Properties

 Base field 4.4.15952.1 Weight [2, 2, 2, 2] Level norm 18 Level $[18, 18, -w^{2} - w + 2]$ Label 4.4.15952.1-18.1-h Dimension 2 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 $[18, 18, -w^{2} - w + 2]$ Label 4.4.15952.1-18.1-h Dimension 2 Is CM no Is base change no Parent newspace dimension 16

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

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