Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[23, 23, w^{3} - w^{2} - 6w + 6]$ |
Dimension: | $6$ |
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:
\(x^{6} + 2x^{5} - 16x^{4} + 10x^{3} + 23x^{2} - 18x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, w^{3} - 5w + 3]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - 5w + 2]$ | $-\frac{1}{2}e^{5} - 2e^{4} + 4e^{3} + 3e^{2} - \frac{11}{2}e + 2$ |
13 | $[13, 13, w + 1]$ | $-e^{4} - 4e^{3} + 8e^{2} + 6e - 5$ |
13 | $[13, 13, w^{3} - 6w + 4]$ | $-\frac{7}{2}e^{5} - 13e^{4} + 34e^{3} + 24e^{2} - \frac{85}{2}e - 7$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{9}{2}e^{5} + 16e^{4} - 48e^{3} - 32e^{2} + \frac{131}{2}e + 18$ |
17 | $[17, 17, w^{2} + w - 2]$ | $-4e^{5} - 14e^{4} + 43e^{3} + 24e^{2} - 57e - 6$ |
17 | $[17, 17, w^{2} + w - 5]$ | $-4e^{5} - 15e^{4} + 38e^{3} + 28e^{2} - 44e - 11$ |
23 | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $-1$ |
23 | $[23, 23, w^{3} + w^{2} - 4w - 1]$ | $-\frac{13}{2}e^{5} - 22e^{4} + 73e^{3} + 35e^{2} - \frac{189}{2}e - 18$ |
25 | $[25, 5, -w^{2} + 3]$ | $\phantom{-}e^{5} + 3e^{4} - 14e^{3} - 8e^{2} + 23e + 9$ |
25 | $[25, 5, -w^{3} - w^{2} + 5w + 1]$ | $-\frac{5}{2}e^{5} - 8e^{4} + 30e^{3} + 10e^{2} - \frac{83}{2}e - 4$ |
29 | $[29, 29, -w^{2} - 2w + 3]$ | $\phantom{-}e^{5} + 3e^{4} - 14e^{3} - 8e^{2} + 22e + 11$ |
29 | $[29, 29, -w^{3} + w^{2} + 7w - 7]$ | $-1$ |
43 | $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ | $\phantom{-}\frac{7}{2}e^{5} + 11e^{4} - 42e^{3} - 9e^{2} + \frac{101}{2}e - 1$ |
43 | $[43, 43, -w^{3} + w^{2} + 5w - 7]$ | $-3e^{5} - 9e^{4} + 38e^{3} + 6e^{2} - 49e - 2$ |
53 | $[53, 53, w^{3} - w^{2} - 7w + 5]$ | $-\frac{7}{2}e^{5} - 11e^{4} + 44e^{3} + 17e^{2} - \frac{129}{2}e - 9$ |
53 | $[53, 53, w^{2} + 2w - 5]$ | $\phantom{-}14e^{5} + 49e^{4} - 150e^{3} - 84e^{2} + 190e + 45$ |
61 | $[61, 61, 2w^{3} + w^{2} - 10w]$ | $-\frac{5}{2}e^{5} - 8e^{4} + 30e^{3} + 9e^{2} - \frac{83}{2}e + 2$ |
61 | $[61, 61, w^{3} - 7w + 3]$ | $-\frac{17}{2}e^{5} - 29e^{4} + 95e^{3} + 49e^{2} - \frac{251}{2}e - 23$ |
61 | $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ | $\phantom{-}\frac{15}{2}e^{5} + 26e^{4} - 83e^{3} - 49e^{2} + \frac{237}{2}e + 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $1$ |