Properties

Base field 4.4.2624.1
Weight [2, 2, 2, 2]
Level norm 68
Level $[68,34,w^{2} - 3w - 3]$
Label 4.4.2624.1-68.2-b
Dimension 2
CM no
Base change no

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Base field 4.4.2624.1

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

Form

Weight [2, 2, 2, 2]
Level $[68,34,w^{2} - 3w - 3]$
Label 4.4.2624.1-68.2-b
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 5

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut 2x \) \(\mathstrut -\mathstrut 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $\phantom{-}1$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}2$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $\phantom{-}2e - 4$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $\phantom{-}1$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $-2e$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $-2e + 6$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-e - 4$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $-2e + 10$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $-e + 2$
49 $[49, 7, w^{2} - 4w - 1]$ $-3e + 2$
71 $[71, 71, 2w - 3]$ $-2e - 2$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}2e - 4$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $\phantom{-}2e + 4$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $-2e + 6$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $\phantom{-}e + 6$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-2e - 6$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $-2e + 6$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $\phantom{-}2e - 8$
81 $[81, 3, -3]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4,2,w^{3} - 2w^{2} - 2w + 1]$ $-1$
17 $[17,17,-w^{3} + w^{2} + 4w]$ $-1$