Base field \(\Q(\sqrt{41}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 10\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[23, 23, 2w - 9]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 5x^{6} + 2x^{5} + 19x^{4} - 17x^{3} - 13x^{2} + 8x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 4]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w - 3]$ | $\phantom{-}\frac{1}{2}e^{6} - 2e^{5} + \frac{13}{2}e^{3} - 4e^{2} - \frac{5}{2}e + \frac{1}{2}$ |
| 5 | $[5, 5, -2w - 5]$ | $\phantom{-}\frac{1}{2}e^{6} - 3e^{5} + 2e^{4} + \frac{23}{2}e^{3} - 11e^{2} - \frac{15}{2}e + \frac{7}{2}$ |
| 5 | $[5, 5, -2w + 7]$ | $-e^{3} + 2e^{2} + 3e - 2$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{5} - 2e^{4} - 5e^{3} + 6e^{2} + 6e$ |
| 23 | $[23, 23, 2w - 9]$ | $-1$ |
| 23 | $[23, 23, -2w - 7]$ | $\phantom{-}e^{6} - 5e^{5} + 23e^{3} - 9e^{2} - 22e + 4$ |
| 31 | $[31, 31, -6w - 17]$ | $\phantom{-}e^{5} - 3e^{4} - 4e^{3} + 12e^{2} + e - 3$ |
| 31 | $[31, 31, 6w - 23]$ | $\phantom{-}\frac{1}{2}e^{6} - 3e^{5} + 3e^{4} + \frac{21}{2}e^{3} - 16e^{2} - \frac{13}{2}e + \frac{19}{2}$ |
| 37 | $[37, 37, 2w - 3]$ | $-e^{6} + 3e^{5} + 3e^{4} - 11e^{3} - e^{2} + 10e - 1$ |
| 37 | $[37, 37, -2w - 1]$ | $-\frac{1}{2}e^{6} + 3e^{5} - 2e^{4} - \frac{25}{2}e^{3} + 11e^{2} + \frac{29}{2}e - \frac{3}{2}$ |
| 41 | $[41, 41, 2w - 1]$ | $-\frac{1}{2}e^{6} + 7e^{4} - \frac{5}{2}e^{3} - 20e^{2} + \frac{9}{2}e + \frac{19}{2}$ |
| 43 | $[43, 43, -4w - 9]$ | $-e^{6} + 3e^{5} + 4e^{4} - 13e^{3} - 4e^{2} + 10e - 3$ |
| 43 | $[43, 43, 4w - 13]$ | $\phantom{-}2e^{6} - 10e^{5} + 5e^{4} + 34e^{3} - 35e^{2} - 12e + 12$ |
| 49 | $[49, 7, -7]$ | $-e^{5} + 4e^{4} + e^{3} - 14e^{2} + 2e + 6$ |
| 59 | $[59, 59, 2w - 11]$ | $\phantom{-}2e^{5} - 4e^{4} - 11e^{3} + 14e^{2} + 13e - 2$ |
| 59 | $[59, 59, -2w - 9]$ | $-\frac{5}{2}e^{6} + 11e^{5} - 3e^{4} - \frac{71}{2}e^{3} + 30e^{2} + \frac{25}{2}e - \frac{17}{2}$ |
| 61 | $[61, 61, -4w + 17]$ | $-e^{6} + 4e^{5} + e^{4} - 15e^{3} + 2e^{2} + 13e + 6$ |
| 61 | $[61, 61, 4w + 13]$ | $-\frac{3}{2}e^{6} + 3e^{5} + 10e^{4} - \frac{27}{2}e^{3} - 21e^{2} + \frac{21}{2}e + \frac{21}{2}$ |
| 73 | $[73, 73, 8w + 23]$ | $-e^{6} + 4e^{5} + 4e^{4} - 22e^{3} - 5e^{2} + 24e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, 2w - 9]$ | $1$ |