# Properties

 Label 4.4.4525.1-45.4-d Base field 4.4.4525.1 Weight $[2, 2, 2, 2]$ Level norm $45$ Level $[45,15,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 4]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.4525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 3x + 9$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[45,15,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 4]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 3x^{3} - 5x^{2} + 11x + 10$$
Norm Prime Eigenvalue
5 $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ $\phantom{-}1$
9 $[9, 3, -w]$ $-e^{3} + 2e^{2} + 3e$
9 $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}1$
16 $[16, 2, 2]$ $\phantom{-}e^{2} - 3e - 1$
19 $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ $-e^{3} + 2e^{2} + 5e - 2$
19 $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ $\phantom{-}e^{2} - 2e - 4$
31 $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ $\phantom{-}e^{3} - 8e$
31 $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ $\phantom{-}e^{3} - 7e - 6$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ $-4e^{2} + 6e + 14$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ $\phantom{-}e^{3} - 6e^{2} + 4e + 18$
61 $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ $\phantom{-}3e^{2} - 6e - 10$
61 $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ $-3e^{2} + 4e + 10$
71 $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ $\phantom{-}3e^{3} - 8e^{2} - 5e + 14$
71 $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ $-2e^{2} + 8$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ $-2e^{3} + 7e^{2} + 2e - 14$
89 $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-2e^{2} + 3e + 8$
101 $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ $\phantom{-}e^{3} - 2e^{2} - 7e$
101 $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}e^{3} + 2e^{2} - 5e - 20$
101 $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ $-e^{3} - e^{2} + 13e + 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,-\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 3]$ $-1$
$9$ $[9,3,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $-1$