# Properties

 Label 4.4.16225.1-16.2-a Base field 4.4.16225.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 4, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 13x^{2} + 6x + 36$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 4, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w]$ Dimension: $8$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{8} - 11x^{6} + 22x^{4} - 9x^{2} + 1$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $\phantom{-}0$
4 $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ $\phantom{-}e^{6} - 11e^{4} + 21e^{2} - 5$
9 $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ $-2$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ $-7e^{7} + 75e^{5} - 133e^{3} + 29e$
19 $[19, 19, w + 1]$ $-e^{7} + 11e^{5} - 21e^{3} + 3e$
19 $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ $-11e^{7} + 119e^{5} - 220e^{3} + 56e$
25 $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $\phantom{-}4e^{6} - 43e^{4} + 76e^{2} - 15$
29 $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ $\phantom{-}4e^{7} - 42e^{5} + 67e^{3} - 3e$
29 $[29, 29, w - 1]$ $\phantom{-}e^{7} - 12e^{5} + 32e^{3} - 23e$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ $-6e^{7} + 64e^{5} - 111e^{3} + 17e$
31 $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ $\phantom{-}18e^{7} - 193e^{5} + 343e^{3} - 72e$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ $\phantom{-}23e^{7} - 248e^{5} + 452e^{3} - 105e$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ $\phantom{-}7e^{7} - 75e^{5} + 133e^{3} - 31e$
59 $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-9e^{6} + 97e^{4} - 177e^{2} + 37$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ $-3e^{6} + 33e^{4} - 65e^{2} + 11$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ $\phantom{-}e^{6} - 11e^{4} + 23e^{2} - 9$
79 $[79, 79, w^{2} - 11]$ $\phantom{-}e^{6} - 9e^{4} + 3e^{2} + 9$
79 $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ $\phantom{-}2e^{6} - 22e^{4} + 46e^{2} - 22$
89 $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ $\phantom{-}11e^{7} - 120e^{5} + 229e^{3} - 62e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $-1$