# Properties

 Label 4.4.5125.1-45.1-d Base field 4.4.5125.1 Weight $[2, 2, 2, 2]$ Level norm $45$ Level $[45, 15, -w^{3} + 3w^{2} + 2w - 6]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.5125.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 6x^{2} + 7x + 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[45, 15, -w^{3} + 3w^{2} + 2w - 6]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + 8x^{2} + 15x - 2$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $\phantom{-}1$
9 $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ $-1$
9 $[9, 3, -w^{3} + 5w + 5]$ $\phantom{-}e$
11 $[11, 11, w]$ $\phantom{-}e^{2} + 6e + 4$
11 $[11, 11, w - 1]$ $-e^{2} - 5e - 2$
16 $[16, 2, 2]$ $\phantom{-}e^{2} + 3e - 5$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-e^{2} - 5e - 2$
19 $[19, 19, w^{3} - w^{2} - 4w + 2]$ $-2e^{2} - 9e - 6$
29 $[29, 29, w^{3} - 4w^{2} - w + 10]$ $\phantom{-}e^{2} + 3e - 4$
29 $[29, 29, -w^{3} + 3w^{2} + w - 7]$ $\phantom{-}2e^{2} + 6e - 10$
41 $[41, 41, 3w^{2} - 2w - 10]$ $\phantom{-}e^{2} + 6e + 2$
49 $[49, 7, -2w^{2} + 3w + 8]$ $\phantom{-}3e^{2} + 12e - 6$
49 $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ $-3e^{2} - 12e + 2$
71 $[71, 71, -w - 3]$ $\phantom{-}e^{2} + 2e - 8$
71 $[71, 71, w - 4]$ $-4e^{2} - 19e - 6$
79 $[79, 79, -w^{3} + w^{2} + 3w + 3]$ $-e^{2} - 5e + 2$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}e^{2} + 9e + 6$
89 $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}5e^{2} + 20e - 6$
89 $[89, 89, w^{3} - 6w - 2]$ $-3e^{2} - 12e - 6$
101 $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ $-4e^{2} - 18e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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