Base field 4.4.725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 3x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[109,109,-w^{3} + 3w^{2} - w - 4]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
11 | $[11, 11, -w^{3} + 2w^{2} + w - 3]$ | $\phantom{-}1$ |
11 | $[11, 11, w^{3} - 3w]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{2}e$ |
19 | $[19, 19, -w^{3} + 2w + 2]$ | $-2e$ |
19 | $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ | $-\frac{1}{2}e + 4$ |
25 | $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ | $-e - 6$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{5}{2}e$ |
31 | $[31, 31, w^{3} - 4w + 1]$ | $-e$ |
31 | $[31, 31, -w^{2} + 2w + 3]$ | $\phantom{-}e - 2$ |
41 | $[41, 41, 2w^{2} - w - 3]$ | $-2e$ |
41 | $[41, 41, -w^{3} + 3w^{2} + w - 4]$ | $-e - 1$ |
49 | $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ | $-e - 4$ |
49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}6$ |
61 | $[61, 61, 2w^{3} - 3w^{2} - 4w]$ | $\phantom{-}e + 6$ |
61 | $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ | $-\frac{1}{2}e + 2$ |
79 | $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ | $\phantom{-}2e + 1$ |
79 | $[79, 79, w^{3} + w^{2} - 3w - 5]$ | $\phantom{-}\frac{3}{2}e - 4$ |
81 | $[81, 3, -3]$ | $\phantom{-}e - 7$ |
89 | $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ | $-\frac{1}{2}e - 14$ |
89 | $[89, 89, 3w^{3} - 2w^{2} - 7w]$ | $\phantom{-}2e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$109$ | $[109,109,-w^{3} + 3w^{2} - w - 4]$ | $1$ |