# Properties

 Label 4.4.19525.1-9.1-b Base field 4.4.19525.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, -w + 3]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.19525.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 14x^{2} + 15x + 45$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, -w + 3]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 8x^{2} + 8$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ $\phantom{-}e$
5 $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ $\phantom{-}\frac{1}{4}e^{3} - 2e$
9 $[9, 3, -w + 3]$ $\phantom{-}1$
9 $[9, 3, w + 2]$ $-\frac{1}{2}e^{2} + 2$
11 $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ $\phantom{-}\frac{1}{2}e^{3} - 3e$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{2}e^{2} - 7$
19 $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ $\phantom{-}\frac{1}{4}e^{3} - 2e$
19 $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ $-e^{3} + 6e$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ $-\frac{5}{4}e^{3} + 5e$
29 $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-\frac{1}{2}e^{3} + 3e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{4}e^{3} + e$
31 $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ $-e^{3} + 9e$
49 $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ $-\frac{3}{2}e^{3} + 9e$
49 $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ $-3e^{2} + 8$
59 $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ $-e^{2} - 2$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ $-e^{2} + 4$
61 $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ $-5e$
61 $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ $\phantom{-}\frac{5}{2}e^{3} - 14e$
61 $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ $\phantom{-}3e^{2} - 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, -w + 3]$ $-1$