# Properties

 Label 4.4.9909.1-21.1-h Base field 4.4.9909.1 Weight $[2, 2, 2, 2]$ Level norm $21$ Level $[21, 21, -w^{2} + 2w + 3]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.9909.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[21, 21, -w^{2} + 2w + 3]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 24x^{2} + 96$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + w + 2]$ $-\frac{1}{4}e^{3} + 4e$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}2$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{2}e^{2} - 7$
17 $[17, 17, -w^{3} + 5w + 2]$ $\phantom{-}0$
29 $[29, 29, -w^{2} + w + 1]$ $-\frac{1}{4}e^{3} + 3e$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}2$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}\frac{1}{4}e^{3} - 4e$
41 $[41, 41, w^{2} - 5]$ $-\frac{1}{4}e^{3} + 4e$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{1}{4}e^{3} - 4e$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{4}e^{3} - 4e$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}\frac{1}{4}e^{3} - 2e$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $-\frac{1}{4}e^{3} + 2e$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}2$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}\frac{1}{4}e^{3} - 7e$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}8$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $-e^{2} + 8$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $-10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $-1$
$7$ $[7, 7, w^{3} - w^{2} - 4w + 1]$ $-1$