Properties

Label 4.4.11324.1-13.1-d
Base field 4.4.11324.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{2} + 3]$
Dimension $14$
CM no
Base change no

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Base field 4.4.11324.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{2} + 3]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} - 5x^{13} - 12x^{12} + 89x^{11} + 15x^{10} - 575x^{9} + 271x^{8} + 1694x^{7} - 1131x^{6} - 2383x^{5} + 1514x^{4} + 1486x^{3} - 644x^{2} - 284x + 24\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 4w + 1]$ $...$
5 $[5, 5, w + 1]$ $...$
13 $[13, 13, -w^{2} + 3]$ $-1$
17 $[17, 17, -w^{3} + w^{2} + 3w - 1]$ $...$
19 $[19, 19, -w^{3} + 3w - 1]$ $...$
23 $[23, 23, -w + 3]$ $...$
31 $[31, 31, -w^{2} - 2w + 1]$ $...$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $...$
43 $[43, 43, 2w - 1]$ $...$
53 $[53, 53, -w - 3]$ $...$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $...$
61 $[61, 61, w^{3} - 3w - 5]$ $...$
67 $[67, 67, w^{3} + w^{2} - 5w - 1]$ $...$
81 $[81, 3, -3]$ $...$
83 $[83, 83, -w^{3} + 5w - 3]$ $...$
89 $[89, 89, w^{2} + 1]$ $...$
97 $[97, 97, w^{3} - w^{2} - 5w + 1]$ $...$
97 $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ $...$
97 $[97, 97, w^{3} - 3w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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