Base field \(\Q(\sqrt{2}, \sqrt{13})\)
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 9x^{2} + 10x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17,17,-\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{13}{5}]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 5x^{5} + 2x^{4} - 13x^{3} - 3x^{2} + 5x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{2}{5}w^{3} + \frac{3}{5}w^{2} + \frac{17}{5}w - \frac{9}{5}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{2}{5}w^{3} + \frac{3}{5}w^{2} + \frac{22}{5}w - \frac{9}{5}]$ | $\phantom{-}e^{3} + 4e^{2} + e - 5$ |
| 9 | $[9, 3, \frac{2}{5}w^{3} - \frac{3}{5}w^{2} - \frac{22}{5}w + \frac{14}{5}]$ | $\phantom{-}e^{5} + 5e^{4} + 2e^{3} - 13e^{2} - 2e + 4$ |
| 17 | $[17, 17, w + 1]$ | $-e^{4} - 6e^{3} - 5e^{2} + 11e + 1$ |
| 17 | $[17, 17, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{13}{5}]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{28}{5}]$ | $-e^{3} - 4e^{2} - e + 3$ |
| 17 | $[17, 17, -w + 2]$ | $-e^{4} - 4e^{3} + 7e - 2$ |
| 23 | $[23, 23, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{6}{5}w - \frac{22}{5}]$ | $\phantom{-}2e^{4} + 9e^{3} + 4e^{2} - 14e - 3$ |
| 23 | $[23, 23, -\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{3}{5}]$ | $\phantom{-}e^{5} + 3e^{4} - 7e^{3} - 16e^{2} + 14e + 5$ |
| 23 | $[23, 23, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{6}{5}w - \frac{12}{5}]$ | $-2e^{5} - 9e^{4} - e^{3} + 23e^{2} - e - 7$ |
| 23 | $[23, 23, -\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{13}{5}]$ | $-2e^{5} - 9e^{4} + e^{3} + 28e^{2} - 5e - 10$ |
| 25 | $[25, 5, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{33}{5}]$ | $\phantom{-}2e^{5} + 10e^{4} + 5e^{3} - 23e^{2} - 6e + 7$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 10w - 2]$ | $-e^{5} - 5e^{4} - 2e^{3} + 10e^{2} - 6e$ |
| 49 | $[49, 7, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{34}{5}w - \frac{23}{5}]$ | $\phantom{-}e^{5} + 6e^{4} + 6e^{3} - 14e^{2} - 12e + 1$ |
| 49 | $[49, 7, \frac{4}{5}w^{3} - \frac{6}{5}w^{2} - \frac{34}{5}w + \frac{13}{5}]$ | $-4e^{5} - 18e^{4} + 51e^{2} - 7e - 16$ |
| 79 | $[79, 79, \frac{3}{5}w^{3} - \frac{7}{5}w^{2} - \frac{28}{5}w + \frac{21}{5}]$ | $-e^{3} - e^{2} + 10e + 2$ |
| 79 | $[79, 79, \frac{1}{5}w^{3} + \frac{1}{5}w^{2} - \frac{16}{5}w - \frac{13}{5}]$ | $-e^{5} - 4e^{4} + 5e^{3} + 17e^{2} - 22e - 6$ |
| 79 | $[79, 79, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{11}{5}w - \frac{27}{5}]$ | $-2e^{5} - 10e^{4} - 3e^{3} + 28e^{2} - 3e - 14$ |
| 79 | $[79, 79, \frac{3}{5}w^{3} - \frac{2}{5}w^{2} - \frac{33}{5}w + \frac{11}{5}]$ | $\phantom{-}6e^{5} + 29e^{4} + 7e^{3} - 77e^{2} - e + 20$ |
| 103 | $[103, 103, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{1}{5}w - \frac{17}{5}]$ | $-3e^{5} - 14e^{4} - 6e^{3} + 22e^{2} - 3e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,-\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{13}{5}]$ | $-1$ |