Properties

Base field 4.4.10512.1
Weight [2, 2, 2, 2]
Level norm 36
Level $[36, 6, -w^{3} + w^{2} + 5w + 4]$
Label 4.4.10512.1-36.1-l
Dimension 2
CM no
Base change no

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Base field 4.4.10512.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - 6x + 1\); narrow class number \(4\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[36, 6, -w^{3} + w^{2} + 5w + 4]$
Label 4.4.10512.1-36.1-l
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 24

Hecke eigenvalues ($q$-expansion)

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}1$
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $\phantom{-}1$
11 $[11, 11, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $-e$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}2$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}2$
23 $[23, 23, w^{2} - 2w - 2]$ $\phantom{-}e$
23 $[23, 23, w^{3} - w^{2} - 6w - 3]$ $\phantom{-}3e$
23 $[23, 23, -w^{2} + 2w + 5]$ $-e$
23 $[23, 23, -w + 2]$ $-3e$
37 $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ $\phantom{-}2$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ $\phantom{-}8$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}8$
37 $[37, 37, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}2$
47 $[47, 47, w^{2} - 2w - 1]$ $\phantom{-}e$
47 $[47, 47, w^{2} - 2w - 6]$ $-e$
59 $[59, 59, 2w - 1]$ $\phantom{-}0$
59 $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ $\phantom{-}0$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $\phantom{-}14$
83 $[83, 83, -w^{3} + w^{2} + 4w + 3]$ $-6e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $-1$
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $-1$