# Properties

 Base field 4.4.4205.1 Weight [2, 2, 2, 2] Level norm 49 Level $[49, 7, w^{3} - w^{2} - 6w - 1]$ Label 4.4.4205.1-49.1-c Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.4205.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 5x^{2} - x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[49, 7, w^{3} - w^{2} - 6w - 1]$ Label 4.4.4205.1-49.1-c Dimension 4 Is CM no Is base change no Parent newspace dimension 13

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut 6x^{3}$$ $$\mathstrut -\mathstrut 6x^{2}$$ $$\mathstrut -\mathstrut 80x$$ $$\mathstrut -\mathstrut 100$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + w^{2} + 5w]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{1}{5}e^{2} - \frac{16}{5}e - 5$
7 $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w]$ $-\frac{1}{5}e^{3} - \frac{1}{5}e^{2} + \frac{11}{5}e$
13 $[13, 13, -w^{2} + w + 3]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{7}{5}e^{2} - \frac{27}{5}e - 15$
13 $[13, 13, -w^{2} + w + 2]$ $-\frac{3}{5}e^{3} - \frac{8}{5}e^{2} + \frac{43}{5}e + 21$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{1}{5}e^{2} - \frac{16}{5}e - 3$
23 $[23, 23, -w^{2} + 3w + 1]$ $-\frac{3}{5}e^{3} - \frac{8}{5}e^{2} + \frac{38}{5}e + 14$
23 $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ $\phantom{-}\frac{3}{5}e^{3} + \frac{8}{5}e^{2} - \frac{38}{5}e - 22$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{2}{5}e^{2} - \frac{32}{5}e - 9$
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $\phantom{-}1$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $-e^{3} - 3e^{2} + 12e + 35$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ $\phantom{-}\frac{7}{5}e^{3} + \frac{17}{5}e^{2} - \frac{92}{5}e - 37$
67 $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ $-\frac{3}{5}e^{3} - \frac{8}{5}e^{2} + \frac{53}{5}e + 22$
67 $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ $\phantom{-}e^{2} - e - 14$
81 $[81, 3, -3]$ $-\frac{4}{5}e^{3} - \frac{4}{5}e^{2} + \frac{64}{5}e + 15$
83 $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ $\phantom{-}e^{3} + 2e^{2} - 14e - 26$
83 $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ $-\frac{1}{5}e^{3} - \frac{6}{5}e^{2} + \frac{6}{5}e + 10$
103 $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{6}{5}e^{2} - \frac{31}{5}e - 22$
103 $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ $-e^{2} + 3e + 14$
107 $[107, 107, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}\frac{2}{5}e^{3} + \frac{7}{5}e^{2} - \frac{27}{5}e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $-1$