Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,4,-2w + 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - x^{6} - 12x^{5} + 5x^{4} + 40x^{3} + 9x^{2} - 20x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -4w + 37]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 2]$ | $-2e^{6} + 3e^{5} + 22e^{4} - 21e^{3} - 65e^{2} + 16e + 26$ |
| 7 | $[7, 7, w + 4]$ | $-e^{6} + 2e^{5} + 11e^{4} - 15e^{3} - 34e^{2} + 16e + 16$ |
| 9 | $[9, 3, 3]$ | $-\frac{3}{2}e^{6} + \frac{5}{2}e^{5} + 16e^{4} - \frac{37}{2}e^{3} - 46e^{2} + \frac{41}{2}e + 20$ |
| 17 | $[17, 17, w + 6]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 6e^{4} - \frac{7}{2}e^{3} - 20e^{2} + \frac{5}{2}e + 10$ |
| 17 | $[17, 17, w + 10]$ | $-\frac{5}{2}e^{6} + \frac{9}{2}e^{5} + 27e^{4} - \frac{67}{2}e^{3} - 79e^{2} + \frac{69}{2}e + 34$ |
| 19 | $[19, 19, -2w + 19]$ | $-e^{6} + 2e^{5} + 11e^{4} - 15e^{3} - 32e^{2} + 13e + 8$ |
| 19 | $[19, 19, -2w - 17]$ | $-e^{6} + 2e^{5} + 11e^{4} - 15e^{3} - 35e^{2} + 16e + 20$ |
| 23 | $[23, 23, w + 5]$ | $-e^{3} + e^{2} + 7e$ |
| 23 | $[23, 23, w + 17]$ | $-2e^{6} + 3e^{5} + 23e^{4} - 22e^{3} - 73e^{2} + 20e + 34$ |
| 37 | $[37, 37, w + 1]$ | $-\frac{5}{2}e^{6} + \frac{9}{2}e^{5} + 27e^{4} - \frac{63}{2}e^{3} - 79e^{2} + \frac{45}{2}e + 26$ |
| 37 | $[37, 37, w + 35]$ | $\phantom{-}\frac{7}{2}e^{6} - \frac{11}{2}e^{5} - 40e^{4} + \frac{81}{2}e^{3} + 125e^{2} - \frac{77}{2}e - 54$ |
| 41 | $[41, 41, -22w + 203]$ | $-\frac{7}{2}e^{6} + \frac{11}{2}e^{5} + 38e^{4} - \frac{75}{2}e^{3} - 112e^{2} + \frac{47}{2}e + 44$ |
| 41 | $[41, 41, -6w + 55]$ | $-\frac{7}{2}e^{6} + \frac{11}{2}e^{5} + 38e^{4} - \frac{81}{2}e^{3} - 109e^{2} + \frac{83}{2}e + 44$ |
| 43 | $[43, 43, w + 20]$ | $\phantom{-}4e^{6} - 6e^{5} - 45e^{4} + 42e^{3} + 138e^{2} - 31e - 52$ |
| 43 | $[43, 43, w + 22]$ | $\phantom{-}e^{6} - 2e^{5} - 11e^{4} + 15e^{3} + 33e^{2} - 12e - 14$ |
| 53 | $[53, 53, w + 13]$ | $-e^{6} + e^{5} + 12e^{4} - 7e^{3} - 37e^{2} + 4e + 12$ |
| 53 | $[53, 53, w + 39]$ | $-2e^{4} - e^{3} + 15e^{2} + 10e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $-1$ |
| $2$ | $[2,2,-w + 2]$ | $-1$ |