Properties

Label 4.4.5225.1-44.5-a
Base field 4.4.5225.1
Weight $[2, 2, 2, 2]$
Level norm $44$
Level $[44,22,-w^{3} + w^{2} + 6w]$
Dimension $5$
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: $[44,22,-w^{3} + w^{2} + 6w]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - x^{4} - 13x^{3} + 15x^{2} + 6x - 4\)

  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 $[4, 2, w + 1]$ $\phantom{-}1$
11 $[11, 11, w]$ $\phantom{-}1$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{5}{2}]$ $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 2e - 4$
11 $[11, 11, -w + 2]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e - 2$
19 $[19, 19, -\frac{1}{2}w^{3} + 3w + \frac{3}{2}]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{13}{2}e^{2} + \frac{15}{2}e + 5$
25 $[25, 5, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}e^{4} - e^{3} - 13e^{2} + 13e + 6$
31 $[31, 31, w^{3} - 2w^{2} - 5w + 3]$ $-\frac{3}{2}e^{4} + e^{3} + \frac{39}{2}e^{2} - 15e - 8$
31 $[31, 31, -\frac{1}{2}w^{3} + w^{2} + w - \frac{1}{2}]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 3e - 4$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{15}{2}]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{13}{2}e^{2} - \frac{19}{2}e - 3$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w - \frac{5}{2}]$ $\phantom{-}e^{4} - 13e^{2} + 2e + 14$
61 $[61, 61, -2w^{3} + 5w^{2} + 8w - 12]$ $-\frac{3}{2}e^{4} + \frac{1}{2}e^{3} + \frac{39}{2}e^{2} - \frac{19}{2}e - 9$
61 $[61, 61, \frac{1}{2}w^{3} - 2w - \frac{5}{2}]$ $\phantom{-}e^{4} - \frac{1}{2}e^{3} - 14e^{2} + \frac{15}{2}e + 10$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} - \frac{15}{2}]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + \frac{11}{2}e - 2$
71 $[71, 71, \frac{3}{2}w^{3} - 4w^{2} - 5w + \frac{23}{2}]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{15}{2}e^{2} - \frac{7}{2}e + 12$
79 $[79, 79, -\frac{5}{2}w^{3} + 6w^{2} + 9w - \frac{31}{2}]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{13}{2}e^{2} + 2e + 8$
79 $[79, 79, -4w^{3} + 10w^{2} + 17w - 28]$ $\phantom{-}\frac{3}{2}e^{4} - \frac{1}{2}e^{3} - \frac{39}{2}e^{2} + \frac{23}{2}e + 9$
79 $[79, 79, -w^{3} + w^{2} + 4w + 1]$ $-\frac{1}{2}e^{4} + e^{3} + \frac{15}{2}e^{2} - 14e - 4$
79 $[79, 79, \frac{5}{2}w^{3} - 6w^{2} - 9w + \frac{23}{2}]$ $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - \frac{41}{2}e^{2} - \frac{3}{2}e + 18$
81 $[81, 3, -3]$ $-e^{4} + 2e^{3} + 13e^{2} - 26e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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