Base field 3.3.316.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, 2w - 3]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - x^{8} - 16x^{7} + 16x^{6} + 82x^{5} - 76x^{4} - 148x^{3} + 108x^{2} + 80x - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 1]$ | $-\frac{1}{8}e^{8} - \frac{1}{8}e^{7} + \frac{7}{4}e^{6} + \frac{3}{2}e^{5} - \frac{31}{4}e^{4} - \frac{11}{2}e^{3} + \frac{23}{2}e^{2} + \frac{11}{2}e - 3$ |
| 11 | $[11, 11, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{4}e^{8} - \frac{13}{4}e^{6} + e^{5} + \frac{25}{2}e^{4} - \frac{15}{2}e^{3} - 14e^{2} + 10e + 4$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-\frac{1}{4}e^{8} + \frac{13}{4}e^{6} - e^{5} - \frac{25}{2}e^{4} + \frac{13}{2}e^{3} + 13e^{2} - 4e$ |
| 19 | $[19, 19, w^{2} - w + 1]$ | $-\frac{1}{2}e^{7} - \frac{1}{2}e^{6} + 6e^{5} + 4e^{4} - 20e^{3} - 6e^{2} + 16e$ |
| 23 | $[23, 23, 2w - 3]$ | $\phantom{-}1$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{2}e^{7} - \frac{11}{4}e^{6} - 5e^{5} + \frac{15}{2}e^{4} + \frac{27}{2}e^{3} - 12e - 4$ |
| 29 | $[29, 29, 2w + 1]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{4}e^{7} - \frac{7}{2}e^{6} - 3e^{5} + \frac{29}{2}e^{4} + 12e^{3} - 15e^{2} - 17e - 2$ |
| 31 | $[31, 31, 2w^{2} - 2w - 9]$ | $-\frac{1}{4}e^{8} - \frac{1}{4}e^{7} + \frac{7}{2}e^{6} + 2e^{5} - \frac{31}{2}e^{4} - 2e^{3} + 21e^{2} - 5e - 2$ |
| 37 | $[37, 37, 2w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{4}e^{7} - \frac{7}{2}e^{6} - 2e^{5} + \frac{33}{2}e^{4} + 3e^{3} - 29e^{2} - e + 10$ |
| 41 | $[41, 41, 2w^{2} - 9]$ | $-\frac{1}{2}e^{8} + \frac{15}{2}e^{6} - e^{5} - 35e^{4} + 7e^{3} + 52e^{2} - 6e - 14$ |
| 43 | $[43, 43, w^{2} + w - 5]$ | $-\frac{1}{4}e^{7} + \frac{1}{4}e^{6} + 4e^{5} - 3e^{4} - \frac{39}{2}e^{3} + 8e^{2} + 27e - 2$ |
| 43 | $[43, 43, -3w^{2} + w + 15]$ | $-\frac{3}{4}e^{7} - \frac{5}{4}e^{6} + 8e^{5} + 11e^{4} - \frac{45}{2}e^{3} - 22e^{2} + 13e + 10$ |
| 43 | $[43, 43, -2w^{2} + 2w + 11]$ | $\phantom{-}\frac{1}{2}e^{8} + \frac{1}{2}e^{7} - 7e^{6} - 5e^{5} + 31e^{4} + 13e^{3} - 44e^{2} - 8e + 8$ |
| 53 | $[53, 53, w^{2} - w - 7]$ | $\phantom{-}\frac{1}{4}e^{8} - \frac{17}{4}e^{6} - e^{5} + \frac{43}{2}e^{4} + \frac{19}{2}e^{3} - 31e^{2} - 20e + 8$ |
| 61 | $[61, 61, 4w^{2} - 2w - 15]$ | $\phantom{-}\frac{1}{2}e^{7} + \frac{1}{2}e^{6} - 6e^{5} - 3e^{4} + 21e^{3} - 2e^{2} - 18e + 8$ |
| 67 | $[67, 67, -5w^{2} + 3w + 23]$ | $-\frac{1}{2}e^{7} + \frac{1}{2}e^{6} + 7e^{5} - 6e^{4} - 28e^{3} + 18e^{2} + 26e - 12$ |
| 73 | $[73, 73, 2w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{4}e^{7} - \frac{9}{2}e^{6} - 4e^{5} + \frac{53}{2}e^{4} + 18e^{3} - 55e^{2} - 19e + 26$ |
| 73 | $[73, 73, -3w^{2} - w + 7]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{1}{2}e^{7} - \frac{11}{4}e^{6} - 5e^{5} + \frac{17}{2}e^{4} + \frac{25}{2}e^{3} - 10e^{2} - 4e + 10$ |
| 73 | $[73, 73, -6w^{2} + 4w + 25]$ | $\phantom{-}\frac{1}{4}e^{8} + \frac{3}{4}e^{7} - 2e^{6} - 8e^{5} + \frac{1}{2}e^{4} + 24e^{3} + 15e^{2} - 19e - 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, 2w - 3]$ | $-1$ |