Base field \(\Q(\sqrt{7}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[29, 29, -w - 6]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 22x^{6} + 162x^{4} - 464x^{2} + 448\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 3]$ | $-\frac{1}{8}e^{6} + \frac{9}{4}e^{4} - \frac{49}{4}e^{2} + 20$ |
3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $-\frac{1}{16}e^{7} + \frac{9}{8}e^{5} - \frac{45}{8}e^{3} + \frac{13}{2}e$ |
7 | $[7, 7, w]$ | $-\frac{1}{8}e^{7} + \frac{5}{2}e^{5} - \frac{59}{4}e^{3} + \frac{45}{2}e$ |
19 | $[19, 19, 2w - 3]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{31}{8}e^{5} + \frac{191}{8}e^{3} - \frac{81}{2}e$ |
19 | $[19, 19, 2w + 3]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{9}{2}e^{5} + \frac{47}{2}e^{3} - 33e$ |
25 | $[25, 5, 5]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{9}{2}e^{4} + \frac{47}{2}e^{2} - 32$ |
29 | $[29, 29, -w - 6]$ | $-1$ |
29 | $[29, 29, w - 6]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{11}{4}e^{4} + \frac{73}{4}e^{2} - 30$ |
31 | $[31, 31, 4w + 9]$ | $-\frac{1}{4}e^{7} + \frac{19}{4}e^{5} - 27e^{3} + \frac{91}{2}e$ |
31 | $[31, 31, -4w + 9]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{9}{4}e^{5} + \frac{45}{4}e^{3} - 13e$ |
37 | $[37, 37, -3w + 10]$ | $-e^{4} + 11e^{2} - 22$ |
37 | $[37, 37, -6w + 17]$ | $-\frac{3}{8}e^{6} + \frac{25}{4}e^{4} - \frac{115}{4}e^{2} + 34$ |
47 | $[47, 47, -3w - 4]$ | $\phantom{-}\frac{3}{8}e^{7} - \frac{27}{4}e^{5} + \frac{143}{4}e^{3} - 53e$ |
47 | $[47, 47, 3w - 4]$ | $-\frac{1}{16}e^{7} + \frac{9}{8}e^{5} - \frac{45}{8}e^{3} + \frac{15}{2}e$ |
53 | $[53, 53, 2w - 9]$ | $\phantom{-}\frac{1}{2}e^{6} - 10e^{4} + 60e^{2} - 94$ |
53 | $[53, 53, 2w + 9]$ | $-\frac{1}{2}e^{6} + 10e^{4} - 60e^{2} + 102$ |
59 | $[59, 59, 3w - 2]$ | $\phantom{-}\frac{5}{8}e^{7} - 12e^{5} + \frac{271}{4}e^{3} - \frac{209}{2}e$ |
59 | $[59, 59, -3w - 2]$ | $-\frac{1}{4}e^{7} + \frac{19}{4}e^{5} - 27e^{3} + \frac{85}{2}e$ |
83 | $[83, 83, -6w - 13]$ | $-\frac{3}{8}e^{7} + \frac{29}{4}e^{5} - \frac{171}{4}e^{3} + 75e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29, 29, -w - 6]$ | $1$ |