Base field 4.4.8957.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13,13,w^{2} - 3w]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 3x^{4} - 5x^{3} - 13x^{2} + 6x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $-\frac{1}{3}e^{4} - e^{3} + \frac{2}{3}e^{2} + \frac{7}{3}e + 1$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-\frac{1}{3}e^{4} + \frac{11}{3}e^{2} - \frac{2}{3}e - 6$ |
13 | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $\phantom{-}\frac{1}{3}e^{4} + e^{3} - \frac{2}{3}e^{2} - \frac{10}{3}e - 3$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ | $\phantom{-}1$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{4} + e^{3} - \frac{2}{3}e^{2} - \frac{7}{3}e - 5$ |
23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 7e + 6$ |
23 | $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}\frac{1}{3}e^{4} + e^{3} - \frac{5}{3}e^{2} - \frac{16}{3}e - 2$ |
49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 4e + 8$ |
49 | $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ | $\phantom{-}\frac{1}{3}e^{4} - 2e^{3} - \frac{29}{3}e^{2} + \frac{20}{3}e + 19$ |
53 | $[53, 53, w^{3} - 3w^{2} + 3]$ | $\phantom{-}e^{4} + 3e^{3} - 3e^{2} - 12e - 1$ |
53 | $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{5}{3}e^{2} + \frac{8}{3}e - 1$ |
53 | $[53, 53, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{4}{3}e^{4} - 3e^{3} + \frac{20}{3}e^{2} + \frac{16}{3}e - 7$ |
61 | $[61, 61, -w - 3]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 6e + 3$ |
61 | $[61, 61, -w^{3} + w^{2} + 5w - 4]$ | $-e^{4} - 4e^{3} + 2e^{2} + 15e$ |
79 | $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}2e^{4} + 5e^{3} - 6e^{2} - 10e - 2$ |
79 | $[79, 79, w^{2} - 5]$ | $\phantom{-}\frac{2}{3}e^{4} + 2e^{3} - \frac{7}{3}e^{2} - \frac{14}{3}e - 10$ |
101 | $[101, 101, w^{3} - 6w]$ | $\phantom{-}2e^{4} + 5e^{3} - 9e^{2} - 10e + 11$ |
101 | $[101, 101, w^{2} - 2w - 4]$ | $-\frac{4}{3}e^{4} - 7e^{3} + \frac{2}{3}e^{2} + \frac{79}{3}e + 1$ |
103 | $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ | $-e^{4} + e^{3} + 12e^{2} - 5e - 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13,13,w^{2} - 3w]$ | $-1$ |