Properties

Label 4.4.16448.1-1.1-a
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $8$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.16448.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 30x^{6} + 260x^{4} - 600x^{2} + 400\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-\frac{3}{200}e^{7} + \frac{2}{5}e^{5} - \frac{27}{10}e^{3} + 2e$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}\frac{1}{10}e^{6} - \frac{14}{5}e^{4} + 21e^{2} - 26$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $-\frac{9}{100}e^{7} + \frac{13}{5}e^{5} - \frac{101}{5}e^{3} + 26e$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{50}e^{7} - \frac{3}{5}e^{5} + \frac{23}{5}e^{3} - 3e$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $-\frac{9}{100}e^{7} + \frac{13}{5}e^{5} - \frac{101}{5}e^{3} + 27e$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-\frac{1}{10}e^{6} + \frac{14}{5}e^{4} - 20e^{2} + 20$
25 $[25, 5, -w^{2} + 3w + 1]$ $-\frac{7}{100}e^{7} + 2e^{5} - \frac{78}{5}e^{3} + 23e$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $\phantom{-}\frac{1}{10}e^{7} - \frac{14}{5}e^{5} + 21e^{3} - 27e$
31 $[31, 31, -w^{2} + 2w + 1]$ $\phantom{-}\frac{3}{25}e^{7} - \frac{17}{5}e^{5} + \frac{128}{5}e^{3} - 32e$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $-\frac{1}{5}e^{4} + 2e^{2} + 8$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $\phantom{-}\frac{3}{100}e^{7} - \frac{4}{5}e^{5} + \frac{27}{5}e^{3} - 6e$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $-\frac{1}{10}e^{6} + \frac{13}{5}e^{4} - 18e^{2} + 20$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $-\frac{9}{100}e^{7} + \frac{12}{5}e^{5} - \frac{81}{5}e^{3} + 11e$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $-\frac{1}{10}e^{6} + \frac{16}{5}e^{4} - 28e^{2} + 44$
81 $[81, 3, -3]$ $\phantom{-}\frac{2}{5}e^{4} - 7e^{2} + 14$
83 $[83, 83, -w - 3]$ $\phantom{-}\frac{3}{10}e^{6} - \frac{43}{5}e^{4} + 66e^{2} - 84$
83 $[83, 83, w^{2} - 3w - 7]$ $-\frac{1}{5}e^{6} + \frac{27}{5}e^{4} - 38e^{2} + 40$
89 $[89, 89, w^{2} - 2w - 7]$ $\phantom{-}\frac{2}{5}e^{4} - 7e^{2} + 22$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $-\frac{1}{50}e^{7} + \frac{3}{5}e^{5} - \frac{28}{5}e^{3} + 17e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).