Properties

Label 4.4.16448.1-13.1-a
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$
Dimension $2$
CM no
Base change no

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Base field 4.4.16448.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $-e - 2$
5 $[5, 5, w - 1]$ $-e + 3$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $-2e + 3$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}1$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $\phantom{-}4e - 6$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $\phantom{-}e - 1$
25 $[25, 5, -w^{2} + 3w + 1]$ $-5$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $-e + 2$
31 $[31, 31, -w^{2} + 2w + 1]$ $-e - 7$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $-5$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $\phantom{-}2e - 3$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $\phantom{-}5e - 9$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $-6e + 6$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $-6e + 6$
81 $[81, 3, -3]$ $-5e + 11$
83 $[83, 83, -w - 3]$ $-2e + 8$
83 $[83, 83, w^{2} - 3w - 7]$ $-2e + 1$
89 $[89, 89, w^{2} - 2w - 7]$ $\phantom{-}5e - 7$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $\phantom{-}4e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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