Base field \(\Q(\sqrt{101}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[36, 6, 6]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, -w + 5]$ | $\phantom{-}0$ |
5 | $[5, 5, -w - 4]$ | $\phantom{-}0$ |
9 | $[9, 3, 3]$ | $-1$ |
13 | $[13, 13, w + 3]$ | $\phantom{-}2$ |
13 | $[13, 13, w - 4]$ | $\phantom{-}2$ |
17 | $[17, 17, w + 6]$ | $\phantom{-}7$ |
17 | $[17, 17, -w + 7]$ | $\phantom{-}7$ |
19 | $[19, 19, w + 2]$ | $\phantom{-}1$ |
19 | $[19, 19, w - 3]$ | $\phantom{-}1$ |
23 | $[23, 23, w + 1]$ | $\phantom{-}2$ |
23 | $[23, 23, -w + 2]$ | $\phantom{-}2$ |
31 | $[31, 31, -w - 7]$ | $-10$ |
31 | $[31, 31, w - 8]$ | $-10$ |
37 | $[37, 37, 2w - 9]$ | $\phantom{-}0$ |
37 | $[37, 37, 2w + 7]$ | $\phantom{-}0$ |
43 | $[43, 43, 4w + 17]$ | $\phantom{-}5$ |
43 | $[43, 43, 4w - 21]$ | $\phantom{-}5$ |
47 | $[47, 47, -w - 8]$ | $\phantom{-}8$ |
47 | $[47, 47, w - 9]$ | $\phantom{-}8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $1$ |
$9$ | $[9, 3, 3]$ | $1$ |