Properties

Label 4.4.7053.1-13.1-a
Base field 4.4.7053.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, w^{3} - 3w^{2} - w + 5]$
Dimension $2$
CM no
Base change no

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Base field 4.4.7053.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, w^{3} - 3w^{2} - w + 5]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
7 $[7, 7, w^{2} - w - 2]$ $-1$
9 $[9, 3, w^{2} - 2w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 3w^{2} - w + 5]$ $\phantom{-}1$
13 $[13, 13, w^{3} - 3w^{2} - w + 2]$ $-e$
16 $[16, 2, 2]$ $\phantom{-}e + 1$
17 $[17, 17, -w^{3} + 2w^{2} + 2w - 2]$ $-2e - 1$
19 $[19, 19, -w^{3} + 2w^{2} + 2w - 1]$ $\phantom{-}2e$
29 $[29, 29, -2w^{3} + 5w^{2} + 4w - 7]$ $-3$
31 $[31, 31, w^{3} - 2w^{2} - 4w + 2]$ $-e - 9$
47 $[47, 47, -w^{3} + 4w^{2} - w - 5]$ $-6$
53 $[53, 53, -w^{3} + 4w^{2} - w - 7]$ $-2e - 1$
67 $[67, 67, 2w^{3} - 3w^{2} - 8w + 1]$ $-2e - 2$
67 $[67, 67, 2w^{3} - 5w^{2} - 4w + 4]$ $-e - 9$
71 $[71, 71, w^{3} - 3w^{2} - 2w + 2]$ $-3e + 3$
79 $[79, 79, w^{2} - 3w - 4]$ $-3e - 4$
83 $[83, 83, 2w^{2} - 3w - 4]$ $-3e - 12$
89 $[89, 89, -3w^{3} + 7w^{2} + 8w - 11]$ $-12$
101 $[101, 101, w^{3} - 2w^{2} - 3w - 2]$ $\phantom{-}7e + 8$
103 $[103, 103, -2w^{3} + 4w^{2} + 5w - 1]$ $-2e + 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w^{3} - 3w^{2} - w + 5]$ $-1$