# Properties

 Label 4.4.14272.1-13.2-d Base field 4.4.14272.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13, 13, -w + 2]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## 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: $[13, 13, -w + 2]$ 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:

 $$x^{8} - 21x^{6} + 134x^{4} - 288x^{2} + 196$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $\phantom{-}\frac{2}{7}e^{7} - \frac{11}{2}e^{5} + \frac{403}{14}e^{3} - \frac{233}{7}e$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 49e^{2} - 55$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}e$
13 $[13, 13, -w + 2]$ $-1$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $-\frac{3}{14}e^{7} + 4e^{5} - \frac{283}{14}e^{3} + \frac{166}{7}e$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 49e^{2} - 56$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}\frac{1}{7}e^{7} - 3e^{5} + \frac{127}{7}e^{3} - \frac{190}{7}e$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}\frac{5}{14}e^{7} - 7e^{5} + \frac{523}{14}e^{3} - \frac{293}{7}e$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $-\frac{4}{7}e^{7} + 11e^{5} - \frac{403}{7}e^{3} + \frac{459}{7}e$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}\frac{1}{14}e^{7} - \frac{3}{2}e^{5} + \frac{67}{7}e^{3} - \frac{130}{7}e$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $-\frac{1}{2}e^{7} + \frac{19}{2}e^{5} - 49e^{3} + 58e$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}\frac{5}{7}e^{7} - 14e^{5} + \frac{530}{7}e^{3} - \frac{649}{7}e$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 48e^{2} - 48$
59 $[59, 59, w - 4]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{19}{2}e^{4} + 47e^{2} - 50$
67 $[67, 67, 2w^{2} - 3w - 8]$ $\phantom{-}e^{4} - 12e^{2} + 21$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $\phantom{-}\frac{13}{14}e^{7} - 18e^{5} + \frac{1329}{14}e^{3} - \frac{787}{7}e$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $-\frac{2}{7}e^{7} + \frac{11}{2}e^{5} - \frac{403}{14}e^{3} + \frac{233}{7}e$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $-\frac{1}{2}e^{6} + \frac{19}{2}e^{4} - 50e^{2} + 53$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $-\frac{9}{14}e^{7} + \frac{25}{2}e^{5} - \frac{456}{7}e^{3} + \frac{470}{7}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w + 2]$ $1$