Properties

Label 4.4.19821.1-16.1-a
Base field 4.4.19821.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $15$
CM no
Base change no

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Base field 4.4.19821.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $15$
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:

\(x^{15} + 4x^{14} - 19x^{13} - 84x^{12} + 121x^{11} + 661x^{10} - 215x^{9} - 2402x^{8} - 628x^{7} + 3865x^{6} + 2564x^{5} - 1817x^{4} - 2105x^{3} - 455x^{2} + 56x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ $...$
9 $[9, 3, w + 1]$ $...$
13 $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ $...$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ $...$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ $...$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ $...$
25 $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ $...$
25 $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ $...$
29 $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ $...$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ $...$
37 $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $...$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ $...$
43 $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ $...$
47 $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ $...$
59 $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ $...$
59 $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ $...$
67 $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ $...$
71 $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $-1$