Properties

Label 4.4.15952.1-13.1-b
Base field 4.4.15952.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w^{3} + w^{2} + 4w + 1]$
Dimension $14$
CM no
Base change no

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Base field 4.4.15952.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, -w^{3} + w^{2} + 4w + 1]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} + 3x^{13} - 16x^{12} - 52x^{11} + 88x^{10} + 332x^{9} - 189x^{8} - 990x^{7} + 65x^{6} + 1421x^{5} + 281x^{4} - 867x^{3} - 285x^{2} + 129x + 34\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $...$
11 $[11, 11, -w^{3} + 5w + 1]$ $...$
11 $[11, 11, -w + 2]$ $...$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $...$
17 $[17, 17, -w^{2} - w + 3]$ $...$
23 $[23, 23, w^{3} - 6w]$ $...$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $...$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $...$
41 $[41, 41, 2w^{3} - 11w - 4]$ $...$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $...$
59 $[59, 59, 2w^{3} - 11w - 2]$ $...$
67 $[67, 67, w^{3} - 7w - 1]$ $...$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $...$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $...$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $...$
101 $[101, 101, -2w^{3} + 13w + 6]$ $...$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $...$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $-1$