Base field 3.3.1901.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[12, 6, w^{2} - 3w - 1]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} - 10x^{5} + 30x^{3} - x^{2} - 26x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $-1$ |
4 | $[4, 2, -w^{2} + 3w + 3]$ | $-1$ |
9 | $[9, 3, -w^{2} + 2w + 7]$ | $-e^{3} + e^{2} + 4e - 4$ |
13 | $[13, 13, w + 3]$ | $-e^{5} + e^{4} + 8e^{3} - 6e^{2} - 15e + 7$ |
13 | $[13, 13, -w + 3]$ | $-e^{6} + e^{5} + 8e^{4} - 6e^{3} - 16e^{2} + 7e + 5$ |
13 | $[13, 13, -w + 1]$ | $-e^{5} + 8e^{3} - 2e^{2} - 14e + 5$ |
17 | $[17, 17, -w^{2} - 2w + 1]$ | $\phantom{-}e^{5} - 7e^{3} + e^{2} + 12e - 5$ |
23 | $[23, 23, w^{2} - 2w - 5]$ | $\phantom{-}e^{5} - e^{4} - 8e^{3} + 6e^{2} + 13e - 7$ |
31 | $[31, 31, 2w + 3]$ | $\phantom{-}e^{6} - 9e^{4} + 20e^{2} - 4$ |
31 | $[31, 31, -2w^{2} + 3w + 15]$ | $\phantom{-}e^{6} - 8e^{4} + 16e^{2} - e - 6$ |
31 | $[31, 31, 3w + 7]$ | $-e^{6} + 2e^{5} + 8e^{4} - 15e^{3} - 17e^{2} + 25e + 6$ |
37 | $[37, 37, 3w^{2} - 4w - 27]$ | $-e^{6} + 8e^{4} - 16e^{2} - e + 6$ |
41 | $[41, 41, -2w^{2} + 7w + 1]$ | $-2e^{5} + 14e^{3} + 2e^{2} - 22e - 6$ |
59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}e^{6} - 9e^{4} + 22e^{2} - 2e - 12$ |
61 | $[61, 61, 4w^{2} - 12w - 11]$ | $\phantom{-}e^{6} - 2e^{5} - 10e^{4} + 12e^{3} + 26e^{2} - 13e - 6$ |
71 | $[71, 71, w^{2} - 2w - 11]$ | $-e^{6} - e^{5} + 7e^{4} + 6e^{3} - 12e^{2} - 6e + 5$ |
97 | $[97, 97, 3w + 5]$ | $\phantom{-}2e^{6} - 2e^{5} - 14e^{4} + 14e^{3} + 14e^{2} - 22e + 22$ |
101 | $[101, 101, 2w^{2} - 6w - 7]$ | $\phantom{-}e^{6} - 6e^{4} - 3e^{3} + 5e^{2} + 11e + 2$ |
103 | $[103, 103, 2w^{2} - 3w - 19]$ | $\phantom{-}e^{6} - 8e^{4} + e^{3} + 15e^{2} - e - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $1$ |
$4$ | $[4, 2, -w^{2} + 3w + 3]$ | $1$ |