# Properties

 Base field 4.4.6125.1 Weight [2, 2, 2, 2] Level norm 55 Level $[55, 55, -w^{3} - 2w^{2} + 5w + 11]$ Label 4.4.6125.1-55.1-b Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.6125.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 9x^{2} + 9x + 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[55, 55, -w^{3} - 2w^{2} + 5w + 11]$ Label 4.4.6125.1-55.1-b Dimension 4 Is CM no Is base change no Parent newspace dimension 18

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut 5x^{3}$$ $$\mathstrut -\mathstrut 5x^{2}$$ $$\mathstrut -\mathstrut 21x$$ $$\mathstrut +\mathstrut 12$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $\phantom{-}1$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $-1$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $\phantom{-}e$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $-\frac{1}{4}e^{3} - \frac{3}{2}e^{2} - \frac{1}{4}e + 3$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - e - 7$
19 $[19, 19, -w^{2} + 4]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e - 2$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 2$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $\phantom{-}\frac{1}{4}e^{3} + e^{2} - \frac{13}{4}e - 5$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + 4$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $-\frac{1}{4}e^{3} - e^{2} - \frac{3}{4}e - 5$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $-\frac{1}{4}e^{3} - e^{2} - \frac{7}{4}e - 3$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 3e$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $\phantom{-}\frac{3}{2}e^{2} + \frac{15}{2}e - 6$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $\phantom{-}e^{3} + \frac{9}{2}e^{2} - \frac{5}{2}e - 6$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{4}e + 3$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $-\frac{1}{4}e^{3} + \frac{17}{4}e - 3$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $\phantom{-}e^{3} + \frac{13}{2}e^{2} + \frac{5}{2}e - 18$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $-\frac{3}{2}e^{2} - \frac{9}{2}e + 6$
81 $[81, 3, -3]$ $-\frac{3}{4}e^{3} - 2e^{2} + \frac{27}{4}e + 1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $-1$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $1$