Properties

 Label 4.4.16317.1-9.1-a Base field 4.4.16317.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, w^{3} - w^{2} - 4w]$ Dimension $3$ CM no Base change no

Related objects

• L-function not available

Base field 4.4.16317.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 4x^{2} + 5x + 1$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, w^{3} - w^{2} - 4w]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{3} - 4x^{2} - 2x + 14$$
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $-e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-e^{2} + e + 4$
7 $[7, 7, -w^{2} + 2]$ $-e^{2} + e + 4$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $\phantom{-}1$
16 $[16, 2, 2]$ $\phantom{-}3e^{2} - 4e - 13$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $-3e^{2} + 4e + 14$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}3e^{2} - 4e - 14$
25 $[25, 5, w^{2} - w - 3]$ $-e^{2} + 2e - 2$
37 $[37, 37, 2w - 1]$ $-2e^{2} + 6e + 8$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $\phantom{-}e^{2} - 3e - 8$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}e^{2} - 3e - 8$
59 $[59, 59, 2w - 5]$ $-e^{2} + 14$
59 $[59, 59, -2w - 3]$ $\phantom{-}e^{2} - 14$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $\phantom{-}2e^{2} - 6e - 4$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}2e^{2} - 6e - 4$
83 $[83, 83, -w^{3} + 7w]$ $-e^{2} + 14$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $-2e^{2} + 2e$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}2e^{2} - 2e$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}e^{2} - 14$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - w^{2} - 4w]$ $-1$