Base field 4.4.15188.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 8x^{4} + 10x^{2} - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $\phantom{-}e^{5} - 8e^{3} + 9e$ |
11 | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $-e^{4} + 7e^{2} - 4$ |
11 | $[11, 11, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}2e^{5} - 16e^{3} + 20e$ |
13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $-e^{5} + 8e^{3} - 9e$ |
19 | $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ | $\phantom{-}e^{5} - 8e^{3} + 9e$ |
23 | $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ | $-e^{4} + 9e^{2} - 10$ |
31 | $[31, 31, -w^{3} + w^{2} + 6w - 1]$ | $-4e^{5} + 30e^{3} - 26e$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $-2e^{5} + 14e^{3} - 10e$ |
43 | $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ | $\phantom{-}3e^{5} - 22e^{3} + 15e$ |
67 | $[67, 67, w^{2} - w - 5]$ | $\phantom{-}e^{4} - 5e^{2} - 2$ |
67 | $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ | $-2e^{5} + 18e^{3} - 34e$ |
73 | $[73, 73, w^{2} + w + 1]$ | $\phantom{-}6$ |
79 | $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ | $-2e^{4} + 12e^{2} - 2$ |
81 | $[81, 3, -3]$ | $\phantom{-}e^{4} - 3e^{2} - 6$ |
83 | $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ | $\phantom{-}5e^{5} - 38e^{3} + 33e$ |
83 | $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ | $-e^{4} + 7e^{2}$ |
89 | $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ | $-2e^{5} + 16e^{3} - 20e$ |
89 | $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ | $-4e$ |
97 | $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ | $\phantom{-}2e^{4} - 16e^{2} + 12$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).