Base field 6.6.1229312.1
Generator \(w\), with minimal polynomial \(x^{6} - 10x^{4} + 24x^{2} - 8\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[41,41,\frac{1}{4}w^{5} + \frac{1}{4}w^{4} - \frac{5}{2}w^{3} - 2w^{2} + 5w + 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 5x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $\phantom{-}e^{2} + 2e - 4$ |
7 | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}e$ |
8 | $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ | $-e^{2} - e + 2$ |
41 | $[41, 41, -\frac{1}{4}w^{4} - \frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 1]$ | $\phantom{-}2e^{2} + 3e - 12$ |
41 | $[41, 41, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}2e^{2} + 2e - 8$ |
41 | $[41, 41, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + 2w^{2} - 5w - 2]$ | $\phantom{-}1$ |
41 | $[41, 41, \frac{1}{4}w^{5} - \frac{1}{4}w^{4} - \frac{5}{2}w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}2$ |
41 | $[41, 41, \frac{1}{2}w^{2} - w - 2]$ | $-5e^{2} - 10e + 14$ |
41 | $[41, 41, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 1]$ | $-2e^{2} - 5e + 4$ |
71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + w^{2} - 5w + 1]$ | $-2e^{2} + e + 8$ |
71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + \frac{3}{2}w^{2} - 6w - 2]$ | $\phantom{-}4e^{2} + 4e - 8$ |
71 | $[71, 71, \frac{1}{4}w^{4} - \frac{1}{2}w^{3} - \frac{5}{2}w^{2} + 3w + 4]$ | $\phantom{-}2e^{2} + 2e - 4$ |
71 | $[71, 71, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - 3w + 4]$ | $\phantom{-}2e^{2} + 7e - 6$ |
71 | $[71, 71, \frac{1}{2}w^{4} - \frac{7}{2}w^{2} + w + 3]$ | $-4$ |
71 | $[71, 71, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + \frac{5}{2}w^{3} - w^{2} - 5w - 1]$ | $-4e^{2} - 10e + 14$ |
97 | $[97, 97, \frac{1}{4}w^{5} - \frac{5}{2}w^{3} - \frac{1}{2}w^{2} + 5w]$ | $-4e^{2} - 9e + 10$ |
97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{3}{2}w^{2} + w + 1]$ | $\phantom{-}3e^{2} + 6e - 10$ |
97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + 2w^{2} - 3w - 4]$ | $-4e^{2} - 10e + 18$ |
97 | $[97, 97, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - 2w^{2} - 3w + 4]$ | $\phantom{-}4e^{2} + 10e - 10$ |
97 | $[97, 97, \frac{1}{4}w^{4} - \frac{3}{2}w^{2} + w - 1]$ | $\phantom{-}4e^{2} + 10e - 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$41$ | $[41,41,\frac{1}{4}w^{5} + \frac{1}{4}w^{4} - \frac{5}{2}w^{3} - 2w^{2} + 5w + 2]$ | $-1$ |