# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 17 Level $[17, 17, -w^{2} + w + 4]$ Label 3.3.1129.1-17.1-e Dimension 14 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 3.3.1129.1

Generator $$w$$, with minimal polynomial $$x^{3} - 7x - 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[17, 17, -w^{2} + w + 4]$ Label 3.3.1129.1-17.1-e Dimension 14 Is CM no Is base change no Parent newspace dimension 34

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{14}$$ $$\mathstrut -\mathstrut 30x^{12}$$ $$\mathstrut +\mathstrut 8x^{11}$$ $$\mathstrut +\mathstrut 329x^{10}$$ $$\mathstrut -\mathstrut 175x^{9}$$ $$\mathstrut -\mathstrut 1602x^{8}$$ $$\mathstrut +\mathstrut 1255x^{7}$$ $$\mathstrut +\mathstrut 3262x^{6}$$ $$\mathstrut -\mathstrut 3415x^{5}$$ $$\mathstrut -\mathstrut 1605x^{4}$$ $$\mathstrut +\mathstrut 2650x^{3}$$ $$\mathstrut -\mathstrut 744x^{2}$$ $$\mathstrut -\mathstrut 8x$$ $$\mathstrut +\mathstrut 16$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $...$
3 $[3, 3, w + 2]$ $...$
8 $[8, 2, 2]$ $...$
11 $[11, 11, -w^{2} + 5]$ $...$
13 $[13, 13, w^{2} - w - 7]$ $...$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}1$
19 $[19, 19, -w^{2} - w + 4]$ $...$
29 $[29, 29, 2w^{2} - 2w - 11]$ $...$
31 $[31, 31, w^{2} - 2w - 4]$ $...$
37 $[37, 37, -2w^{2} + 3w + 7]$ $...$
41 $[41, 41, w^{2} - 2]$ $...$
59 $[59, 59, 2w^{2} - 13]$ $...$
61 $[61, 61, w^{2} + w - 10]$ $...$
67 $[67, 67, 2w^{2} - w - 11]$ $...$
73 $[73, 73, -w^{2} - 1]$ $...$
83 $[83, 83, w^{2} - w - 10]$ $...$
89 $[89, 89, -w^{2} + 4w - 2]$ $...$
97 $[97, 97, w^{2} - 2w - 7]$ $...$
97 $[97, 97, -w^{2} - 4w - 5]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{2} + w + 4]$ $-1$