Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[25, 5, -w^{2} + w + 6]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 7x^{3} + 5x^{2} - 39x - 45\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}0$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{5}{3}e^{2} - \frac{17}{3}e - 6$ |
7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - \frac{7}{3}e - 6$ |
7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - \frac{7}{3}e - 7$ |
8 | $[8, 2, 2]$ | $-e^{3} - 3e^{2} + 7e + 12$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{2}{3}e^{3} - \frac{5}{3}e^{2} + \frac{17}{3}e + 5$ |
19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{10}{3}e + 3$ |
23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 9$ |
27 | $[27, 3, 3]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 10$ |
29 | $[29, 29, w^{2} - w - 3]$ | $-e^{3} - 4e^{2} + 6e + 18$ |
31 | $[31, 31, w^{2} - w - 8]$ | $-\frac{4}{3}e^{3} - \frac{10}{3}e^{2} + \frac{34}{3}e + 13$ |
37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{5}{3}e^{3} + \frac{17}{3}e^{2} - \frac{29}{3}e - 26$ |
43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{4}{3}e^{3} - \frac{16}{3}e^{2} + \frac{22}{3}e + 21$ |
47 | $[47, 47, w^{2} - 3]$ | $-e^{3} - 4e^{2} + 5e + 12$ |
53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}e^{3} + 3e^{2} - 7e - 9$ |
59 | $[59, 59, w^{2} - 2w - 4]$ | $-e^{3} - 2e^{2} + 8e$ |
67 | $[67, 67, w^{2} + w - 8]$ | $\phantom{-}e^{3} + 3e^{2} - 9e - 14$ |
71 | $[71, 71, w^{2} + w - 11]$ | $-2e^{3} - 7e^{2} + 11e + 21$ |
73 | $[73, 73, -w^{2} + 4w - 2]$ | $-\frac{11}{3}e^{3} - \frac{38}{3}e^{2} + \frac{62}{3}e + 45$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w + 2]$ | $1$ |