# Properties

 Label 4.4.8069.1-35.1-e Base field 4.4.8069.1 Weight $[2, 2, 2, 2]$ Level norm $35$ Level $[35, 35, 2w - 1]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8069.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[35, 35, 2w - 1]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + 2x^{2} - 5x - 8$$
Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}1$
7 $[7, 7, w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 4w - 1]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $-2e - 2$
16 $[16, 2, 2]$ $-e^{2} + e + 9$
17 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}2e + 2$
17 $[17, 17, -w^{3} + 5w - 2]$ $-2e^{2} - e + 10$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}2e + 4$
19 $[19, 19, -w^{2} - w + 1]$ $-e^{2} + 4$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $-2e - 2$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}2e^{2} - 6$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}2e^{2} + e - 12$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}2e^{2} + 2e - 4$
47 $[47, 47, -w^{3} - w^{2} + 5w]$ $-e + 8$
49 $[49, 7, w^{2} + 2w - 2]$ $-e^{2} + 2e + 2$
59 $[59, 59, 2w^{3} - 8w + 3]$ $\phantom{-}2e - 4$
67 $[67, 67, w^{2} - w - 4]$ $-4e^{2} + 20$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}6e^{2} + 3e - 24$
81 $[81, 3, -3]$ $\phantom{-}2e^{2} + 2e + 2$
97 $[97, 97, w^{3} + w^{2} - 5w + 1]$ $-e^{2} - 8e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w^{3} - 4w]$ $-1$
$7$ $[7, 7, -w^{3} + 4w - 1]$ $-1$