# Properties

 Label 4.4.8789.1-31.1-h Base field 4.4.8789.1 Weight $[2, 2, 2, 2]$ Level norm $31$ Level $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## 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: $4$ CM: no Base change: no Newspace dimension: $21$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 2x^{3} - 9x^{2} + 14x - 3$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-1$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{11}{2}e$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - \frac{11}{2}$
16 $[16, 2, 2]$ $-e^{3} + 2e^{2} + 9e - 10$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-e^{3} + e^{2} + 8e - 3$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e - 6$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}e^{3} - e^{2} - 10e + 6$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 5e + \frac{19}{2}$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-e^{2} + 3$
29 $[29, 29, w^{2} - w - 3]$ $-e^{2} + 3$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}1$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $\phantom{-}e^{3} - 2e^{2} - 8e + 11$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}\frac{5}{2}e^{3} - 3e^{2} - 23e + \frac{39}{2}$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $-\frac{3}{2}e^{3} + 2e^{2} + 12e - \frac{27}{2}$
61 $[61, 61, -w - 3]$ $\phantom{-}e^{3} - 2e^{2} - 10e + 5$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-\frac{3}{2}e^{3} + \frac{5}{2}e^{2} + \frac{35}{2}e - 13$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{13}{2}e - 1$
81 $[81, 3, -3]$ $-e^{3} + 12e + 1$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $-\frac{5}{2}e^{3} + \frac{3}{2}e^{2} + \frac{49}{2}e - 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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