Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[14, 14, -w - 4]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 6x^{2} + x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
3 | $[3, 3, w]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 5]$ | $\phantom{-}e^{3} - e^{2} - 6e - 1$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 3e + \frac{3}{2}$ |
7 | $[7, 7, w + 4]$ | $\phantom{-}1$ |
13 | $[13, 13, w + 2]$ | $\phantom{-}e^{3} - 7e - 1$ |
13 | $[13, 13, w + 11]$ | $-e^{3} + e^{2} + 4e + 1$ |
17 | $[17, 17, w + 8]$ | $-e^{3} + 8e + 1$ |
17 | $[17, 17, w + 9]$ | $-\frac{1}{2}e^{3} + 2e^{2} - \frac{11}{2}$ |
19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 2e + \frac{1}{2}$ |
19 | $[19, 19, -w + 7]$ | $-\frac{5}{2}e^{3} + 2e^{2} + 15e - \frac{3}{2}$ |
29 | $[29, 29, -w - 1]$ | $\phantom{-}e^{3} - e^{2} - 5e - 4$ |
29 | $[29, 29, w - 1]$ | $-3e^{3} + 3e^{2} + 16e - 2$ |
37 | $[37, 37, w + 17]$ | $-e^{2} + e + 7$ |
37 | $[37, 37, w + 20]$ | $\phantom{-}\frac{5}{2}e^{3} - 3e^{2} - 12e + \frac{5}{2}$ |
71 | $[71, 71, 2w - 7]$ | $\phantom{-}\frac{7}{2}e^{3} - 3e^{2} - 22e + \frac{3}{2}$ |
71 | $[71, 71, -2w - 7]$ | $\phantom{-}\frac{3}{2}e^{3} - 3e^{2} - 8e - \frac{5}{2}$ |
83 | $[83, 83, w + 14]$ | $-3e^{3} + e^{2} + 15e + 6$ |
83 | $[83, 83, w + 69]$ | $-3e^{3} + e^{2} + 23e + 4$ |
101 | $[101, 101, -7w + 37]$ | $-\frac{5}{2}e^{3} + 5e^{2} + 8e - \frac{25}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $1$ |
$7$ | $[7, 7, w + 4]$ | $-1$ |