# Properties

 Label 2.2.21.1-175.1-a Base field $$\Q(\sqrt{21})$$ Weight $[2, 2]$ Level norm $175$ Level $[175, 35, -5w - 15]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{21})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 5$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[175, 35, -5w - 15]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}1$
4 $[4, 2, 2]$ $-4$
5 $[5, 5, w]$ $-1$
5 $[5, 5, w - 1]$ $-1$
7 $[7, 7, -w - 3]$ $\phantom{-}1$
17 $[17, 17, -2w + 3]$ $\phantom{-}3$
17 $[17, 17, -2w - 1]$ $\phantom{-}3$
37 $[37, 37, w + 6]$ $\phantom{-}2$
37 $[37, 37, -w + 7]$ $\phantom{-}2$
41 $[41, 41, 3w + 1]$ $-12$
41 $[41, 41, -3w + 4]$ $-12$
43 $[43, 43, 3w + 8]$ $-10$
43 $[43, 43, 3w - 11]$ $-10$
47 $[47, 47, 3w - 2]$ $\phantom{-}9$
47 $[47, 47, 3w - 1]$ $\phantom{-}9$
59 $[59, 59, -5w - 6]$ $\phantom{-}0$
59 $[59, 59, -4w - 3]$ $\phantom{-}0$
67 $[67, 67, -w - 8]$ $-4$
67 $[67, 67, w - 9]$ $-4$
79 $[79, 79, 2w - 11]$ $-1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $1$
$5$ $[5, 5, w - 1]$ $1$
$7$ $[7, 7, -w - 3]$ $-1$