# Properties

 Base field 4.4.15952.1 Weight [2, 2, 2, 2] Level norm 13 Level $[13, 13, -w^{3} + w^{2} + 4w + 1]$ Label 4.4.15952.1-13.1-b Dimension 14 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 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ Label 4.4.15952.1-13.1-b Dimension 14 Is CM no Is base change no Parent newspace dimension 28

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{14}$$ $$\mathstrut +\mathstrut 3x^{13}$$ $$\mathstrut -\mathstrut 16x^{12}$$ $$\mathstrut -\mathstrut 52x^{11}$$ $$\mathstrut +\mathstrut 88x^{10}$$ $$\mathstrut +\mathstrut 332x^{9}$$ $$\mathstrut -\mathstrut 189x^{8}$$ $$\mathstrut -\mathstrut 990x^{7}$$ $$\mathstrut +\mathstrut 65x^{6}$$ $$\mathstrut +\mathstrut 1421x^{5}$$ $$\mathstrut +\mathstrut 281x^{4}$$ $$\mathstrut -\mathstrut 867x^{3}$$ $$\mathstrut -\mathstrut 285x^{2}$$ $$\mathstrut +\mathstrut 129x$$ $$\mathstrut +\mathstrut 34$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $...$
11 $[11, 11, -w^{3} + 5w + 1]$ $...$
11 $[11, 11, -w + 2]$ $...$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $...$
17 $[17, 17, -w^{2} - w + 3]$ $...$
23 $[23, 23, w^{3} - 6w]$ $...$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $...$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $...$
41 $[41, 41, 2w^{3} - 11w - 4]$ $...$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $...$
59 $[59, 59, 2w^{3} - 11w - 2]$ $...$
67 $[67, 67, w^{3} - 7w - 1]$ $...$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $...$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $...$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $...$
101 $[101, 101, -2w^{3} + 13w + 6]$ $...$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $...$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $-1$