# Properties

 Label 4.4.18097.1-9.1-c Base field 4.4.18097.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 9, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 4]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18097.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 6x + 4$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 9, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 4]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 10x^{2} + 1$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}0$
4 $[4, 2, w]$ $-\frac{1}{2}e^{3} + \frac{11}{2}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $\phantom{-}2$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $-\frac{5}{2}e^{3} + \frac{49}{2}e$
27 $[27, 3, -w^{3} + 7w + 1]$ $-e^{3} + 9e$
31 $[31, 31, w + 3]$ $\phantom{-}e^{2} - 3$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}2e^{3} - 20e$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{27}{2}e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $-e^{3} + 9e$
47 $[47, 47, w^{3} - 5w - 3]$ $-2e^{3} + 22e$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{45}{2}e$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $-\frac{1}{2}e^{2} + \frac{5}{2}$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}2e$
83 $[83, 83, -w^{3} + 5w + 1]$ $-2e^{2} + 12$
83 $[83, 83, 2w - 1]$ $-3e^{3} + 29e$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $\phantom{-}4$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $-\frac{1}{2}e^{2} - \frac{3}{2}$
89 $[89, 89, w^{3} - 5w + 5]$ $-\frac{3}{2}e^{2} + \frac{15}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 1]$ $1$