Properties

Label 4.4.5125.1-55.1-h
Base field 4.4.5125.1
Weight $[2, 2, 2, 2]$
Level norm $55$
Level $[55, 55, -3w^{2} + 2w + 11]$
Dimension $6$
CM no
Base change no

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Base field 4.4.5125.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 7x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[55, 55, -3w^{2} + 2w + 11]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 22x^{4} + 128x^{2} - 160\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $\phantom{-}1$
9 $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 5w + 5]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{9}{4}e^{3} + 8e$
11 $[11, 11, w]$ $\phantom{-}1$
11 $[11, 11, w - 1]$ $\phantom{-}e^{2} - 8$
16 $[16, 2, 2]$ $-\frac{1}{4}e^{4} + \frac{9}{2}e^{2} - 13$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1}{2}e^{3} + 6e$
19 $[19, 19, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{9}{4}e^{3} + 9e$
29 $[29, 29, w^{3} - 4w^{2} - w + 10]$ $-\frac{1}{8}e^{5} + \frac{9}{4}e^{3} - 8e$
29 $[29, 29, -w^{3} + 3w^{2} + w - 7]$ $-e$
41 $[41, 41, 3w^{2} - 2w - 10]$ $\phantom{-}2$
49 $[49, 7, -2w^{2} + 3w + 8]$ $-3e$
49 $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ $-\frac{1}{2}e^{3} + 5e$
71 $[71, 71, -w - 3]$ $-e^{2} + 12$
71 $[71, 71, w - 4]$ $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 12$
79 $[79, 79, -w^{3} + w^{2} + 3w + 3]$ $-\frac{1}{2}e^{3} + 4e$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $-\frac{1}{8}e^{5} + \frac{9}{4}e^{3} - 7e$
89 $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{7}{4}e^{3} + 4e$
89 $[89, 89, w^{3} - 6w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 7e$
101 $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ $-2e^{2} + 22$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, -w^{2} + 2w + 3]$ $-1$
$11$ $[11, 11, w]$ $-1$