# Properties

 Label 2.2.12.1-69.1-b Base field $$\Q(\sqrt{3})$$ Weight $[2, 2]$ Level norm $69$ Level $[69, 69, 2w - 9]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{3})$$

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

## Form

 Weight: $[2, 2]$ Level: $[69, 69, 2w - 9]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + x^{2} - 4x - 2$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $\phantom{-}1$
11 $[11, 11, -2w + 1]$ $\phantom{-}2e^{2} - 6$
11 $[11, 11, 2w + 1]$ $-e^{2} - e + 2$
13 $[13, 13, w + 4]$ $-e^{2} - e + 4$
13 $[13, 13, -w + 4]$ $-e^{2} - e + 4$
23 $[23, 23, -3w + 2]$ $\phantom{-}1$
23 $[23, 23, 3w + 2]$ $-2e^{2} - 2e + 4$
25 $[25, 5, 5]$ $-e^{2} + 3e + 4$
37 $[37, 37, 2w - 7]$ $\phantom{-}4e^{2} + 4e - 10$
37 $[37, 37, -2w - 7]$ $-2e$
47 $[47, 47, -4w - 1]$ $\phantom{-}3e^{2} + 3e - 10$
47 $[47, 47, 4w - 1]$ $\phantom{-}2e^{2} - 2e - 8$
49 $[49, 7, -7]$ $\phantom{-}2e^{2} - 2e - 6$
59 $[59, 59, 5w - 4]$ $\phantom{-}e^{2} - 3e - 6$
59 $[59, 59, -5w - 4]$ $-4e^{2} + 8$
61 $[61, 61, -w - 8]$ $\phantom{-}6e$
61 $[61, 61, w - 8]$ $\phantom{-}2e^{2} + 2e - 6$
71 $[71, 71, 5w - 2]$ $-2e^{2} - 4e + 14$
71 $[71, 71, -5w - 2]$ $\phantom{-}2e^{2} + 6e - 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $-1$
$23$ $[23, 23, -3w + 2]$ $-1$