Properties

Label 4.4.4400.1-44.1-b
Base field 4.4.4400.1
Weight $[2, 2, 2, 2]$
Level norm $44$
Level $[44, 22, w^{3} + w^{2} - 3w]$
Dimension $4$
CM no
Base change no

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Base field 4.4.4400.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[44, 22, w^{3} + w^{2} - 3w]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $-1$
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e - 1$
11 $[11, 11, w]$ $-1$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e + 1$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $\phantom{-}e + 2$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - \frac{3}{2}e - 6$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + \frac{3}{2}e + 10$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{9}{2}e + 6$
41 $[41, 41, w^{3} - 5w + 2]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e - 5$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}2e^{3} + 4e^{2} - 12e - 4$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $-2e^{3} - 4e^{2} + 12e + 6$
59 $[59, 59, -3w^{2} - w + 10]$ $-\frac{3}{2}e^{3} - \frac{5}{2}e^{2} + \frac{21}{2}e + 8$
59 $[59, 59, -3w^{2} + w + 10]$ $\phantom{-}e^{3} + 2e^{2} - 5e + 4$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $\phantom{-}e^{3} + 2e^{2} - 3e - 4$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $-\frac{5}{2}e^{3} - \frac{7}{2}e^{2} + \frac{39}{2}e - 2$
71 $[71, 71, 2w^{2} + w - 9]$ $\phantom{-}2e^{3} + 4e^{2} - 10e - 6$
71 $[71, 71, 2w^{2} - w - 9]$ $-3e^{3} - 5e^{2} + 21e + 2$
81 $[81, 3, -3]$ $-e^{3} - e^{2} + 11e + 2$
101 $[101, 101, 2w^{2} - w - 10]$ $-2e^{2} - 5e + 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + w + 3]$ $1$
$11$ $[11, 11, w]$ $1$