Properties

Label 4.4.13824.1-13.2-a
Base field 4.4.13824.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13,13,-w^{3} + 4w + 1]$
Dimension $6$
CM no
Base change no

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Base field 4.4.13824.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13,13,-w^{3} + 4w + 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 7x^{4} + 13x^{2} - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 3]$ $-e^{3} + 3e$
11 $[11, 11, -w^{2} + w + 1]$ $-e^{5} + 6e^{3} - 8e$
11 $[11, 11, -w^{2} - w + 1]$ $\phantom{-}e^{5} - 5e^{3} + 4e$
13 $[13, 13, w^{3} - 4w + 1]$ $-e^{4} + 3e^{2} - 1$
13 $[13, 13, -w^{3} + 4w + 1]$ $\phantom{-}1$
25 $[25, 5, -w^{2} - 2w + 1]$ $\phantom{-}4e^{2} - 11$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}e^{4} - 8e^{2} + 9$
37 $[37, 37, w^{3} - 3w - 1]$ $-2e^{4} + 9e^{2} - 7$
37 $[37, 37, w^{3} - 3w + 1]$ $-2e^{4} + 9e^{2} - 7$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}3e^{5} - 12e^{3} + 4e$
59 $[59, 59, -w^{2} - w + 5]$ $-2e^{5} + 8e^{3} - 2e$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $\phantom{-}6e^{4} - 28e^{2} + 18$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $\phantom{-}e^{4} - 2e^{2} + 3$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}2e^{4} - 8e^{2} - 4$
73 $[73, 73, 2w - 1]$ $-6e^{4} + 27e^{2} - 21$
73 $[73, 73, -2w - 1]$ $\phantom{-}3e^{4} - 15e^{2} + 9$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}5e^{4} - 23e^{2} + 16$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $\phantom{-}2e^{5} - 9e^{3} + 5e$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $-4e^{5} + 26e^{3} - 34e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,-w^{3} + 4w + 1]$ $-1$