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:
\(x^{4} + 7x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-\frac{1}{3}e^{3} - \frac{8}{3}e$ |
3 | $[3, 3, w]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 5]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{8}{3}$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{8}{3}e$ |
7 | $[7, 7, w + 4]$ | $-\frac{5}{3}e^{3} - \frac{31}{3}e$ |
13 | $[13, 13, w + 2]$ | $-\frac{1}{3}e^{3} - \frac{5}{3}e$ |
13 | $[13, 13, w + 11]$ | $\phantom{-}2e^{3} + 11e$ |
17 | $[17, 17, w + 8]$ | $\phantom{-}\frac{8}{3}e^{3} + \frac{49}{3}e$ |
17 | $[17, 17, w + 9]$ | $\phantom{-}2e^{3} + 12e$ |
19 | $[19, 19, w + 7]$ | $-2e^{2} - 8$ |
19 | $[19, 19, -w + 7]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{4}{3}$ |
29 | $[29, 29, -w - 1]$ | $-\frac{1}{3}e^{2} + \frac{13}{3}$ |
29 | $[29, 29, w - 1]$ | $-\frac{2}{3}e^{2} + \frac{8}{3}$ |
37 | $[37, 37, w + 17]$ | $\phantom{-}2e^{3} + 12e$ |
37 | $[37, 37, w + 20]$ | $\phantom{-}2e^{3} + 12e$ |
71 | $[71, 71, 2w - 7]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{34}{3}$ |
71 | $[71, 71, -2w - 7]$ | $-2e^{2}$ |
83 | $[83, 83, w + 14]$ | $\phantom{-}4e^{3} + 26e$ |
83 | $[83, 83, w + 69]$ | $-\frac{16}{3}e^{3} - \frac{128}{3}e$ |
101 | $[101, 101, -7w + 37]$ | $-\frac{8}{3}e^{2} - \frac{10}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w]$ | $\frac{1}{3}e^{3} + \frac{8}{3}e$ |
$7$ | $[7,7,-w + 4]$ | $-\frac{1}{3}e^{3} - \frac{8}{3}e$ |