# Properties

 Label 4.4.9909.1-25.1-j Base field 4.4.9909.1 Weight $[2, 2, 2, 2]$ Level norm $25$ Level $[25, 25, w^{3} - 2w^{2} - 4w + 5]$ Dimension $4$ CM yes 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: $[25, 25, w^{3} - 2w^{2} - 4w + 5]$ Dimension: $4$ CM: yes 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:

 $$x^{4} - 3x^{3} - 12x^{2} + 30x + 21$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}0$
7 $[7, 7, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}7e^{3} + 2e^{2} - 75e - 38$
11 $[11, 11, -w^{2} + w + 2]$ $\phantom{-}0$
13 $[13, 13, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}5e^{3} + 2e^{2} - 54e - 35$
16 $[16, 2, 2]$ $-4e^{3} - 2e^{2} + 42e + 32$
17 $[17, 17, -w^{3} + 5w + 2]$ $\phantom{-}0$
29 $[29, 29, -w^{2} + w + 1]$ $\phantom{-}0$
37 $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ $-11e^{3} - 5e^{2} + 117e + 80$
41 $[41, 41, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}0$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}0$
47 $[47, 47, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}0$
47 $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}0$
53 $[53, 53, w^{3} - 4w - 4]$ $\phantom{-}0$
53 $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ $\phantom{-}0$
61 $[61, 61, -w^{3} + w^{2} + 6w - 2]$ $-15e^{3} - 3e^{2} + 159e + 76$
71 $[71, 71, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}0$
103 $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}21e^{3} + 8e^{2} - 225e - 140$
103 $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ $-26e^{3} - 8e^{2} + 276e + 155$
109 $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ $-e^{3} + 2e^{2} + 9e - 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w - 1]$ $1$