# Properties

 Label 4.4.16609.1-1.1-a Base field 4.4.16609.1 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 4.4.16609.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} - x + 9$$; narrow class number $$1$$ 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:

 $$x^{4} + x^{3} - 6x^{2} - 7x + 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + w + 3]$ $\phantom{-}e^{3} - e^{2} - 5e + 1$
5 $[5, 5, w^{2} - 4]$ $-e^{3} + 5e + 1$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $\phantom{-}e^{3} - e^{2} - 4e + 3$
17 $[17, 17, -w^{2} + w + 5]$ $\phantom{-}e - 2$
27 $[27, 3, -w^{3} + 4w - 2]$ $-e^{3} + 5e + 6$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}e^{3} - e^{2} - 2e + 1$
29 $[29, 29, -w^{3} + 4w + 2]$ $\phantom{-}e^{3} - 6e + 4$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $\phantom{-}2e^{3} - e^{2} - 8e$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $-4e^{3} + 20e + 5$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $-3e^{3} + 17e + 6$
61 $[61, 61, w^{2} - 2w - 2]$ $\phantom{-}2e^{2} - 7$
61 $[61, 61, 2w^{2} - w - 8]$ $\phantom{-}e^{2} - e + 5$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $\phantom{-}e^{3} - 9e$
73 $[73, 73, -w^{2} - 2w + 2]$ $\phantom{-}e^{3} + 3e^{2} - 6e - 13$
79 $[79, 79, w^{2} - 2w - 4]$ $-2e^{3} + 10e + 2$
89 $[89, 89, w^{2} + w - 5]$ $-3e^{3} + 2e^{2} + 14e - 8$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $\phantom{-}e^{3} - e^{2} - 4e - 1$
89 $[89, 89, w^{3} - 5w - 5]$ $-3e^{2} - 4e + 10$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}3e^{3} - e^{2} - 11e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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