# Properties

 Label 2.2.28.1-126.1-f Base field $$\Q(\sqrt{7})$$ Weight $[2, 2]$ Level norm $126$ Level $[126, 42, -9w + 21]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{7})$$

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

## Form

 Weight: $[2, 2]$ Level: $[126, 42, -9w + 21]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w - 3]$ $\phantom{-}1$
3 $[3, 3, w - 2]$ $-1$
3 $[3, 3, w + 2]$ $-1$
7 $[7, 7, w]$ $-1$
19 $[19, 19, 2w - 3]$ $-4$
19 $[19, 19, 2w + 3]$ $-4$
25 $[25, 5, 5]$ $-6$
29 $[29, 29, -w - 6]$ $-2$
29 $[29, 29, w - 6]$ $-2$
31 $[31, 31, 4w + 9]$ $\phantom{-}0$
31 $[31, 31, -4w + 9]$ $\phantom{-}0$
37 $[37, 37, -3w + 10]$ $-10$
37 $[37, 37, -6w + 17]$ $-10$
47 $[47, 47, -3w - 4]$ $\phantom{-}0$
47 $[47, 47, 3w - 4]$ $\phantom{-}0$
53 $[53, 53, 2w - 9]$ $\phantom{-}6$
53 $[53, 53, 2w + 9]$ $\phantom{-}6$
59 $[59, 59, 3w - 2]$ $\phantom{-}4$
59 $[59, 59, -3w - 2]$ $\phantom{-}4$
83 $[83, 83, -6w - 13]$ $-4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w - 3]$ $-1$
$3$ $[3, 3, w - 2]$ $1$
$3$ $[3, 3, w + 2]$ $1$
$7$ $[7, 7, w]$ $1$