# Properties

 Base field 3.3.1849.1 Weight [2, 2, 2] Level norm 4 Level $[4, 2, w^{2} - 4w - 2]$ Label 3.3.1849.1-4.1-c Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1849.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 14x - 8$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[4, 2, w^{2} - 4w - 2]$ Label 3.3.1849.1-4.1-c Dimension 3 Is CM no Is base change no Parent newspace dimension 5

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} - 2x^{2} - 3x + 2$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $\phantom{-}1$
2 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $-1$
2 $[2, 2, w + 3]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 3w + 7]$ $-e^{2} + 4e + 1$
11 $[11, 11, -2w - 1]$ $-2e^{2} + 2e + 4$
11 $[11, 11, -w^{2} + w + 11]$ $-e^{2} + 2e + 1$
27 $[27, 3, 3]$ $-2e^{2} + 4e$
41 $[41, 41, 2w + 5]$ $-e^{2} + 4e + 1$
41 $[41, 41, -w^{2} + 3w + 3]$ $\phantom{-}2e - 2$
41 $[41, 41, -w^{2} + w + 15]$ $-2e + 8$
43 $[43, 43, -3w^{2} + 11w + 11]$ $-6$
47 $[47, 47, -w^{2} - w + 5]$ $\phantom{-}2e^{2} - 4e - 2$
47 $[47, 47, w^{2} - 5w - 3]$ $-e^{2} + 3$
47 $[47, 47, -2w^{2} + 4w + 23]$ $-3e^{2} + 2e + 5$
59 $[59, 59, -w^{2} + w + 13]$ $-4e + 8$
59 $[59, 59, w^{2} - 3w - 5]$ $-2e^{2} + 10$
59 $[59, 59, -2w - 3]$ $\phantom{-}2e^{2} - 2e - 10$
97 $[97, 97, 7w^{2} - 11w - 91]$ $-2e^{2} + 2e + 6$
97 $[97, 97, -2w^{2} - 8w - 5]$ $\phantom{-}6e^{2} - 12e - 12$
97 $[97, 97, 5w^{2} - 19w - 15]$ $\phantom{-}4e^{2} - 12e - 10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $-1$
2 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $1$