# Properties

 Base field 4.4.19225.1 Weight [2, 2, 2, 2] Level norm 4 Level $[4,2,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 10]$ Label 4.4.19225.1-4.2-b Dimension 2 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.19225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 15x^{2} + 2x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[4,2,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 10]$ Label 4.4.19225.1-4.2-b Dimension 2 Is CM no Is base change no Parent newspace dimension 5

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - 5$$
Norm Prime Eigenvalue
4 $[4, 2, w + 2]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ $-1$
9 $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ $-2e$
9 $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ $\phantom{-}2e$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ $-e - 1$
11 $[11, 11, -w - 3]$ $\phantom{-}4$
25 $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ $\phantom{-}2e - 4$
29 $[29, 29, w + 1]$ $\phantom{-}2e$
29 $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ $-e + 5$
31 $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ $-e - 1$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ $\phantom{-}4$
31 $[31, 31, -w + 3]$ $\phantom{-}2e - 6$
31 $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ $\phantom{-}4$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}0$
59 $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ $\phantom{-}e + 5$
61 $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ $\phantom{-}e - 1$
61 $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ $-2e + 4$
71 $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ $\phantom{-}4e + 4$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ $\phantom{-}2e - 6$
79 $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ $\phantom{-}4e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4,2,\frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 10]$ $1$