Properties

Label 4.4.19429.1-16.1-c
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $14$
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: $[16, 2, 2]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $41$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} + 3x^{13} - 25x^{12} - 77x^{11} + 223x^{10} + 721x^{9} - 849x^{8} - 3038x^{7} + 1203x^{6} + 5664x^{5} - 26x^{4} - 3826x^{3} - 658x^{2} + 585x + 67\)

  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 $[13, 13, -w^{2} + w + 4]$ $...$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $...$
16 $[16, 2, 2]$ $\phantom{-}1$
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
$16$ $[16, 2, 2]$ $-1$