Properties

Label 4.4.5225.1-44.4-e
Base field 4.4.5225.1
Weight $[2, 2, 2, 2]$
Level norm $44$
Level $[44, 22, -w^{2} + w + 2]$
Dimension $3$
CM no
Base change no

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Base field 4.4.5225.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[44, 22, -w^{2} + w + 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - x^{2} - 11x + 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 3w - \frac{7}{2}]$ $\phantom{-}e$
4 $[4, 2, w + 1]$ $-1$
11 $[11, 11, w]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{5}{2}]$ $-\frac{1}{2}e^{2} + e + \frac{11}{2}$
11 $[11, 11, -w + 2]$ $-1$
19 $[19, 19, -\frac{1}{2}w^{3} + 3w + \frac{3}{2}]$ $-\frac{1}{2}e^{2} - e + \frac{11}{2}$
25 $[25, 5, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}4$
31 $[31, 31, w^{3} - 2w^{2} - 5w + 3]$ $-2e + 2$
31 $[31, 31, -\frac{1}{2}w^{3} + w^{2} + w - \frac{1}{2}]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{15}{2}]$ $-e^{2} + 2e + 7$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w - \frac{5}{2}]$ $\phantom{-}e^{2} - 9$
61 $[61, 61, -2w^{3} + 5w^{2} + 8w - 12]$ $-2e - 6$
61 $[61, 61, \frac{1}{2}w^{3} - 2w - \frac{5}{2}]$ $-\frac{1}{2}e^{2} + 2e + \frac{9}{2}$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} - \frac{15}{2}]$ $-e^{2} + 9$
71 $[71, 71, \frac{3}{2}w^{3} - 4w^{2} - 5w + \frac{23}{2}]$ $\phantom{-}6$
79 $[79, 79, -\frac{5}{2}w^{3} + 6w^{2} + 9w - \frac{31}{2}]$ $-\frac{1}{2}e^{2} + \frac{9}{2}$
79 $[79, 79, -4w^{3} + 10w^{2} + 17w - 28]$ $-e^{2} - 4e + 13$
79 $[79, 79, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}\frac{1}{2}e^{2} + 3e - \frac{23}{2}$
79 $[79, 79, \frac{5}{2}w^{3} - 6w^{2} - 9w + \frac{23}{2}]$ $-e^{2} - 2e + 7$
81 $[81, 3, -3]$ $\phantom{-}e^{2} - 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w + 1]$ $1$
$11$ $[11, 11, -w + 2]$ $1$