# Properties

 Base field $$\Q(\sqrt{17})$$ Weight [2, 2] Level norm 144 Level $[144,48,-3w + 15]$ Label 2.2.17.1-144.5-f Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{17})$$

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

## Form

 Weight [2, 2] Level $[144,48,-3w + 15]$ Label 2.2.17.1-144.5-f Dimension 3 Is CM no Is base change no Parent newspace dimension 8

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut 7x$$ $$\mathstrut -\mathstrut 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}0$
9 $[9, 3, 3]$ $-1$
13 $[13, 13, -2w + 3]$ $\phantom{-}e^{2} - 2e - 5$
13 $[13, 13, 2w + 1]$ $-e^{2} + 3$
17 $[17, 17, -2w + 1]$ $\phantom{-}2e$
19 $[19, 19, -2w + 7]$ $-e^{2} + 5$
19 $[19, 19, 2w + 5]$ $\phantom{-}e^{2} - 2e - 3$
25 $[25, 5, -5]$ $-e^{2} - 2e + 5$
43 $[43, 43, 4w - 7]$ $-e^{2} - 2e + 7$
43 $[43, 43, 4w + 3]$ $-e^{2} + 2e + 3$
47 $[47, 47, -2w + 9]$ $-2e + 2$
47 $[47, 47, 2w + 7]$ $-2e^{2} + 10$
49 $[49, 7, -7]$ $-2e^{2} + 2e + 6$
53 $[53, 53, 4w - 13]$ $\phantom{-}6$
53 $[53, 53, 6w - 13]$ $\phantom{-}2e^{2} - 2e - 10$
59 $[59, 59, -4w - 1]$ $\phantom{-}4$
59 $[59, 59, 4w - 5]$ $\phantom{-}4$
67 $[67, 67, 4w - 3]$ $\phantom{-}2e^{2} + 2e - 8$
67 $[67, 67, 4w - 1]$ $\phantom{-}4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,w + 1]$ $1$
9 $[9,3,3]$ $1$