Properties

Label 4.4.14272.1-16.1-c
Base field 4.4.14272.1
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.14272.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[16, 2, 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 16x^{6} + 72x^{4} - 104x^{2} + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $\phantom{-}0$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} + 5e^{2} + 2$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $-\frac{1}{4}e^{7} + 3e^{5} - 5e^{3} - 6e$
13 $[13, 13, -w + 2]$ $-\frac{1}{4}e^{6} + 3e^{4} - 6e^{2} - 2$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - 17e^{3} + 5e$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{4}e^{6} - 3e^{4} + 6e^{2} - 2$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + 10e^{3} + 13e$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}\frac{1}{4}e^{7} - 4e^{5} + 17e^{3} - 18e$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $-\frac{1}{4}e^{7} + 4e^{5} - 17e^{3} + 19e$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}\frac{3}{4}e^{7} - 10e^{5} + 28e^{3} - 14e$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $-\frac{1}{2}e^{7} + 7e^{5} - 23e^{3} + 16e$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - 17e^{3} + 5e$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $-\frac{1}{4}e^{6} + 3e^{4} - 4e^{2} - 10$
59 $[59, 59, w - 4]$ $\phantom{-}\frac{5}{4}e^{6} - 16e^{4} + 38e^{2} - 6$
67 $[67, 67, 2w^{2} - 3w - 8]$ $-\frac{3}{4}e^{6} + 10e^{4} - 27e^{2} + 6$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $\phantom{-}\frac{3}{4}e^{7} - \frac{21}{2}e^{5} + 36e^{3} - 39e$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $\phantom{-}e^{7} - \frac{27}{2}e^{5} + 40e^{3} - 21e$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $-2e^{6} + 25e^{4} - 57e^{2} + 2$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}\frac{3}{4}e^{7} - \frac{21}{2}e^{5} + 35e^{3} - 35e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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