17]$ | $\phantom{-}6$ |
11 | $[11, 11, 3w - 20]$ | $\phantom{-}6$ |
13 | $[13, 13, 2w - 13]$ | $-5$ |
13 | $[13, 13, 2w + 11]$ | $-5$ |
17 | $[17, 17, w + 7]$ | $\phantom{-}3$ |
17 | $[17, 17, -w + 8]$ | $\phantom{-}3$ |
19 | $[19, 19, -w - 4]$ | $\phantom{-}0$ |
19 | $[19, 19, -w + 5]$ | $\phantom{-}0$ |
25 | $[25, 5, 5]$ | $-6$ |
31 | $[31, 31, -6w - 35]$ | $\phantom{-}0$ |
31 | $[31, 31, -6w + 41]$ | $\phantom{-}0$ |
37 | $[37, 37, -w - 1]$ | $-3$ |
37 | $[37, 37, w - 2]$ | $-3$ |
47 | $[47, 47, 3w + 16]$ | $\phantom{-}6$ |
47 | $[47, 47, -3w + 19]$ | $\phantom{-}6$ |
49 | $[49, 7, -7]$ | $\phantom{-}5$ |
67 | $[67, 67, 3w - 22]$ | $\phantom{-}4$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).