# Properties

 Label 4.4.16357.1-1.1-a Base field 4.4.16357.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16357.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[1, 1, 1]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 10x^{2} + 8$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{5}{2}e$
5 $[5, 5, w - 1]$ $-\frac{1}{2}e^{2} + 1$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}\frac{1}{2}e^{3} - 5e$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e$
16 $[16, 2, 2]$ $-e^{2} + 7$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - 3e$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}0$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $-e^{3} + 10e$
31 $[31, 31, -w - 3]$ $\phantom{-}6$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-\frac{3}{4}e^{3} + \frac{17}{2}e$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}\frac{1}{2}e^{3} - 4e$
43 $[43, 43, w^{3} - 7w - 2]$ $-e^{2} + 8$
47 $[47, 47, -2w^{3} + 11w + 2]$ $-\frac{3}{2}e^{3} + 10e$
61 $[61, 61, w^{2} - 3]$ $-\frac{1}{2}e^{3} + 4e$
67 $[67, 67, w^{2} + w - 4]$ $-3e^{2} + 12$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $-2e^{3} + 13e$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $-\frac{1}{2}e^{2} + 15$
97 $[97, 97, -w^{3} + 6w - 3]$ $\phantom{-}\frac{1}{2}e^{2} - 1$
97 $[97, 97, -3w^{3} + 16w]$ $-e^{3} + 8e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.