Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[16, 4, 4]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + x^{6} - 11x^{5} - 10x^{4} + 31x^{3} + 17x^{2} - 22x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, 4w + 25]$ | $-\frac{1}{2}e^{6} - \frac{1}{2}e^{5} + \frac{11}{2}e^{4} + 5e^{3} - \frac{29}{2}e^{2} - \frac{19}{2}e + 6$ |
| 5 | $[5, 5, -4w + 29]$ | $-\frac{1}{2}e^{6} - \frac{1}{2}e^{5} + \frac{11}{2}e^{4} + 5e^{3} - \frac{29}{2}e^{2} - \frac{19}{2}e + 6$ |
| 11 | $[11, 11, w - 8]$ | $-e^{6} - e^{5} + 10e^{4} + 11e^{3} - 23e^{2} - 22e + 10$ |
| 11 | $[11, 11, -w - 7]$ | $-e^{6} - e^{5} + 10e^{4} + 11e^{3} - 23e^{2} - 22e + 10$ |
| 13 | $[13, 13, 3w + 19]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - \frac{9}{2}e^{4} - 5e^{3} + \frac{15}{2}e^{2} + \frac{15}{2}e - 1$ |
| 13 | $[13, 13, 3w - 22]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{1}{2}e^{5} - \frac{9}{2}e^{4} - 5e^{3} + \frac{15}{2}e^{2} + \frac{15}{2}e - 1$ |
| 29 | $[29, 29, 6w + 37]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + \frac{9}{2}e^{4} - 3e^{3} - \frac{17}{2}e^{2} + \frac{7}{2}e - 1$ |
| 29 | $[29, 29, 6w - 43]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + \frac{9}{2}e^{4} - 3e^{3} - \frac{17}{2}e^{2} + \frac{7}{2}e - 1$ |
| 37 | $[37, 37, 2w - 13]$ | $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + \frac{11}{2}e^{4} + 15e^{3} - \frac{29}{2}e^{2} - \frac{59}{2}e + 10$ |
| 37 | $[37, 37, 2w + 11]$ | $-\frac{1}{2}e^{6} - \frac{3}{2}e^{5} + \frac{11}{2}e^{4} + 15e^{3} - \frac{29}{2}e^{2} - \frac{59}{2}e + 10$ |
| 43 | $[43, 43, -w - 1]$ | $-e^{6} + 9e^{4} + e^{3} - 17e^{2} + e + 4$ |
| 43 | $[43, 43, w - 2]$ | $-e^{6} + 9e^{4} + e^{3} - 17e^{2} + e + 4$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{2}e^{6} + \frac{5}{2}e^{5} - \frac{13}{2}e^{4} - 22e^{3} + \frac{37}{2}e^{2} + \frac{75}{2}e - 6$ |
| 59 | $[59, 59, 5w - 37]$ | $-e^{6} - 3e^{5} + 12e^{4} + 29e^{3} - 36e^{2} - 57e + 26$ |
| 59 | $[59, 59, 5w + 32]$ | $-e^{6} - 3e^{5} + 12e^{4} + 29e^{3} - 36e^{2} - 57e + 26$ |
| 67 | $[67, 67, 21w + 131]$ | $-2e^{6} - 3e^{5} + 21e^{4} + 28e^{3} - 52e^{2} - 45e + 28$ |
| 67 | $[67, 67, 21w - 152]$ | $-2e^{6} - 3e^{5} + 21e^{4} + 28e^{3} - 52e^{2} - 45e + 28$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |