Properties

Label 4.4.13768.1-13.1-a
Base field 4.4.13768.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{2} + 3]$
Dimension $2$
CM no
Base change no

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Base field 4.4.13768.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{2} + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $27$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}2$
4 $[4, 2, -w^{2} - w + 1]$ $-1$
13 $[13, 13, -w^{2} + 3]$ $-1$
17 $[17, 17, -w + 3]$ $\phantom{-}2e - 2$
27 $[27, 3, w^{3} - 2w^{2} - 3w + 5]$ $\phantom{-}4$
31 $[31, 31, -w^{2} - 2w + 1]$ $-2e - 2$
41 $[41, 41, -w^{2} + 5]$ $-2e$
43 $[43, 43, w^{3} - w^{2} - 5w - 1]$ $\phantom{-}0$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}2e$
59 $[59, 59, -w - 3]$ $-2e - 6$
59 $[59, 59, -2w^{3} + 2w^{2} + 9w - 5]$ $\phantom{-}4e + 8$
59 $[59, 59, -w^{3} - 3w^{2} - w + 3]$ $\phantom{-}12$
59 $[59, 59, w^{3} - 7w + 1]$ $\phantom{-}2e + 8$
61 $[61, 61, -w^{3} + w^{2} + 2w + 5]$ $\phantom{-}6e + 6$
61 $[61, 61, -w^{3} - w^{2} + 4w + 3]$ $\phantom{-}4$
67 $[67, 67, 4w^{3} - 4w^{2} - 18w + 7]$ $-12$
73 $[73, 73, -2w^{3} + 6w - 3]$ $-6e - 2$
73 $[73, 73, -2w + 3]$ $\phantom{-}12$
97 $[97, 97, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{2} + 3]$ $1$