Base field 4.4.7232.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[17, 17, w^{2} - w - 5]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + x^{4} - 7x^{3} - 3x^{2} + 11x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$ | $\phantom{-}e$ |
2 | $[2, 2, -w - 1]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 9e + 7$ |
17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}1$ |
17 | $[17, 17, -\frac{1}{2}w^{3} + 2w^{2} + \frac{1}{2}w - 2]$ | $\phantom{-}e^{2} - 8$ |
23 | $[23, 23, \frac{1}{2}w^{3} - 2w^{2} - \frac{1}{2}w + 4]$ | $\phantom{-}e^{4} - e^{3} - 8e^{2} + 4e + 8$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $-4e^{4} - 6e^{3} + 23e^{2} + 23e - 24$ |
41 | $[41, 41, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}4e^{4} + 5e^{3} - 23e^{2} - 20e + 20$ |
41 | $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w]$ | $\phantom{-}e^{4} - 5e^{2} + e - 4$ |
41 | $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ | $\phantom{-}2e^{4} + 4e^{3} - 11e^{2} - 15e + 14$ |
41 | $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w]$ | $\phantom{-}e^{4} + 3e^{3} - 5e^{2} - 14e + 4$ |
47 | $[47, 47, \frac{3}{2}w^{3} - 4w^{2} - \frac{7}{2}w + 6]$ | $-6e^{4} - 10e^{3} + 37e^{2} + 44e - 40$ |
47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $\phantom{-}6e^{4} + 11e^{3} - 35e^{2} - 43e + 38$ |
49 | $[49, 7, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 10e + 6$ |
49 | $[49, 7, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w - 2]$ | $-6e^{4} - 12e^{3} + 34e^{2} + 49e - 42$ |
71 | $[71, 71, \frac{5}{2}w^{3} - 6w^{2} - \frac{17}{2}w + 12]$ | $\phantom{-}e^{4} + 3e^{3} - 9e^{2} - 14e + 16$ |
71 | $[71, 71, 2w^{2} - 4w - 7]$ | $\phantom{-}4e^{4} + 7e^{3} - 26e^{2} - 32e + 32$ |
73 | $[73, 73, -w^{3} + 2w^{2} + 5w - 3]$ | $-7e^{4} - 10e^{3} + 37e^{2} + 38e - 34$ |
73 | $[73, 73, 2w - 1]$ | $\phantom{-}3e^{4} + 6e^{3} - 22e^{2} - 30e + 32$ |
79 | $[79, 79, \frac{3}{2}w^{3} - 4w^{2} - \frac{11}{2}w + 12]$ | $-5e^{4} - 10e^{3} + 32e^{2} + 43e - 42$ |
79 | $[79, 79, -w^{2} - w - 1]$ | $-12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, w^{2} - w - 5]$ | $-1$ |