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: | $[17,17,-w + 2]$ |
| 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:
| \(x^6 + 5 x^5 + 2 x^4 - 13 x^3 - 3 x^2 + 5 x + 1\) |
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 | $[9, 3, -\frac{2}{5} w^3 + \frac{3}{5} w^2 + \frac{22}{5} w - \frac{9}{5}]$ | $\phantom{-}e^5 + 5 e^4 + 2 e^3 - 13 e^2 - 2 e + 4$ |
| 9 | $[9, 3, \frac{2}{5} w^3 - \frac{3}{5} w^2 - \frac{22}{5} w + \frac{14}{5}]$ | $\phantom{-}e^3 + 4 e^2 + e - 5$ |
| 17 | $[17, 17, w + 1]$ | $-e^3 - 4 e^2 - e + 3$ |
| 17 | $[17, 17, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{13}{5}]$ | $-e^4 - 4 e^3 + 7 e - 2$ |
| 17 | $[17, 17, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{28}{5}]$ | $-e^4 - 6 e^3 - 5 e^2 + 11 e + 1$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{6}{5} w - \frac{22}{5}]$ | $\phantom{-}e^5 + 3 e^4 - 7 e^3 - 16 e^2 + 14 e + 5$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{3}{5}]$ | $\phantom{-}2 e^4 + 9 e^3 + 4 e^2 - 14 e - 3$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{6}{5} w - \frac{12}{5}]$ | $-2 e^5 - 9 e^4 + e^3 + 28 e^2 - 5 e - 10$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{13}{5}]$ | $-2 e^5 - 9 e^4 - e^3 + 23 e^2 - e - 7$ |
| 25 | $[25, 5, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{33}{5}]$ | $-e^5 - 5 e^4 - 2 e^3 + 10 e^2 - 6 e$ |
| 25 | $[25, 5, -w^3 + w^2 + 10 w - 2]$ | $\phantom{-}2 e^5 + 10 e^4 + 5 e^3 - 23 e^2 - 6 e + 7$ |
| 49 | $[49, 7, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{34}{5} w - \frac{23}{5}]$ | $\phantom{-}e^5 + 6 e^4 + 6 e^3 - 14 e^2 - 12 e + 1$ |
| 49 | $[49, 7, \frac{4}{5} w^3 - \frac{6}{5} w^2 - \frac{34}{5} w + \frac{13}{5}]$ | $-4 e^5 - 18 e^4 + 51 e^2 - 7 e - 16$ |
| 79 | $[79, 79, \frac{3}{5} w^3 - \frac{7}{5} w^2 - \frac{28}{5} w + \frac{21}{5}]$ | $-2 e^5 - 10 e^4 - 3 e^3 + 28 e^2 - 3 e - 14$ |
| 79 | $[79, 79, \frac{1}{5} w^3 + \frac{1}{5} w^2 - \frac{16}{5} w - \frac{13}{5}]$ | $\phantom{-}6 e^5 + 29 e^4 + 7 e^3 - 77 e^2 - e + 20$ |
| 79 | $[79, 79, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{11}{5} w - \frac{27}{5}]$ | $-e^3 - e^2 + 10 e + 2$ |
| 79 | $[79, 79, \frac{3}{5} w^3 - \frac{2}{5} w^2 - \frac{33}{5} w + \frac{11}{5}]$ | $-e^5 - 4 e^4 + 5 e^3 + 17 e^2 - 22 e - 6$ |
| 103 | $[103, 103, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{1}{5} w - \frac{17}{5}]$ | $\phantom{-}5 e^5 + 21 e^4 - 9 e^3 - 71 e^2 + 27 e + 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,-w + 2]$ | $-1$ |