Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23, 23, w^{2} - 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 5x^{9} - 19x^{8} - 114x^{7} + 99x^{6} + 898x^{5} + 41x^{4} - 2800x^{3} - 1327x^{2} + 2696x + 1753\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $...$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $...$ |
| 13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $...$ |
| 19 | $[19, 19, w^{3} - 5w]$ | $...$ |
| 19 | $[19, 19, -w + 3]$ | $-\frac{27463}{3452199}e^{9} - \frac{74004}{1150733}e^{8} - \frac{378353}{3452199}e^{7} + \frac{2545054}{3452199}e^{6} + \frac{12728620}{3452199}e^{5} + \frac{489528}{1150733}e^{4} - \frac{74992010}{3452199}e^{3} - \frac{62651389}{3452199}e^{2} + \frac{33020647}{1150733}e + \frac{82417435}{3452199}$ |
| 23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $...$ |
| 23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}1$ |
| 25 | $[25, 5, w^{2} - 3]$ | $-\frac{50053}{3452199}e^{9} - \frac{58030}{1150733}e^{8} + \frac{783298}{3452199}e^{7} + \frac{3058045}{3452199}e^{6} - \frac{1988171}{3452199}e^{5} - \frac{5250942}{1150733}e^{4} - \frac{12818093}{3452199}e^{3} + \frac{22348394}{3452199}e^{2} + \frac{11535431}{1150733}e + \frac{448642}{3452199}$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $...$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $...$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $...$ |
| 47 | $[47, 47, w^{3} - 6w + 1]$ | $...$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $...$ |
| 67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $...$ |
| 67 | $[67, 67, w^{3} - 7w + 3]$ | $...$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $-\frac{13239}{1150733}e^{9} + \frac{117943}{1150733}e^{8} + \frac{723429}{1150733}e^{7} - \frac{2059049}{1150733}e^{6} - \frac{9029680}{1150733}e^{5} + \frac{10464611}{1150733}e^{4} + \frac{35351293}{1150733}e^{3} - \frac{13618282}{1150733}e^{2} - \frac{30225613}{1150733}e + \frac{2016767}{1150733}$ |
| 81 | $[81, 3, -3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, w^{2} - 2]$ | $-1$ |