Base field 4.4.16448.2
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 14\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14,14,w^{3} - 2w^{2} - 4w + 7]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - x^{7} - 13x^{6} + 9x^{5} + 53x^{4} - 17x^{3} - 66x^{2} - 10x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w^{3} - 6w - 5]$ | $-1$ |
| 7 | $[7, 7, -w^{3} + 3w^{2} + 2w - 7]$ | $-1$ |
| 7 | $[7, 7, -w^{3} + 5w + 3]$ | $-\frac{1}{2}e^{7} + \frac{1}{2}e^{6} + \frac{11}{2}e^{5} - \frac{9}{2}e^{4} - \frac{35}{2}e^{3} + \frac{21}{2}e^{2} + 14e - 2$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ | $-e^{7} + e^{6} + 12e^{5} - 11e^{4} - 41e^{3} + 32e^{2} + 32e - 8$ |
| 31 | $[31, 31, -w^{2} - w + 1]$ | $-e^{7} + 2e^{6} + 11e^{5} - 19e^{4} - 36e^{3} + 47e^{2} + 32e - 12$ |
| 31 | $[31, 31, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - \frac{11}{2}e^{5} + \frac{11}{2}e^{4} + \frac{31}{2}e^{3} - \frac{37}{2}e^{2} - 3e + 12$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - \frac{13}{2}e^{5} + \frac{9}{2}e^{4} + \frac{51}{2}e^{3} - \frac{19}{2}e^{2} - 26e + 2$ |
| 41 | $[41, 41, -w^{3} + 3w^{2} + 2w - 9]$ | $-2e^{3} + 2e^{2} + 10e - 4$ |
| 41 | $[41, 41, w^{3} + w^{2} - 8w - 11]$ | $-e^{5} + 8e^{3} + e^{2} - 12e - 2$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - \frac{9}{2}e^{5} + \frac{11}{2}e^{4} + \frac{15}{2}e^{3} - \frac{35}{2}e^{2} + 7e + 12$ |
| 47 | $[47, 47, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}e^{6} - e^{5} - 8e^{4} + 7e^{3} + 13e^{2} - 12e$ |
| 49 | $[49, 7, 2w^{2} - 2w - 9]$ | $-\frac{1}{2}e^{7} + \frac{3}{2}e^{6} + \frac{11}{2}e^{5} - \frac{31}{2}e^{4} - \frac{37}{2}e^{3} + \frac{81}{2}e^{2} + 17e - 10$ |
| 71 | $[71, 71, 5w^{3} - 16w^{2} - 17w + 61]$ | $-e^{6} + 10e^{4} + e^{3} - 24e^{2} - 2e + 4$ |
| 71 | $[71, 71, -2w^{3} - 2w^{2} + 10w + 13]$ | $-\frac{1}{2}e^{7} + \frac{1}{2}e^{6} + \frac{11}{2}e^{5} - \frac{11}{2}e^{4} - \frac{35}{2}e^{3} + \frac{29}{2}e^{2} + 17e + 4$ |
| 73 | $[73, 73, 3w^{3} + w^{2} - 18w - 17]$ | $-\frac{1}{2}e^{7} + \frac{3}{2}e^{6} + \frac{13}{2}e^{5} - \frac{29}{2}e^{4} - \frac{57}{2}e^{3} + \frac{71}{2}e^{2} + 40e - 8$ |
| 73 | $[73, 73, w^{3} - 5w - 1]$ | $-e^{7} + e^{6} + 12e^{5} - 11e^{4} - 39e^{3} + 32e^{2} + 22e - 10$ |
| 73 | $[73, 73, w^{3} - 7w - 3]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{3}{2}e^{6} - \frac{15}{2}e^{5} + \frac{35}{2}e^{4} + \frac{65}{2}e^{3} - \frac{101}{2}e^{2} - 33e + 10$ |
| 73 | $[73, 73, -3w^{3} + 10w^{2} + 7w - 31]$ | $\phantom{-}2e^{4} - 14e^{2} + 2e + 12$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{5} - 6e^{3} - e^{2} + 2e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w^{3} + 6w + 5]$ | $1$ |
| $7$ | $[7,7,w^{3} - 3w^{2} - 2w + 7]$ | $1$ |