Base field 3.3.1556.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 26x^{8} + 226x^{6} - 736x^{4} + 784x^{2} - 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{2} + w - 7]$ | $\phantom{-}\frac{1}{32}e^{9} - \frac{13}{16}e^{7} + \frac{105}{16}e^{5} - 16e^{3} + \frac{9}{2}e$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{1}{8}e^{8} - \frac{13}{4}e^{6} + \frac{109}{4}e^{4} - 77e^{2} + 44$ |
| 11 | $[11, 11, -2w + 3]$ | $\phantom{-}\frac{1}{16}e^{9} - \frac{13}{8}e^{7} + \frac{109}{8}e^{5} - 38e^{3} + 19e$ |
| 11 | $[11, 11, -w^{2} + 3w - 1]$ | $-\frac{1}{8}e^{9} + \frac{13}{4}e^{7} - \frac{109}{4}e^{5} + 77e^{3} - 45e$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{1}{8}e^{8} + \frac{11}{4}e^{6} - \frac{77}{4}e^{4} + 45e^{2} - 22$ |
| 17 | $[17, 17, -2w + 5]$ | $\phantom{-}\frac{3}{32}e^{9} - \frac{35}{16}e^{7} + \frac{267}{16}e^{5} - \frac{89}{2}e^{3} + \frac{49}{2}e$ |
| 17 | $[17, 17, -w^{2} - w + 5]$ | $-\frac{3}{32}e^{9} + \frac{39}{16}e^{7} - \frac{331}{16}e^{5} + 61e^{3} - \frac{83}{2}e$ |
| 23 | $[23, 23, w - 4]$ | $-\frac{1}{8}e^{8} + \frac{13}{4}e^{6} - \frac{109}{4}e^{4} + 76e^{2} - 40$ |
| 29 | $[29, 29, w^{2} - 6]$ | $\phantom{-}\frac{5}{32}e^{9} - \frac{61}{16}e^{7} + \frac{485}{16}e^{5} - \frac{167}{2}e^{3} + \frac{103}{2}e$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{16}e^{9} - \frac{13}{8}e^{7} + \frac{109}{8}e^{5} - 39e^{3} + 28e$ |
| 37 | $[37, 37, -w^{2} - 2w + 6]$ | $\phantom{-}\frac{5}{32}e^{9} - \frac{61}{16}e^{7} + \frac{485}{16}e^{5} - \frac{167}{2}e^{3} + \frac{107}{2}e$ |
| 43 | $[43, 43, w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{8}e^{8} - \frac{15}{4}e^{6} + \frac{137}{4}e^{4} - 98e^{2} + 60$ |
| 47 | $[47, 47, 3w^{2} - 28]$ | $-e^{6} + 16e^{4} - 64e^{2} + 48$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $-\frac{5}{32}e^{9} + \frac{65}{16}e^{7} - \frac{549}{16}e^{5} + 99e^{3} - \frac{121}{2}e$ |
| 61 | $[61, 61, -5w + 6]$ | $-\frac{1}{8}e^{8} + \frac{11}{4}e^{6} - \frac{81}{4}e^{4} + 55e^{2} - 26$ |
| 71 | $[71, 71, w^{2} - w - 7]$ | $-\frac{1}{8}e^{8} + \frac{11}{4}e^{6} - \frac{81}{4}e^{4} + 57e^{2} - 40$ |
| 83 | $[83, 83, -2w^{2} - w + 14]$ | $\phantom{-}\frac{1}{8}e^{9} - \frac{13}{4}e^{7} + \frac{109}{4}e^{5} - 77e^{3} + 45e$ |
| 89 | $[89, 89, w^{2} + 3w - 3]$ | $-\frac{1}{8}e^{8} + \frac{11}{4}e^{6} - \frac{81}{4}e^{4} + 57e^{2} - 46$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 1]$ | $-1$ |