# Properties

 Base field 4.4.6125.1 Weight [2, 2, 2, 2] Level norm 49 Level $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ Label 4.4.6125.1-49.1-e 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 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ Label 4.4.6125.1-49.1-e 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:
$$x^{4}$$ $$\mathstrut +\mathstrut 7x^{3}$$ $$\mathstrut -\mathstrut 6x^{2}$$ $$\mathstrut -\mathstrut 92x$$ $$\mathstrut -\mathstrut 89$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $\phantom{-}1$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $\phantom{-}e$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{4}{5}e^{2} - \frac{18}{5}e - \frac{53}{5}$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $-\frac{1}{15}e^{3} + \frac{9}{5}e + \frac{29}{15}$
11 $[11, 11, w - 1]$ $\phantom{-}\frac{1}{15}e^{3} - \frac{9}{5}e + \frac{31}{15}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{4}{5}e^{2} - \frac{13}{5}e - \frac{38}{5}$
19 $[19, 19, -w^{2} + 4]$ $-\frac{2}{15}e^{3} - \frac{3}{5}e^{2} + 2e + \frac{112}{15}$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $\phantom{-}\frac{1}{3}e^{3} + e^{2} - 5e - \frac{20}{3}$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $-\frac{1}{15}e^{3} - \frac{1}{5}e^{2} + \frac{3}{5}e + \frac{32}{15}$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $\phantom{-}\frac{4}{15}e^{3} + \frac{7}{5}e^{2} - \frac{14}{5}e - \frac{182}{15}$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $-1$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $-\frac{2}{15}e^{3} - e^{2} + \frac{18}{5}e + \frac{283}{15}$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $\phantom{-}\frac{1}{15}e^{3} + \frac{2}{5}e^{2} - \frac{12}{5}e - \frac{10}{3}$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $-\frac{4}{15}e^{3} - \frac{6}{5}e^{2} + 5e + \frac{269}{15}$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{9}{5}e^{2} - \frac{31}{5}e - \frac{277}{15}$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $-\frac{1}{5}e^{3} - \frac{4}{5}e^{2} + \frac{13}{5}e + \frac{58}{5}$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $-\frac{3}{5}e^{3} - 3e^{2} + \frac{36}{5}e + \frac{132}{5}$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $-\frac{1}{5}e^{3} - \frac{4}{5}e^{2} + \frac{13}{5}e + \frac{58}{5}$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $-\frac{3}{5}e^{3} - \frac{9}{5}e^{2} + \frac{42}{5}e + \frac{51}{5}$
81 $[81, 3, -3]$ $-\frac{1}{5}e^{3} - \frac{4}{5}e^{2} + \frac{13}{5}e + \frac{8}{5}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $1$