Properties

Label 4.4.5225.1-44.1-c
Base field 4.4.5225.1
Weight $[2, 2, 2, 2]$
Level norm $44$
Level $[44, 22, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{11}{2}]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more

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: $[44, 22, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{11}{2}]$
Dimension: $2$
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:

\(x^{2} - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 3w - \frac{7}{2}]$ $-1$
4 $[4, 2, w + 1]$ $\phantom{-}e$
11 $[11, 11, w]$ $-1$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{5}{2}]$ $\phantom{-}e + 3$
11 $[11, 11, -w + 2]$ $\phantom{-}2e + 2$
19 $[19, 19, -\frac{1}{2}w^{3} + 3w + \frac{3}{2}]$ $-2e - 4$
25 $[25, 5, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}4$
31 $[31, 31, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}4$
31 $[31, 31, -\frac{1}{2}w^{3} + w^{2} + w - \frac{1}{2}]$ $-2$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{15}{2}]$ $\phantom{-}2e + 4$
59 $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w - \frac{5}{2}]$ $\phantom{-}e + 11$
61 $[61, 61, -2w^{3} + 5w^{2} + 8w - 12]$ $-4e - 2$
61 $[61, 61, \frac{1}{2}w^{3} - 2w - \frac{5}{2}]$ $\phantom{-}4e + 8$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} - \frac{15}{2}]$ $-7e - 1$
71 $[71, 71, \frac{3}{2}w^{3} - 4w^{2} - 5w + \frac{23}{2}]$ $\phantom{-}7e - 3$
79 $[79, 79, -\frac{5}{2}w^{3} + 6w^{2} + 9w - \frac{31}{2}]$ $\phantom{-}0$
79 $[79, 79, -4w^{3} + 10w^{2} + 17w - 28]$ $-7e - 5$
79 $[79, 79, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}2e - 6$
79 $[79, 79, \frac{5}{2}w^{3} - 6w^{2} - 9w + \frac{23}{2}]$ $-4e + 10$
81 $[81, 3, -3]$ $-2e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 3w - \frac{7}{2}]$ $1$
$11$ $[11, 11, w]$ $1$