Base field 3.3.1620.1
Generator \(w\), with minimal polynomial \(x^{3} - 12x - 14\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 3x^{7} - 15x^{6} + 39x^{5} + 80x^{4} - 152x^{3} - 180x^{2} + 176x + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w - 3]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{13}{16}e^{6} - \frac{25}{16}e^{5} + \frac{137}{16}e^{4} + \frac{7}{4}e^{3} - 22e^{2} + \frac{13}{4}e + 9$ |
| 5 | $[5, 5, -2w^{2} + 3w + 19]$ | $-\frac{1}{16}e^{7} + \frac{7}{16}e^{6} + \frac{3}{16}e^{5} - \frac{83}{16}e^{4} + \frac{11}{4}e^{3} + \frac{33}{2}e^{2} - \frac{31}{4}e - 11$ |
| 7 | $[7, 7, -w^{2} + 2w + 7]$ | $\phantom{-}e^{2} - e - 4$ |
| 13 | $[13, 13, w^{2} - 3w - 5]$ | $-\frac{1}{16}e^{7} + \frac{7}{16}e^{6} + \frac{3}{16}e^{5} - \frac{83}{16}e^{4} + \frac{11}{4}e^{3} + \frac{35}{2}e^{2} - \frac{35}{4}e - 15$ |
| 17 | $[17, 17, w^{2} - w - 3]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{13}{16}e^{6} - \frac{25}{16}e^{5} + \frac{137}{16}e^{4} + \frac{7}{4}e^{3} - 22e^{2} + \frac{9}{4}e + 9$ |
| 23 | $[23, 23, -w + 3]$ | $-\frac{1}{4}e^{7} + \frac{5}{4}e^{6} + \frac{5}{4}e^{5} - \frac{53}{4}e^{4} + \frac{13}{2}e^{3} + 37e^{2} - 24e - 24$ |
| 37 | $[37, 37, 3w + 5]$ | $\phantom{-}\frac{7}{16}e^{7} - \frac{25}{16}e^{6} - \frac{69}{16}e^{5} + \frac{261}{16}e^{4} + \frac{35}{4}e^{3} - 40e^{2} + \frac{9}{4}e + 13$ |
| 43 | $[43, 43, w^{2} + 3w + 3]$ | $\phantom{-}e^{3} - e^{2} - 7e + 8$ |
| 47 | $[47, 47, -w^{2} + 3]$ | $-\frac{1}{2}e^{7} + 2e^{6} + 4e^{5} - 20e^{4} - \frac{5}{2}e^{3} + 48e^{2} - 15e - 20$ |
| 49 | $[49, 7, -w^{2} + 5]$ | $-\frac{1}{4}e^{7} + \frac{5}{4}e^{6} + \frac{5}{4}e^{5} - \frac{53}{4}e^{4} + \frac{13}{2}e^{3} + 38e^{2} - 26e - 30$ |
| 53 | $[53, 53, -w^{2} + w + 13]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{5}{4}e^{6} - \frac{5}{4}e^{5} + \frac{53}{4}e^{4} - \frac{15}{2}e^{3} - 36e^{2} + 30e + 22$ |
| 61 | $[61, 61, -w^{2} + 15]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{21}{16}e^{6} - \frac{1}{16}e^{5} + \frac{225}{16}e^{4} - \frac{51}{4}e^{3} - 38e^{2} + \frac{121}{4}e + 21$ |
| 61 | $[61, 61, w^{2} - 2w - 13]$ | $-\frac{5}{16}e^{7} + \frac{19}{16}e^{6} + \frac{47}{16}e^{5} - \frac{207}{16}e^{4} - \frac{21}{4}e^{3} + \frac{75}{2}e^{2} - \frac{11}{4}e - 23$ |
| 61 | $[61, 61, -4w - 5]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{21}{16}e^{6} - \frac{1}{16}e^{5} + \frac{225}{16}e^{4} - \frac{47}{4}e^{3} - 39e^{2} + \frac{105}{4}e + 21$ |
| 67 | $[67, 67, -2w^{2} + 6w + 13]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{5}{4}e^{6} - \frac{5}{4}e^{5} + \frac{53}{4}e^{4} - \frac{15}{2}e^{3} - 35e^{2} + 32e + 20$ |
| 73 | $[73, 73, 2w^{2} - 2w - 17]$ | $\phantom{-}\frac{3}{16}e^{7} - \frac{29}{16}e^{6} + \frac{23}{16}e^{5} + \frac{313}{16}e^{4} - \frac{109}{4}e^{3} - 55e^{2} + \frac{249}{4}e + 33$ |
| 79 | $[79, 79, -w - 5]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{3}{2}e^{5} - \frac{11}{2}e^{4} + \frac{27}{2}e^{3} + 18e^{2} - 24e - 16$ |
| 79 | $[79, 79, 2w^{2} - 4w - 17]$ | $-\frac{1}{4}e^{7} + \frac{5}{4}e^{6} + \frac{5}{4}e^{5} - \frac{53}{4}e^{4} + \frac{13}{2}e^{3} + 37e^{2} - 26e - 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 2]$ | $-1$ |