Properties

Label 4.4.5725.1-79.1-d
Base field 4.4.5725.1
Weight $[2, 2, 2, 2]$
Level norm $79$
Level $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$
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: $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $27$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 5x^{3} - 3x^{2} - 3x + 1\)

  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 $[9, 3, -w + 1]$ $\phantom{-}e^{3} + 5e^{2} - 3e - 2$
11 $[11, 11, w]$ $\phantom{-}2e^{3} + 11e^{2} - e - 5$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $\phantom{-}e^{2} + 6e$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $-2e^{3} - 11e^{2} + 4$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $\phantom{-}2e^{3} + 10e^{2} - 5e - 4$
16 $[16, 2, 2]$ $-e^{3} - 5e^{2} + 2e + 1$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $-4e^{3} - 20e^{2} + 11e + 7$
29 $[29, 29, -w - 3]$ $-2e^{2} - 10e + 1$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $\phantom{-}2e^{3} + 11e^{2} - 7$
31 $[31, 31, w^{3} - 6w + 1]$ $-4e^{3} - 22e^{2} + e + 8$
31 $[31, 31, w^{3} - 6w - 2]$ $-e^{2} - 7e$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $-e - 10$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $-2e^{3} - 10e^{2} + 3e + 2$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $\phantom{-}2e^{3} + 11e^{2} - 2e - 9$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $-2e^{3} - 10e^{2} + 8e + 2$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $\phantom{-}1$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $-4e^{3} - 21e^{2} + 6e - 2$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $-e^{3} - 7e^{2} - 7e + 4$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $\phantom{-}e^{2} + 7e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$79$ $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $-1$