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: | $[16, 4, 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 64x^{6} + 880x^{4} - 3072x^{2} + 3136\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{224}e^{7} + \frac{61}{224}e^{5} - \frac{87}{28}e^{3} + \frac{127}{28}e$ |
| 5 | $[5, 5, -w + 5]$ | $-\frac{1}{224}e^{7} + \frac{61}{224}e^{5} - \frac{87}{28}e^{3} + \frac{99}{28}e$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{11}{448}e^{6} + \frac{171}{112}e^{4} - \frac{1045}{56}e^{2} + \frac{71}{2}$ |
| 7 | $[7, 7, w + 4]$ | $-\frac{11}{448}e^{6} + \frac{171}{112}e^{4} - \frac{1045}{56}e^{2} + \frac{71}{2}$ |
| 13 | $[13, 13, w + 2]$ | $-\frac{1}{224}e^{6} + \frac{33}{112}e^{4} - \frac{123}{28}e^{2} + \frac{25}{2}$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{1}{224}e^{6} + \frac{33}{112}e^{4} - \frac{123}{28}e^{2} + \frac{25}{2}$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{3}{448}e^{7} + \frac{47}{112}e^{5} - \frac{297}{56}e^{3} + \frac{165}{14}e$ |
| 17 | $[17, 17, w + 9]$ | $-\frac{3}{448}e^{7} + \frac{47}{112}e^{5} - \frac{297}{56}e^{3} + \frac{165}{14}e$ |
| 19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{3}{112}e^{6} - \frac{23}{14}e^{4} + \frac{271}{14}e^{2} - 34$ |
| 19 | $[19, 19, -w + 7]$ | $\phantom{-}\frac{3}{112}e^{6} - \frac{23}{14}e^{4} + \frac{271}{14}e^{2} - 34$ |
| 29 | $[29, 29, -w - 1]$ | $-\frac{11}{448}e^{7} + \frac{339}{224}e^{5} - \frac{1013}{56}e^{3} + \frac{989}{28}e$ |
| 29 | $[29, 29, w - 1]$ | $-\frac{11}{448}e^{7} + \frac{339}{224}e^{5} - \frac{1013}{56}e^{3} + \frac{989}{28}e$ |
| 37 | $[37, 37, w + 17]$ | $-\frac{5}{112}e^{6} + \frac{309}{112}e^{4} - \frac{461}{14}e^{2} + \frac{117}{2}$ |
| 37 | $[37, 37, w + 20]$ | $-\frac{5}{112}e^{6} + \frac{309}{112}e^{4} - \frac{461}{14}e^{2} + \frac{117}{2}$ |
| 71 | $[71, 71, 2w - 7]$ | $\phantom{-}\frac{13}{224}e^{7} - \frac{25}{7}e^{5} + \frac{1187}{28}e^{3} - \frac{544}{7}e$ |
| 71 | $[71, 71, -2w - 7]$ | $\phantom{-}\frac{13}{224}e^{7} - \frac{25}{7}e^{5} + \frac{1187}{28}e^{3} - \frac{544}{7}e$ |
| 83 | $[83, 83, w + 14]$ | $-\frac{11}{224}e^{7} + \frac{681}{224}e^{5} - \frac{147}{4}e^{3} + \frac{1955}{28}e$ |
| 83 | $[83, 83, w + 69]$ | $-\frac{11}{224}e^{7} + \frac{681}{224}e^{5} - \frac{147}{4}e^{3} + \frac{1955}{28}e$ |
| 101 | $[101, 101, -7w + 37]$ | $\phantom{-}\frac{37}{448}e^{7} - \frac{1139}{224}e^{5} + \frac{3387}{56}e^{3} - \frac{3165}{28}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |