# Properties

 Base field 4.4.13968.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.13968.1-16.1-b Dimension 4 CM yes Base change yes

# Related objects

• L-function not available

## Base field 4.4.13968.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 7x^{2} + 8x + 4$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[16, 2, 2]$ Label 4.4.13968.1-16.1-b Dimension 4 Is CM yes Is base change yes Parent newspace dimension 5

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} + x^{3} - 29x^{2} - 51x - 18$$
Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ $\phantom{-}0$
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $\phantom{-}0$
9 $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ $\phantom{-}e$
13 $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{29}{3}e - 12$
13 $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{29}{3}e - 12$
23 $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ $\phantom{-}0$
23 $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ $\phantom{-}0$
37 $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ $\phantom{-}e^{3} - 30e - 26$
37 $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ $\phantom{-}e^{3} - 30e - 26$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ $\phantom{-}0$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ $\phantom{-}0$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{52}{3}e + 10$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}e^{3} - 27e - 20$
61 $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}e^{3} - 27e - 20$
61 $[61, 61, w^{3} - w^{2} - 8w + 1]$ $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{52}{3}e + 10$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ $\phantom{-}0$
71 $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ $\phantom{-}0$
83 $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ $\phantom{-}0$
83 $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ $\phantom{-}0$
97 $[97, 97, 2w - 1]$ $-2e^{3} + 54e + 46$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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