# Properties

 Label 4.4.19429.1-9.1-e Base field 4.4.19429.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 9, -w^{3} + 2w^{2} + 4w - 2]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19429.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 9, -w^{3} + 2w^{2} + 4w - 2]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $13$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 17x^{4} + 17x^{2} - 4$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}0$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{17}{2}e^{3} + \frac{17}{2}e$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{49}{2}e^{3} + \frac{21}{2}e$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-2e^{4} + 33e^{2} - 16$
16 $[16, 2, 2]$ $\phantom{-}\frac{5}{2}e^{5} - \frac{83}{2}e^{3} + \frac{53}{2}e$
17 $[17, 17, -w + 2]$ $-e^{4} + 16e^{2} - 5$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}0$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $\phantom{-}4e^{5} - 66e^{3} + 34e$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-e^{4} + 17e^{2} - 7$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}\frac{7}{2}e^{5} - \frac{115}{2}e^{3} + \frac{55}{2}e$
41 $[41, 41, w^{2} - w - 1]$ $-\frac{9}{2}e^{5} + \frac{149}{2}e^{3} - \frac{87}{2}e$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}e^{5} - 17e^{3} + 15e$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-4e^{5} + 66e^{3} - 38e$
53 $[53, 53, -w - 3]$ $-3e^{4} + 50e^{2} - 30$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{51}{2}e^{3} + \frac{53}{2}e$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-\frac{1}{2}e^{5} + \frac{17}{2}e^{3} - \frac{13}{2}e$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $\phantom{-}e^{5} - 17e^{3} + 17e$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}4e^{4} - 66e^{2} + 40$
79 $[79, 79, w^{2} - 2w - 1]$ $-5e^{4} + 83e^{2} - 45$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $1$