Base field 3.3.473.1
Generator \(w\), with minimal polynomial \(x^{3} - 5x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[25, 5, w^{2} + w - 4]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 18x^{2} - 26x + 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $-\frac{1}{37}e^{3} + \frac{6}{37}e^{2} + \frac{13}{37}e - \frac{65}{37}$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $-\frac{7}{37}e^{3} + \frac{5}{37}e^{2} + \frac{91}{37}e - \frac{85}{37}$ |
9 | $[9, 3, -w^{2} + w + 4]$ | $\phantom{-}\frac{8}{37}e^{3} - \frac{11}{37}e^{2} - \frac{141}{37}e - \frac{35}{37}$ |
11 | $[11, 11, -w^{2} + 3]$ | $-\frac{6}{37}e^{3} - \frac{1}{37}e^{2} + \frac{78}{37}e + \frac{17}{37}$ |
11 | $[11, 11, -w^{2} - w + 1]$ | $-\frac{13}{37}e^{3} + \frac{4}{37}e^{2} + \frac{206}{37}e + \frac{80}{37}$ |
13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{11}{37}e^{3} + \frac{8}{37}e^{2} - \frac{180}{37}e - \frac{136}{37}$ |
17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}\frac{10}{37}e^{3} - \frac{23}{37}e^{2} - \frac{167}{37}e + \frac{132}{37}$ |
25 | $[25, 5, w^{2} + w - 4]$ | $-1$ |
37 | $[37, 37, w^{2} + w - 5]$ | $\phantom{-}\frac{20}{37}e^{3} - \frac{9}{37}e^{2} - \frac{334}{37}e - \frac{180}{37}$ |
41 | $[41, 41, 2w^{2} + w - 6]$ | $\phantom{-}\frac{7}{37}e^{3} - \frac{5}{37}e^{2} - \frac{128}{37}e - \frac{137}{37}$ |
43 | $[43, 43, w^{2} - 3w - 2]$ | $-\frac{3}{37}e^{3} - \frac{19}{37}e^{2} + \frac{39}{37}e + \frac{286}{37}$ |
43 | $[43, 43, -w + 4]$ | $-\frac{14}{37}e^{3} + \frac{10}{37}e^{2} + \frac{182}{37}e - \frac{59}{37}$ |
71 | $[71, 71, w^{2} - 8]$ | $-\frac{9}{37}e^{3} + \frac{17}{37}e^{2} + \frac{117}{37}e - \frac{252}{37}$ |
73 | $[73, 73, 3w + 5]$ | $-\frac{1}{37}e^{3} - \frac{31}{37}e^{2} + \frac{50}{37}e + \frac{416}{37}$ |
73 | $[73, 73, w^{2} - 2w - 5]$ | $\phantom{-}e - 12$ |
73 | $[73, 73, w^{2} - 2w - 7]$ | $-\frac{2}{37}e^{3} + \frac{49}{37}e^{2} - \frac{11}{37}e - \frac{315}{37}$ |
79 | $[79, 79, 2w^{2} + w - 9]$ | $\phantom{-}\frac{25}{37}e^{3} - \frac{2}{37}e^{2} - \frac{473}{37}e - \frac{410}{37}$ |
83 | $[83, 83, 3w^{2} - 2w - 13]$ | $-\frac{24}{37}e^{3} - \frac{4}{37}e^{2} + \frac{386}{37}e - \frac{43}{37}$ |
89 | $[89, 89, -w^{2} - 2w + 9]$ | $-\frac{5}{37}e^{3} - \frac{7}{37}e^{2} + \frac{139}{37}e + \frac{341}{37}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, w^{2} + w - 4]$ | $1$ |