# Properties

 Base field 4.4.15952.1 Weight [2, 2, 2, 2] Level norm 9 Level $[9, 9, w^{3} - w^{2} - 6w + 3]$ Label 4.4.15952.1-9.1-f Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.15952.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - 2x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[9, 9, w^{3} - w^{2} - 6w + 3]$ Label 4.4.15952.1-9.1-f Dimension 4 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 72x^{2}$$ $$\mathstrut +\mathstrut 400$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}\frac{1}{80}e^{3} - \frac{13}{20}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}0$
11 $[11, 11, -w^{3} + 5w + 1]$ $-\frac{1}{40}e^{3} + \frac{13}{10}e$
11 $[11, 11, -w + 2]$ $-\frac{1}{40}e^{3} + \frac{23}{10}e$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $-\frac{1}{80}e^{3} + \frac{1}{8}e^{2} + \frac{13}{20}e - \frac{9}{2}$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}\frac{1}{80}e^{3} + \frac{1}{8}e^{2} - \frac{13}{20}e - \frac{9}{2}$
17 $[17, 17, -w^{2} - w + 3]$ $-4$
23 $[23, 23, w^{3} - 6w]$ $-\frac{1}{40}e^{3} + \frac{23}{10}e + 4$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $\phantom{-}\frac{1}{4}e^{2} - 9$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $-\frac{3}{80}e^{3} + \frac{1}{8}e^{2} + \frac{39}{20}e - \frac{9}{2}$
41 $[41, 41, 2w^{3} - 11w - 4]$ $\phantom{-}\frac{3}{80}e^{3} - \frac{1}{8}e^{2} - \frac{39}{20}e + \frac{9}{2}$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $\phantom{-}\frac{1}{16}e^{3} + \frac{1}{8}e^{2} - \frac{13}{4}e - \frac{9}{2}$
59 $[59, 59, 2w^{3} - 11w - 2]$ $\phantom{-}\frac{1}{40}e^{3} - \frac{23}{10}e + 4$
67 $[67, 67, w^{3} - 7w - 1]$ $\phantom{-}\frac{1}{40}e^{3} - \frac{23}{10}e - 4$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $\phantom{-}\frac{1}{4}e^{2} - 9$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $\phantom{-}\frac{3}{40}e^{3} - \frac{39}{10}e$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $-\frac{1}{80}e^{3} - \frac{3}{8}e^{2} + \frac{13}{20}e + \frac{27}{2}$
101 $[101, 101, -2w^{3} + 13w + 6]$ $\phantom{-}12$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $\phantom{-}6$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $-\frac{3}{80}e^{3} - \frac{1}{8}e^{2} + \frac{39}{20}e + \frac{9}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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