Properties

Label 4.4.16357.1-13.1-a
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{3} + w^{2} + 6w - 3]$
Dimension $13$
CM no
Base change no

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Base field 4.4.16357.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{3} + w^{2} + 6w - 3]$
Dimension: $13$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{13} - 4x^{12} - 21x^{11} + 97x^{10} + 126x^{9} - 825x^{8} - 63x^{7} + 3017x^{6} - 1411x^{5} - 4507x^{4} + 3170x^{3} + 2012x^{2} - 1110x - 473\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 5w + 2]$ $...$
5 $[5, 5, w - 1]$ $...$
11 $[11, 11, -w^{3} + 5w]$ $...$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-1$
16 $[16, 2, 2]$ $...$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $...$
25 $[25, 5, -w^{2} + w + 3]$ $...$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $...$
31 $[31, 31, -w - 3]$ $...$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $...$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $...$
43 $[43, 43, w^{3} - 7w - 2]$ $...$
47 $[47, 47, -2w^{3} + 11w + 2]$ $...$
61 $[61, 61, w^{2} - 3]$ $...$
67 $[67, 67, w^{2} + w - 4]$ $...$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $...$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $...$
97 $[97, 97, -w^{3} + 6w - 3]$ $...$
97 $[97, 97, -3w^{3} + 16w]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $1$