# Properties

 Label 4.4.8789.1-31.1-a Base field 4.4.8789.1 Weight $[2, 2, 2, 2]$ Level norm $31$ Level $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ Dimension $1$ CM no Base change no

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## Base field 4.4.8789.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $21$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}3$
7 $[7, 7, w - 1]$ $-1$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}0$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $\phantom{-}5$
16 $[16, 2, 2]$ $-7$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}3$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-6$
17 $[17, 17, -w^{2} + 2w + 1]$ $-6$
19 $[19, 19, w^{2} - w - 2]$ $-1$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-6$
29 $[29, 29, w^{2} - w - 3]$ $-6$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}1$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-4$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}6$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $\phantom{-}0$
61 $[61, 61, -w - 3]$ $\phantom{-}14$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-16$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $-7$
81 $[81, 3, -3]$ $-5$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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