Properties

Label 3.3.473.1-25.1-a
Base field 3.3.473.1
Weight $[2, 2, 2]$
Level norm $25$
Level $[25, 5, w^{2} + w - 4]$
Dimension $4$
CM no
Base change no

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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 $[89, 89, -w^{2} - 2w + 9]$ $-\frac{5}{37}e^{3} - \frac{7}{37}e^{2} + \frac{139}{37}e + \frac{341}{37}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, w^{2} + w - 4]$ $1$