Properties

Label 4.4.5725.1-59.1-b
Base field 4.4.5725.1
Weight $[2, 2, 2, 2]$
Level norm $59$
Level $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$
Dimension $4$
CM no
Base change no

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Base field 4.4.5725.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{4} + 7x^{3} + 4x^{2} - 30x + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ $\phantom{-}e$
9 $[9, 3, -w + 1]$ $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} + \frac{2}{3}e - 6$
11 $[11, 11, w]$ $-\frac{1}{3}e^{2} - \frac{2}{3}e + 1$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $-\frac{1}{3}e^{3} - \frac{4}{3}e^{2} + \frac{2}{3}e$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{11}{3}e + 5$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $-\frac{1}{3}e^{3} - \frac{4}{3}e^{2} + \frac{5}{3}e + 2$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{7}{3}e^{2} + \frac{4}{3}e - 8$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $-\frac{5}{3}e^{2} - \frac{19}{3}e + 6$
29 $[29, 29, -w - 3]$ $-\frac{2}{3}e^{3} - \frac{8}{3}e^{2} + \frac{1}{3}e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{2}{3}e^{2} - 3e + 3$
31 $[31, 31, w^{3} - 6w + 1]$ $\phantom{-}\frac{5}{3}e^{2} + \frac{16}{3}e - 9$
31 $[31, 31, w^{3} - 6w - 2]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{23}{3}e - 8$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $-\frac{7}{3}e^{2} - \frac{23}{3}e + 9$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $-\frac{1}{3}e^{3} - \frac{2}{3}e^{2} + 3e - 9$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $\phantom{-}1$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{20}{3}e - 2$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $\phantom{-}e^{2} + 4e - 10$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $-\frac{2}{3}e^{3} - 2e^{2} + \frac{11}{3}e + 1$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $\phantom{-}2e^{3} + \frac{25}{3}e^{2} - \frac{16}{3}e - 14$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $\phantom{-}e^{3} + \frac{19}{3}e^{2} + \frac{17}{3}e - 17$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$59$ $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $-1$