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