# 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-d Dimension 6 CM no Base change yes

# 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-d Dimension 6 Is CM no Is base change yes Parent newspace dimension 13

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 23x^{4}$$ $$\mathstrut -\mathstrut 2x^{3}$$ $$\mathstrut +\mathstrut 112x^{2}$$ $$\mathstrut -\mathstrut 40x$$ $$\mathstrut -\mathstrut 8$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + w^{2} + 5w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}\frac{1}{12}e^{5} - \frac{19}{12}e^{3} - \frac{5}{6}e^{2} + 5e + 2$
7 $[7, 7, w^{3} - 2w^{2} - 3w]$ $\phantom{-}\frac{1}{12}e^{5} - \frac{19}{12}e^{3} - \frac{5}{6}e^{2} + 5e + 2$
13 $[13, 13, -w^{2} + w + 3]$ $-\frac{1}{6}e^{5} + \frac{23}{6}e^{3} + \frac{2}{3}e^{2} - \frac{56}{3}e + \frac{10}{3}$
13 $[13, 13, -w^{2} + w + 2]$ $-\frac{1}{6}e^{5} + \frac{23}{6}e^{3} + \frac{2}{3}e^{2} - \frac{56}{3}e + \frac{10}{3}$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{6}e^{5} + \frac{1}{6}e^{4} - \frac{23}{6}e^{3} - \frac{17}{6}e^{2} + 17e - \frac{1}{3}$
23 $[23, 23, -w^{2} + 3w + 1]$ $-\frac{1}{3}e^{3} + \frac{13}{3}e + \frac{10}{3}$
23 $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ $-\frac{1}{3}e^{3} + \frac{13}{3}e + \frac{10}{3}$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{6}e^{5} - \frac{23}{6}e^{3} - \frac{2}{3}e^{2} + \frac{50}{3}e - \frac{4}{3}$
49 $[49, 7, w^{3} - w^{2} - 6w - 1]$ $-1$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ $-\frac{1}{6}e^{5} - \frac{1}{3}e^{4} + \frac{9}{2}e^{3} + 5e^{2} - 26e + \frac{8}{3}$
53 $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ $-\frac{1}{6}e^{5} - \frac{1}{3}e^{4} + \frac{9}{2}e^{3} + 5e^{2} - 26e + \frac{8}{3}$
67 $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ $-\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + \frac{5}{3}e^{2} - 12e - 8$
67 $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ $-\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + \frac{5}{3}e^{2} - 12e - 8$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{6}e^{4} - \frac{13}{6}e^{2} - \frac{5}{3}e + 4$
83 $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{19}{3}e^{3} + 3e^{2} + \frac{70}{3}e - 6$
83 $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{19}{3}e^{3} + 3e^{2} + \frac{70}{3}e - 6$
103 $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ $-\frac{1}{6}e^{4} + \frac{19}{6}e^{2} + \frac{5}{3}e - 4$
103 $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ $-\frac{1}{6}e^{4} + \frac{19}{6}e^{2} + \frac{5}{3}e - 4$
107 $[107, 107, w^{3} - w^{2} - 3w - 3]$ $-\frac{1}{3}e^{4} + \frac{4}{3}e^{3} + \frac{13}{3}e^{2} - 14e - \frac{10}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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