# Properties

 Label 6.6.1541581.1-25.1-l Base field 6.6.1541581.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $25$ Level $[25, 25, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.1541581.1

Generator $$w$$, with minimal polynomial $$x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[25, 25, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $20$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + 3x^{2} - 16x - 24$$
Norm Prime Eigenvalue
5 $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ $\phantom{-}0$
11 $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ $\phantom{-}e + 3$
11 $[11, 11, w^{2} - w - 2]$ $\phantom{-}e$
17 $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ $\phantom{-}e$
27 $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ $\phantom{-}2$
27 $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $-2$
37 $[37, 37, -w^{2} + 2w + 2]$ $-e^{2} - e + 10$
47 $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 3$
53 $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ $\phantom{-}3$
59 $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ $-e^{2} - 2e + 12$
64 $[64, 2, -2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 1$
67 $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e + 5$
67 $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ $-e + 4$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $-\frac{1}{2}e^{2} + \frac{3}{2}e + 9$
71 $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $\phantom{-}e + 9$
73 $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{5}{2}e - 7$
83 $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 3$
83 $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ $\phantom{-}e^{2} + e - 15$
89 $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 9$
97 $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ $\phantom{-}2e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ $1$