Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, -w + 9]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 11x^{6} + 95x^{4} + 286x^{2} + 676\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $-1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{11}{2470}e^{7} + \frac{1}{26}e^{5} + \frac{11}{26}e^{3} + \frac{121}{95}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{9}{1235}e^{6} + \frac{2}{13}e^{4} + \frac{9}{13}e^{2} + \frac{198}{95}$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{22}{1235}e^{6} - \frac{2}{13}e^{4} - \frac{9}{13}e^{2} - \frac{104}{95}$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{1}{95}e^{7} - \frac{284}{95}e$ |
| 7 | $[7, 7, w + 4]$ | $-\frac{4}{247}e^{7} - \frac{3}{13}e^{5} - \frac{20}{13}e^{3} - \frac{88}{19}e$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{31}{1235}e^{6} + \frac{4}{13}e^{4} + \frac{31}{13}e^{2} + \frac{682}{95}$ |
| 13 | $[13, 13, w + 12]$ | $-\frac{44}{1235}e^{6} - \frac{4}{13}e^{4} - \frac{31}{13}e^{2} - \frac{208}{95}$ |
| 43 | $[43, 43, -w - 6]$ | $\phantom{-}\frac{11}{494}e^{7} + \frac{5}{26}e^{5} + \frac{29}{26}e^{3} + \frac{26}{19}e$ |
| 43 | $[43, 43, w - 6]$ | $-\frac{11}{494}e^{7} - \frac{5}{26}e^{5} - \frac{29}{26}e^{3} - \frac{26}{19}e$ |
| 47 | $[47, 47, w + 19]$ | $\phantom{-}\frac{1}{95}e^{7} - \frac{284}{95}e$ |
| 47 | $[47, 47, w + 28]$ | $-\frac{4}{247}e^{7} - \frac{3}{13}e^{5} - \frac{20}{13}e^{3} - \frac{88}{19}e$ |
| 59 | $[59, 59, w + 16]$ | $-\frac{2}{95}e^{7} + \frac{853}{95}e$ |
| 59 | $[59, 59, w + 43]$ | $\phantom{-}\frac{113}{2470}e^{7} + \frac{15}{26}e^{5} + \frac{113}{26}e^{3} + \frac{1243}{95}e$ |
| 71 | $[71, 71, w + 24]$ | $-\frac{4}{247}e^{7} - \frac{3}{13}e^{5} - \frac{20}{13}e^{3} - \frac{88}{19}e$ |
| 71 | $[71, 71, w + 47]$ | $\phantom{-}\frac{1}{95}e^{7} - \frac{284}{95}e$ |
| 73 | $[73, 73, 3w - 28]$ | $-\frac{2}{95}e^{6} + \frac{948}{95}$ |
| 73 | $[73, 73, 12w - 107]$ | $-\frac{2}{95}e^{6} + \frac{948}{95}$ |
| 79 | $[79, 79, -w]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 9]$ | $1$ |