Properties

Label 4.4.4400.1-55.1-d
Base field 4.4.4400.1
Weight $[2, 2, 2, 2]$
Level norm $55$
Level $[55, 55, -w^{3} - 3w^{2} + 4w + 11]$
Dimension $5$
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: $[55, 55, -w^{3} - 3w^{2} + 4w + 11]$
Dimension: $5$
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:

\(x^{5} - 12x^{3} + 27x - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $-1$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
11 $[11, 11, w]$ $-1$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{9}{2}e + 6$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 8$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $-\frac{1}{2}e^{3} - e^{2} + \frac{9}{2}e + 4$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $\phantom{-}2$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $-e^{4} + 9e^{2} + 2e - 6$
41 $[41, 41, w^{3} - 5w + 2]$ $\phantom{-}2e + 2$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{5}{2}e - 6$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $-e^{3} + 2e^{2} + 9e - 10$
59 $[59, 59, -3w^{2} - w + 10]$ $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + \frac{13}{2}e^{2} + \frac{27}{2}e - 12$
59 $[59, 59, -3w^{2} + w + 10]$ $\phantom{-}e^{4} + e^{3} - 11e^{2} - 11e + 18$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{13}{2}e + 6$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 10$
71 $[71, 71, 2w^{2} + w - 9]$ $-\frac{1}{2}e^{4} - e^{3} + \frac{9}{2}e^{2} + 8e$
71 $[71, 71, 2w^{2} - w - 9]$ $\phantom{-}e^{4} + e^{3} - 11e^{2} - 7e + 16$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + e - 2$
101 $[101, 101, 2w^{2} - w - 10]$ $-2e^{2} - 2e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w + 1]$ $1$
$11$ $[11, 11, w]$ $1$