Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 96x^{6} + 2048x^{4} + 12288x^{2} + 16384\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{512}e^{5} + \frac{5}{32}e^{3} + \frac{7}{4}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{1}{256}e^{5} + \frac{5}{16}e^{3} + \frac{7}{2}e$ |
| 11 | $[11, 11, w + 3]$ | $-\frac{1}{512}e^{5} - \frac{5}{32}e^{3} - \frac{3}{4}e$ |
| 11 | $[11, 11, w + 7]$ | $-\frac{3}{2048}e^{7} - \frac{69}{512}e^{5} - \frac{79}{32}e^{3} - \frac{35}{4}e$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{1}{512}e^{6} - \frac{11}{64}e^{4} - \frac{11}{4}e^{2} - 8$ |
| 23 | $[23, 23, w + 4]$ | $\phantom{-}\frac{3}{4096}e^{7} + \frac{17}{256}e^{5} + \frac{37}{32}e^{3} + 4e$ |
| 23 | $[23, 23, w + 18]$ | $-\frac{3}{4096}e^{7} - \frac{17}{256}e^{5} - \frac{37}{32}e^{3} - 4e$ |
| 25 | $[25, 5, 5]$ | $-2$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{1}{512}e^{5} + \frac{5}{32}e^{3} + \frac{3}{4}e$ |
| 29 | $[29, 29, w + 27]$ | $\phantom{-}\frac{3}{2048}e^{7} + \frac{69}{512}e^{5} + \frac{79}{32}e^{3} + \frac{35}{4}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{1}{256}e^{5} + \frac{5}{16}e^{3} + \frac{7}{2}e$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{1}{256}e^{5} + \frac{5}{16}e^{3} + \frac{7}{2}e$ |
| 43 | $[43, 43, -w - 11]$ | $\phantom{-}4$ |
| 43 | $[43, 43, w - 12]$ | $\phantom{-}4$ |
| 47 | $[47, 47, -w - 6]$ | $-\frac{1}{512}e^{6} - \frac{5}{32}e^{4} - \frac{7}{4}e^{2} - 4$ |
| 47 | $[47, 47, w - 7]$ | $-\frac{3}{512}e^{6} - \frac{17}{32}e^{4} - \frac{37}{4}e^{2} - 28$ |
| 59 | $[59, 59, -w - 5]$ | $-\frac{1}{1024}e^{6} - \frac{3}{32}e^{4} - \frac{15}{8}e^{2} - 6$ |
| 59 | $[59, 59, w - 6]$ | $\phantom{-}\frac{1}{1024}e^{6} + \frac{3}{32}e^{4} + \frac{15}{8}e^{2} + 6$ |
| 61 | $[61, 61, w + 16]$ | $-\frac{1}{4096}e^{7} - \frac{11}{512}e^{5} - \frac{3}{8}e^{3} - \frac{11}{4}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |