Properties

Label 4.4.7056.1-36.1-c
Base field \(\Q(\sqrt{3}, \sqrt{7})\)
Weight $[2, 2, 2, 2]$
Level norm $36$
Level $[36,6,w^{3} - 6w + 1]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{3}, \sqrt{7})\)

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[36,6,w^{3} - 6w + 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 90\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 5w + 1]$ $\phantom{-}0$
3 $[3, 3, w - 1]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + 4w - 1]$ $-1$
25 $[25, 5, w^{2} - 3]$ $\phantom{-}2$
25 $[25, 5, w^{2} - 2]$ $\phantom{-}2$
37 $[37, 37, w + 3]$ $-2$
37 $[37, 37, w^{3} - 5w + 3]$ $-8$
37 $[37, 37, -w^{3} + 5w + 3]$ $-2$
37 $[37, 37, -w + 3]$ $-8$
47 $[47, 47, w^{3} - 3w - 3]$ $\phantom{-}e$
47 $[47, 47, w^{3} + w^{2} - 6w - 1]$ $-e$
47 $[47, 47, w^{3} - w^{2} - 6w + 1]$ $-e$
47 $[47, 47, -w^{3} - w^{2} + 6w + 4]$ $\phantom{-}e$
49 $[49, 7, w^{3} - 6w]$ $-4$
59 $[59, 59, -w^{3} + w^{2} + 4w - 5]$ $\phantom{-}0$
59 $[59, 59, -w^{3} + w^{2} + 4w]$ $\phantom{-}0$
59 $[59, 59, w^{3} + w^{2} - 4w]$ $\phantom{-}e$
59 $[59, 59, w^{3} + w^{2} - 4w - 5]$ $-e$
83 $[83, 83, -3w + 2]$ $\phantom{-}0$
83 $[83, 83, -w^{3} + w^{2} + 7w + 1]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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