Properties

Label 4.4.19429.1-13.1-a
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{2} + w + 4]$
Dimension $13$
CM no
Base change no

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Base field 4.4.19429.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{2} + w + 4]$
Dimension: $13$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{13} + 3x^{12} - 19x^{11} - 56x^{10} + 121x^{9} + 339x^{8} - 359x^{7} - 853x^{6} + 545x^{5} + 817x^{4} - 389x^{3} - 122x^{2} + 40x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $...$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $...$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}1$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $...$
16 $[16, 2, 2]$ $...$
17 $[17, 17, -w + 2]$ $...$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $...$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $...$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $...$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $...$
41 $[41, 41, w^{2} - w - 1]$ $...$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $...$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $...$
53 $[53, 53, -w - 3]$ $...$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $...$
59 $[59, 59, 2w^{2} - 3w - 6]$ $...$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $...$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $...$
79 $[79, 79, w^{2} - 2w - 1]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{2} + w + 4]$ $-1$