Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); 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: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 32x^{4} + 304x^{2} - 736\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{5}{2}e^{2} + 9$ |
2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $\phantom{-}\frac{1}{8}e^{4} - 2e^{2} + 4$ |
5 | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $-\frac{1}{8}e^{5} + 2e^{3} - 3e$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 9e$ |
19 | $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{3} - 6e$ |
23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{9}{2}e^{2} + 18$ |
31 | $[31, 31, -w^{2} + w + 1]$ | $-\frac{1}{2}e^{3} + 6e$ |
47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - 5e^{3} + 20e$ |
49 | $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ | $-\frac{1}{4}e^{5} + 5e^{3} - 21e$ |
53 | $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ | $-\frac{1}{2}e^{4} + \frac{17}{2}e^{2} - 20$ |
53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $-\frac{1}{4}e^{4} + 5e^{2} - 10$ |
61 | $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ | $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 13e$ |
61 | $[61, 61, 2w^{2} - 7]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} + 13e$ |
71 | $[71, 71, w^{2} - 3w - 5]$ | $-\frac{3}{4}e^{4} + \frac{29}{2}e^{2} - 50$ |
73 | $[73, 73, 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{9}{2}e^{3} + 15e$ |
73 | $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ | $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - 11e$ |
79 | $[79, 79, 2w^{2} - 5]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{29}{2}e^{2} + 46$ |
81 | $[81, 3, -3]$ | $-\frac{3}{4}e^{4} + 13e^{2} - 38$ |
101 | $[101, 101, 2w^{2} - 4w - 9]$ | $-\frac{3}{8}e^{5} + \frac{13}{2}e^{3} - 17e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).