Base field 4.4.16448.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 30x^{6} + 260x^{4} - 600x^{2} + 400\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-\frac{3}{200}e^{7} + \frac{2}{5}e^{5} - \frac{27}{10}e^{3} + 2e$ |
5 | $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{1}{10}e^{6} - \frac{14}{5}e^{4} + 21e^{2} - 26$ |
11 | $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{9}{100}e^{7} + \frac{13}{5}e^{5} - \frac{101}{5}e^{3} + 26e$ |
13 | $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{50}e^{7} - \frac{3}{5}e^{5} + \frac{23}{5}e^{3} - 3e$ |
17 | $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ | $-\frac{9}{100}e^{7} + \frac{13}{5}e^{5} - \frac{101}{5}e^{3} + 27e$ |
23 | $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ | $-\frac{1}{10}e^{6} + \frac{14}{5}e^{4} - 20e^{2} + 20$ |
25 | $[25, 5, -w^{2} + 3w + 1]$ | $-\frac{7}{100}e^{7} + 2e^{5} - \frac{78}{5}e^{3} + 23e$ |
29 | $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{10}e^{7} - \frac{14}{5}e^{5} + 21e^{3} - 27e$ |
31 | $[31, 31, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{3}{25}e^{7} - \frac{17}{5}e^{5} + \frac{128}{5}e^{3} - 32e$ |
43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ | $-\frac{1}{5}e^{4} + 2e^{2} + 8$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ | $\phantom{-}\frac{3}{100}e^{7} - \frac{4}{5}e^{5} + \frac{27}{5}e^{3} - 6e$ |
59 | $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ | $-\frac{1}{10}e^{6} + \frac{13}{5}e^{4} - 18e^{2} + 20$ |
73 | $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ | $-\frac{9}{100}e^{7} + \frac{12}{5}e^{5} - \frac{81}{5}e^{3} + 11e$ |
79 | $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ | $-\frac{1}{10}e^{6} + \frac{16}{5}e^{4} - 28e^{2} + 44$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{2}{5}e^{4} - 7e^{2} + 14$ |
83 | $[83, 83, -w - 3]$ | $\phantom{-}\frac{3}{10}e^{6} - \frac{43}{5}e^{4} + 66e^{2} - 84$ |
83 | $[83, 83, w^{2} - 3w - 7]$ | $-\frac{1}{5}e^{6} + \frac{27}{5}e^{4} - 38e^{2} + 40$ |
89 | $[89, 89, w^{2} - 2w - 7]$ | $\phantom{-}\frac{2}{5}e^{4} - 7e^{2} + 22$ |
101 | $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ | $-\frac{1}{50}e^{7} + \frac{3}{5}e^{5} - \frac{28}{5}e^{3} + 17e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).