Properties

Base field 4.4.2225.1
Weight [2, 2, 2, 2]
Level norm 1024
Level $[1024, 16, 2w^{3} - 8w]$
Label 4.4.2225.1-1024.4-bo
Dimension 2
CM no
Base change no

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Base field 4.4.2225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 4\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[1024, 16, 2w^{3} - 8w]$
Label 4.4.2225.1-1024.4-bo
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 54

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut 48\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w]$ $\phantom{-}0$
4 $[4, 2, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 1]$ $\phantom{-}1$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + 4]$ $\phantom{-}e$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - 1]$ $\phantom{-}\frac{1}{2}e + 2$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $-e - 2$
29 $[29, 29, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{3}{2}w - 1]$ $-\frac{1}{2}e$
29 $[29, 29, -w^{2} + 5]$ $\phantom{-}6$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}\frac{1}{2}e + 6$
31 $[31, 31, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $\phantom{-}\frac{1}{2}e - 2$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w]$ $-e - 2$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{1}{2}w - 5]$ $\phantom{-}e - 2$
59 $[59, 59, w^{3} - w^{2} - 5w + 1]$ $-e$
59 $[59, 59, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 1]$ $\phantom{-}e + 8$
61 $[61, 61, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 2]$ $-2$
61 $[61, 61, -2w^{2} + w + 7]$ $\phantom{-}6$
71 $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 6]$ $-e - 4$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} - \frac{1}{2}w - 5]$ $-e + 4$
71 $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 5]$ $\phantom{-}\frac{1}{2}e - 2$
71 $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ $-2e$
81 $[81, 3, -3]$ $\phantom{-}\frac{3}{2}e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w]$ $-1$
4 $[4, 2, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 1]$ $-1$