# Properties

 Label 4.4.19429.1-25.1-d Base field 4.4.19429.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 25, -2w^{3} + 5w^{2} + 6w - 5]$ 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: $[25, 25, -2w^{3} + 5w^{2} + 6w - 5]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $53$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 3x^{5} - 6x^{4} + 21x^{3} - 4x^{2} - 13x + 3$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}0$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{7}{2}e^{2} + 5e + \frac{3}{2}$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{1}{2}e^{5} + \frac{3}{2}e^{4} + \frac{7}{2}e^{3} - \frac{19}{2}e^{2} - \frac{5}{2}e + \frac{7}{2}$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{9}{2}e^{3} - \frac{5}{2}e^{2} - \frac{15}{2}e - \frac{3}{2}$
16 $[16, 2, 2]$ $\phantom{-}e^{3} - 6e$
17 $[17, 17, -w + 2]$ $-e^{5} + 2e^{4} + 7e^{3} - 12e^{2} - 3e + 2$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-e^{5} + 2e^{4} + 7e^{3} - 12e^{2} - 3e + 2$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-\frac{1}{2}e^{5} + \frac{3}{2}e^{4} + \frac{7}{2}e^{3} - \frac{23}{2}e^{2} - \frac{1}{2}e + \frac{19}{2}$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-\frac{3}{2}e^{5} + 3e^{4} + \frac{23}{2}e^{3} - 20e^{2} - \frac{25}{2}e + 13$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} + 2e^{2} - \frac{13}{2}e - 5$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}\frac{3}{2}e^{5} - 3e^{4} - \frac{23}{2}e^{3} + 21e^{2} + \frac{21}{2}e - 12$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{1}{2}e^{5} + e^{4} + \frac{5}{2}e^{3} - 6e^{2} + \frac{9}{2}e + 3$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-e^{5} + 2e^{4} + 7e^{3} - 14e^{2} - e + 10$
53 $[53, 53, -w - 3]$ $-e^{5} + \frac{5}{2}e^{4} + 7e^{3} - \frac{33}{2}e^{2} - 3e + \frac{7}{2}$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}e^{5} - 2e^{4} - 7e^{3} + 14e^{2} + e - 4$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-e^{5} + e^{4} + 10e^{3} - 7e^{2} - 20e + 5$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-\frac{3}{2}e^{5} + \frac{7}{2}e^{4} + \frac{25}{2}e^{3} - \frac{51}{2}e^{2} - \frac{35}{2}e + \frac{39}{2}$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{11}{2}e^{3} - \frac{3}{2}e^{2} - \frac{33}{2}e + \frac{1}{2}$
79 $[79, 79, w^{2} - 2w - 1]$ $-2e^{5} + 5e^{4} + 14e^{3} - 31e^{2} - 6e + 7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $1$