Properties

Label 4.4.19225.1-16.3-e
Base field 4.4.19225.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16,4,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 8]$
Dimension $12$
CM no
Base change no

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Base field 4.4.19225.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16,4,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 8]$
Dimension: $12$
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:

\(x^{12} + 4x^{11} - 23x^{10} - 109x^{9} + 126x^{8} + 940x^{7} + 140x^{6} - 3015x^{5} - 1835x^{4} + 3250x^{3} + 1835x^{2} - 1350x - 220\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $\phantom{-}0$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $...$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-e - 1$
11 $[11, 11, -w - 3]$ $...$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $...$
29 $[29, 29, w + 1]$ $...$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $...$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $...$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $...$
31 $[31, 31, -w + 3]$ $...$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $...$
59 $[59, 59, 2w^{2} - w - 13]$ $...$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $...$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $...$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $...$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $...$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $...$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 10]$ $-1$