Base field 4.4.13068.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 6x^{8} + 5x^{7} - 31x^{6} - 61x^{5} + 9x^{4} + 79x^{3} + 26x^{2} - 21x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - w^{2} - 6w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ | $-\frac{1}{3}e^{8} - e^{7} + \frac{7}{3}e^{6} + \frac{22}{3}e^{5} - \frac{14}{3}e^{4} - 14e^{3} + \frac{14}{3}e^{2} + \frac{22}{3}e - 1$ |
| 4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}\frac{5}{3}e^{8} + 7e^{7} - \frac{11}{3}e^{6} - \frac{131}{3}e^{5} - \frac{83}{3}e^{4} + 55e^{3} + \frac{128}{3}e^{2} - \frac{50}{3}e - 11$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w + 2]$ | $-2e^{8} - 10e^{7} - 2e^{6} + 57e^{5} + 72e^{4} - 50e^{3} - 95e^{2} + 7e + 21$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ | $-e^{8} - 5e^{7} + 33e^{5} + 34e^{4} - 50e^{3} - 60e^{2} + 23e + 18$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $-2e^{7} - 5e^{6} + 12e^{5} + 29e^{4} - 14e^{3} - 27e^{2} + 7e$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $\phantom{-}\frac{8}{3}e^{8} + 13e^{7} + \frac{1}{3}e^{6} - \frac{233}{3}e^{5} - \frac{248}{3}e^{4} + 84e^{3} + \frac{341}{3}e^{2} - \frac{71}{3}e - 29$ |
| 31 | $[31, 31, -w^{3} + 7w + 5]$ | $\phantom{-}\frac{8}{3}e^{8} + 15e^{7} + \frac{19}{3}e^{6} - \frac{263}{3}e^{5} - \frac{356}{3}e^{4} + 86e^{3} + \frac{458}{3}e^{2} - \frac{44}{3}e - 35$ |
| 41 | $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ | $-5e^{8} - 24e^{7} + e^{6} + 146e^{5} + 147e^{4} - 170e^{3} - 214e^{2} + 48e + 57$ |
| 41 | $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ | $-e^{8} - 3e^{7} + 5e^{6} + 17e^{5} - 2e^{4} - 13e^{3} + 2e^{2} - e$ |
| 67 | $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ | $-\frac{7}{3}e^{8} - 7e^{7} + \frac{37}{3}e^{6} + \frac{124}{3}e^{5} - \frac{35}{3}e^{4} - 41e^{3} + \frac{74}{3}e^{2} + \frac{1}{3}e - 14$ |
| 67 | $[67, 67, -w^{2} + 4w + 2]$ | $-\frac{10}{3}e^{8} - 13e^{7} + \frac{37}{3}e^{6} + \frac{259}{3}e^{5} + \frac{76}{3}e^{4} - 130e^{3} - \frac{157}{3}e^{2} + \frac{148}{3}e + 16$ |
| 83 | $[83, 83, 2w^{2} - 5w - 2]$ | $-7e^{7} - 23e^{6} + 34e^{5} + 146e^{4} - 3e^{3} - 187e^{2} - 13e + 39$ |
| 83 | $[83, 83, -w^{3} + 8w + 6]$ | $\phantom{-}e^{8} + 6e^{7} + 3e^{6} - 37e^{5} - 49e^{4} + 46e^{3} + 62e^{2} - 18e - 12$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ | $\phantom{-}2e^{6} + 3e^{5} - 13e^{4} - 15e^{3} + 14e^{2} + 4e + 3$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}2e^{8} + 13e^{7} + 10e^{6} - 78e^{5} - 129e^{4} + 87e^{3} + 193e^{2} - 29e - 57$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ | $\phantom{-}\frac{2}{3}e^{8} - 3e^{7} - \frac{53}{3}e^{6} + \frac{52}{3}e^{5} + \frac{271}{3}e^{4} - 19e^{3} - \frac{322}{3}e^{2} + \frac{46}{3}e + 22$ |
| 97 | $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}\frac{14}{3}e^{8} + 22e^{7} - \frac{14}{3}e^{6} - \frac{419}{3}e^{5} - \frac{347}{3}e^{4} + 186e^{3} + \frac{539}{3}e^{2} - \frac{197}{3}e - 56$ |
| 97 | $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ | $-\frac{1}{3}e^{8} - e^{7} + \frac{4}{3}e^{6} + \frac{16}{3}e^{5} + \frac{7}{3}e^{4} - 3e^{3} - \frac{16}{3}e^{2} - \frac{5}{3}e - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-1$ |