Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 17x^{8} + 102x^{6} - 254x^{4} + 232x^{2} - 56\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{8}e^{8} - \frac{15}{8}e^{6} + 9e^{4} - \frac{59}{4}e^{2} + \frac{11}{2}$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}e^{2} - 3$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $-\frac{1}{4}e^{9} + \frac{15}{4}e^{7} - 19e^{5} + \frac{73}{2}e^{3} - 19e$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{8} + \frac{13}{2}e^{6} - 27e^{4} + 40e^{2} - 17$ |
| 29 | $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ | $\phantom{-}e^{4} - 6e^{2} + 3$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $-\frac{1}{4}e^{9} + \frac{15}{4}e^{7} - 19e^{5} + \frac{77}{2}e^{3} - 29e$ |
| 41 | $[41, 41, -w^{3} + 4w^{2} - w - 3]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{15}{2}e^{6} + 37e^{4} - 65e^{2} + 25$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}e^{7} - 12e^{5} + 39e^{3} - 24e$ |
| 47 | $[47, 47, w^{2} - 3w - 3]$ | $\phantom{-}e^{5} - 9e^{3} + 16e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{11}{2}e^{6} + 15e^{4} - e^{2} - 7$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{11}{4}e^{7} + 7e^{5} + \frac{9}{2}e^{3} - 15e$ |
| 61 | $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ | $-\frac{1}{2}e^{8} + \frac{13}{2}e^{6} - 26e^{4} + 33e^{2} - 3$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ | $\phantom{-}e^{7} - 12e^{5} + 41e^{3} - 34e$ |
| 67 | $[67, 67, w^{3} - 4w^{2} + w + 5]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{15}{4}e^{7} + 17e^{5} - \frac{41}{2}e^{3} - 7e$ |
| 67 | $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ | $-\frac{1}{4}e^{9} + \frac{15}{4}e^{7} - 18e^{5} + \frac{55}{2}e^{3} + e$ |
| 67 | $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ | $-\frac{1}{4}e^{9} + \frac{15}{4}e^{7} - 18e^{5} + \frac{55}{2}e^{3} + e$ |
| 71 | $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ | $\phantom{-}e^{5} - 7e^{3} + 6e$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}e^{5} - 7e^{3} + 6e$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ | $-e^{7} + 11e^{5} - 32e^{3} + 14e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).