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: | $[17,17,-\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{13}{5}]$ |
| 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:
| \(x^6 - 7 x^5 + 10 x^4 + 27 x^3 - 83 x^2 + 61 x - 7\) |
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 | $[9, 3, -\frac{2}{5} w^3 + \frac{3}{5} w^2 + \frac{22}{5} w - \frac{9}{5}]$ | $-e^5 + 4 e^4 + 3 e^3 - 21 e^2 + 13 e - 2$ |
| 9 | $[9, 3, \frac{2}{5} w^3 - \frac{3}{5} w^2 - \frac{22}{5} w + \frac{14}{5}]$ | $\phantom{-}4 e^5 - 19 e^4 - 2 e^3 + 100 e^2 - 108 e + 19$ |
| 17 | $[17, 17, w + 1]$ | $-4 e^5 + 19 e^4 + 2 e^3 - 101 e^2 + 107 e - 11$ |
| 17 | $[17, 17, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{13}{5}]$ | $-1$ |
| 17 | $[17, 17, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{28}{5}]$ | $-e^5 + 4 e^4 + 3 e^3 - 21 e^2 + 15 e - 4$ |
| 17 | $[17, 17, -w + 2]$ | $-e^4 + 4 e^3 + 4 e^2 - 23 e + 10$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{6}{5} w - \frac{22}{5}]$ | $-4 e^5 + 18 e^4 + 5 e^3 - 96 e^2 + 94 e - 13$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{3}{5}]$ | $\phantom{-}5 e^5 - 23 e^4 - 5 e^3 + 122 e^2 - 120 e + 15$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{6}{5} w - \frac{12}{5}]$ | $\phantom{-}e^5 - 5 e^4 + e^3 + 26 e^2 - 37 e + 8$ |
| 23 | $[23, 23, -\frac{1}{5} w^3 - \frac{1}{5} w^2 + \frac{11}{5} w + \frac{13}{5}]$ | $-3 e^5 + 15 e^4 - e^3 - 79 e^2 + 93 e - 13$ |
| 25 | $[25, 5, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{33}{5}]$ | $-3 e^5 + 14 e^4 + 3 e^3 - 76 e^2 + 74 e - 2$ |
| 25 | $[25, 5, -w^3 + w^2 + 10 w - 2]$ | $\phantom{-}3 e^5 - 15 e^4 + 80 e^2 - 88 e + 12$ |
| 49 | $[49, 7, -\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{34}{5} w - \frac{23}{5}]$ | $-e^5 + 4 e^4 + 2 e^3 - 20 e^2 + 20 e - 9$ |
| 49 | $[49, 7, \frac{4}{5} w^3 - \frac{6}{5} w^2 - \frac{34}{5} w + \frac{13}{5}]$ | $-2 e^5 + 10 e^4 - 55 e^2 + 61 e - 2$ |
| 79 | $[79, 79, \frac{3}{5} w^3 - \frac{7}{5} w^2 - \frac{28}{5} w + \frac{21}{5}]$ | $-4 e^5 + 20 e^4 - e^3 - 105 e^2 + 122 e - 14$ |
| 79 | $[79, 79, \frac{1}{5} w^3 + \frac{1}{5} w^2 - \frac{16}{5} w - \frac{13}{5}]$ | $-8 e^5 + 36 e^4 + 11 e^3 - 194 e^2 + 178 e - 7$ |
| 79 | $[79, 79, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{11}{5} w - \frac{27}{5}]$ | $\phantom{-}4 e^5 - 18 e^4 - 5 e^3 + 96 e^2 - 91 e + 14$ |
| 79 | $[79, 79, \frac{3}{5} w^3 - \frac{2}{5} w^2 - \frac{33}{5} w + \frac{11}{5}]$ | $\phantom{-}2 e^5 - 9 e^4 - e^3 + 45 e^2 - 55 e + 14$ |
| 103 | $[103, 103, -\frac{1}{5} w^3 + \frac{4}{5} w^2 + \frac{1}{5} w - \frac{17}{5}]$ | $\phantom{-}15 e^5 - 68 e^4 - 20 e^3 + 366 e^2 - 339 e + 32$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,-\frac{4}{5} w^3 + \frac{6}{5} w^2 + \frac{39}{5} w - \frac{13}{5}]$ | $1$ |