# Properties

 Label 4.4.4400.1-31.1-f Base field 4.4.4400.1 Weight $[2, 2, 2, 2]$ Level norm $31$ Level $[31, 31, -w^{3} + w^{2} + 4w - 2]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.4400.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} + 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[31, 31, -w^{3} + w^{2} + 4w - 2]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $-1$
5 $[5, 5, w + 1]$ $-3$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $-3$
11 $[11, 11, w]$ $\phantom{-}1$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $\phantom{-}3$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $-4$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}1$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $-3$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $\phantom{-}7$
41 $[41, 41, w^{3} - 5w + 2]$ $\phantom{-}0$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $-5$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}2$
59 $[59, 59, -3w^{2} - w + 10]$ $\phantom{-}13$
59 $[59, 59, -3w^{2} + w + 10]$ $-8$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $\phantom{-}10$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $-4$
71 $[71, 71, 2w^{2} + w - 9]$ $-3$
71 $[71, 71, 2w^{2} - w - 9]$ $\phantom{-}11$
81 $[81, 3, -3]$ $\phantom{-}7$
101 $[101, 101, 2w^{2} - w - 10]$ $-14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $-1$