Base field \(\Q(\sqrt{377}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[2, 2, w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 3x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-e^{3} - 2e$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
9 | $[9, 3, 3]$ | $\phantom{-}e^{2} - 1$ |
11 | $[11, 11, w + 2]$ | $\phantom{-}3e^{3} + 7e$ |
11 | $[11, 11, w + 8]$ | $\phantom{-}5e^{3} + 10e$ |
13 | $[13, 13, 4w - 41]$ | $\phantom{-}e^{2} + 3$ |
19 | $[19, 19, w + 7]$ | $-2e^{3} - 5e$ |
19 | $[19, 19, w + 11]$ | $\phantom{-}e^{3} + 7e$ |
23 | $[23, 23, -2w + 21]$ | $\phantom{-}e^{2} - 2$ |
23 | $[23, 23, -2w - 19]$ | $\phantom{-}2e^{2} + 7$ |
25 | $[25, 5, -5]$ | $-4e^{2} - 5$ |
29 | $[29, 29, 6w - 61]$ | $-2e^{2} - 3$ |
31 | $[31, 31, w + 12]$ | $-e^{3} + e$ |
31 | $[31, 31, w + 18]$ | $\phantom{-}2e^{3} + 8e$ |
37 | $[37, 37, w + 4]$ | $\phantom{-}e^{3}$ |
37 | $[37, 37, w + 32]$ | $-5e^{3} - 14e$ |
41 | $[41, 41, w + 3]$ | $\phantom{-}e^{3} + 4e$ |
41 | $[41, 41, w + 37]$ | $\phantom{-}7e^{3} + 13e$ |
47 | $[47, 47, w]$ | $-2e^{3} - 2e$ |
47 | $[47, 47, w + 46]$ | $-9e^{3} - 20e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $e^{3} + 2e$ |