Base field 4.4.10273.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 14x^{4} + 22x^{3} + 49x^{2} - 39x - 52\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{3} - 2w^{2} - 5w + 1]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - \frac{11}{5}e^{3} + \frac{39}{5}e^{2} + \frac{21}{5}e - \frac{46}{5}$ |
| 17 | $[17, 17, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{2}{5}e^{5} - \frac{3}{5}e^{4} - \frac{22}{5}e^{3} + \frac{28}{5}e^{2} + \frac{32}{5}e - \frac{22}{5}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - \frac{11}{5}e^{3} + \frac{44}{5}e^{2} + \frac{11}{5}e - \frac{66}{5}$ |
| 27 | $[27, 3, w^{3} - w^{2} - 6w - 5]$ | $-\frac{1}{5}e^{5} - \frac{1}{5}e^{4} + \frac{16}{5}e^{3} + \frac{11}{5}e^{2} - \frac{51}{5}e - \frac{24}{5}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 2w + 1]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - \frac{11}{5}e^{3} + \frac{49}{5}e^{2} + \frac{11}{5}e - \frac{86}{5}$ |
| 47 | $[47, 47, w^{3} - 2w^{2} - 4w - 3]$ | $-\frac{1}{5}e^{5} - \frac{1}{5}e^{4} + \frac{16}{5}e^{3} + \frac{21}{5}e^{2} - \frac{56}{5}e - \frac{64}{5}$ |
| 49 | $[49, 7, w^{3} - 3w^{2} - 3w + 1]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - \frac{6}{5}e^{3} + \frac{39}{5}e^{2} - \frac{14}{5}e - \frac{46}{5}$ |
| 49 | $[49, 7, -2w^{3} + 5w^{2} + 7w - 3]$ | $-\frac{1}{5}e^{5} + \frac{4}{5}e^{4} + \frac{6}{5}e^{3} - \frac{49}{5}e^{2} + \frac{24}{5}e + \frac{106}{5}$ |
| 59 | $[59, 59, -2w^{3} + 6w^{2} + 5w - 7]$ | $\phantom{-}e^{4} - e^{3} - 11e^{2} + 7e + 16$ |
| 61 | $[61, 61, 2w^{3} - 4w^{2} - 9w - 3]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{1}{5}e^{4} - \frac{16}{5}e^{3} - \frac{21}{5}e^{2} + \frac{46}{5}e + \frac{94}{5}$ |
| 71 | $[71, 71, w^{3} - 3w^{2} - 3w + 7]$ | $-\frac{1}{5}e^{5} + \frac{4}{5}e^{4} + \frac{11}{5}e^{3} - \frac{49}{5}e^{2} - \frac{21}{5}e + \frac{76}{5}$ |
| 73 | $[73, 73, 2w^{3} - 6w^{2} - 3w + 5]$ | $-\frac{1}{5}e^{5} + \frac{4}{5}e^{4} + \frac{6}{5}e^{3} - \frac{39}{5}e^{2} + \frac{24}{5}e + \frac{66}{5}$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}\frac{1}{5}e^{5} + \frac{1}{5}e^{4} - \frac{16}{5}e^{3} - \frac{21}{5}e^{2} + \frac{71}{5}e + \frac{54}{5}$ |
| 83 | $[83, 83, -2w^{3} + 5w^{2} + 8w - 3]$ | $-\frac{1}{5}e^{5} + \frac{4}{5}e^{4} + \frac{11}{5}e^{3} - \frac{44}{5}e^{2} - \frac{21}{5}e + \frac{56}{5}$ |
| 89 | $[89, 89, -2w^{3} + 6w^{2} + 4w - 7]$ | $-\frac{1}{5}e^{5} + \frac{4}{5}e^{4} + \frac{11}{5}e^{3} - \frac{44}{5}e^{2} - \frac{21}{5}e + \frac{86}{5}$ |
| 89 | $[89, 89, w^{3} - 2w^{2} - 6w + 3]$ | $-\frac{2}{5}e^{5} + \frac{3}{5}e^{4} + \frac{22}{5}e^{3} - \frac{28}{5}e^{2} - \frac{42}{5}e + \frac{42}{5}$ |
| 97 | $[97, 97, -3w - 1]$ | $-e^{2} - 2e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w]$ | $-1$ |
| $8$ | $[8, 2, w^{3} - 2w^{2} - 5w + 1]$ | $-1$ |