Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[25, 5, w^{2} - 7]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 19x^{2} - 9x + 34\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $-\frac{1}{3}e^{2} + \frac{11}{3}$ |
11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{3}e^{2} - e - \frac{11}{3}$ |
11 | $[11, 11, -w + 2]$ | $-\frac{2}{15}e^{3} + \frac{2}{15}e^{2} + \frac{16}{15}e - \frac{13}{15}$ |
11 | $[11, 11, w - 1]$ | $-\frac{1}{15}e^{3} - \frac{4}{15}e^{2} + \frac{23}{15}e + \frac{26}{15}$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{15}e^{3} + \frac{4}{15}e^{2} - \frac{23}{15}e - \frac{86}{15}$ |
17 | $[17, 17, -w^{2} + w + 8]$ | $\phantom{-}e + 1$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{1}{15}e^{3} + \frac{11}{15}e^{2} + \frac{8}{15}e - \frac{94}{15}$ |
19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{8}{15}e^{2} - \frac{18}{5}e + \frac{22}{15}$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{1}{5}e^{2} - \frac{18}{5}e - \frac{26}{5}$ |
25 | $[25, 5, w^{2} - 7]$ | $-1$ |
27 | $[27, 3, -3]$ | $-e - 3$ |
31 | $[31, 31, w^{2} - 2w - 8]$ | $-\frac{1}{5}e^{3} - \frac{2}{15}e^{2} + \frac{18}{5}e - \frac{32}{15}$ |
37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{13}{15}e^{2} - \frac{13}{5}e + \frac{62}{15}$ |
41 | $[41, 41, -w - 4]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{17}{3}e - \frac{4}{3}$ |
41 | $[41, 41, w^{2} - 2w - 7]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{7}{3}$ |
47 | $[47, 47, 2w^{2} - 3w - 7]$ | $-\frac{4}{15}e^{3} - \frac{2}{5}e^{2} + \frac{62}{15}e + \frac{13}{5}$ |
53 | $[53, 53, -w^{2} + w + 9]$ | $\phantom{-}\frac{4}{15}e^{3} - \frac{4}{15}e^{2} - \frac{47}{15}e + \frac{86}{15}$ |
61 | $[61, 61, 3w^{2} - 2w - 17]$ | $\phantom{-}\frac{1}{3}e^{2} - e + \frac{4}{3}$ |
67 | $[67, 67, 2w - 1]$ | $\phantom{-}\frac{7}{15}e^{3} - \frac{7}{15}e^{2} - \frac{116}{15}e - \frac{52}{15}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, w^{2} - 7]$ | $1$ |