Base field \(\Q(\sqrt{2}, \sqrt{13})\)
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 9 x^2 + 10 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23,23,-\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{3}{5}]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 2 x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{2}{5} w^3 + \frac{3}{5} w^2 + \frac{17}{5} w - \frac{9}{5}]$ | $-1$ |
| 9 | $[9, 3, -\frac{2}{5} w^3 + \frac{3}{5} w^2 + \frac{22}{5} w - \frac{9}{5}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, \frac{2}{5} w^3 - \frac{3}{5} w^2 - \frac{22}{5} w + \frac{14}{5}]$ | $\phantom{-}\frac{1}{2} e - 2$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}e - 4$ |
| 17 | $[17, 17, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{13}{5}]$ | $-e - 2$ |
| 17 | $[17, 17, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{28}{5}]$ | $-\frac{1}{2} e + 5$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}2$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{6}{5} w - \frac{22}{5}]$ | $-\frac{7}{2} e + 5$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{3}{5}]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{6}{5} w - \frac{12}{5}]$ | $-\frac{3}{2} e - 2$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{13}{5}]$ | $\phantom{-}3 e - 4$ |
| 25 | $[25, 5, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{33}{5}]$ | $-\frac{1}{2} e$ |
| 25 | $[25, 5, -w^3 + w^2 + 10 w - 2]$ | $\phantom{-}e - 4$ |
| 49 | $[49, 7, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{34}{5} w - \frac{23}{5}]$ | $\phantom{-}\frac{1}{2} e + 6$ |
| 49 | $[49, 7, \frac{4}{5} w^3 - \frac{6}{5} w^2 - \frac{34}{5} w + \frac{13}{5}]$ | $-\frac{3}{2} e - 2$ |
| 79 | $[79, 79, \frac{3}{5} w^3 - \frac{7}{5} w^2 - \frac{28}{5} w + \frac{21}{5}]$ | $-\frac{9}{2} e + 11$ |
| 79 | $[79, 79, \frac{1}{5} w^3 + \frac{1}{5} w^2 - \frac{16}{5} w - \frac{13}{5}]$ | $\phantom{-}4$ |
| 79 | $[79, 79, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{11}{5} w - \frac{27}{5}]$ | $-5 e + 4$ |
| 79 | $[79, 79, \frac{3}{5} w^3 - \frac{2}{5} w^2 - \frac{33}{5} w + \frac{11}{5}]$ | $\phantom{-}\frac{3}{2} e - 5$ |
| 103 | $[103, 103, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{1}{5} w - \frac{17}{5}]$ | $-4 e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,-\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{3}{5}]$ | $-1$ |