# Properties

 Label 2.2.40.1-45.1-e Base field $$\Q(\sqrt{10})$$ Weight $[2, 2]$ Level norm $45$ Level $[45, 15, 3w]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{10})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 10$$; narrow class number $$2$$ and class number $$2$$.

## Form

 Weight: $[2, 2]$ Level: $[45, 15, 3w]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $\phantom{-}1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
5 $[5, 5, w]$ $-1$
13 $[13, 13, w + 6]$ $\phantom{-}2$
13 $[13, 13, w + 7]$ $\phantom{-}2$
31 $[31, 31, -2w + 3]$ $\phantom{-}0$
31 $[31, 31, 2w + 3]$ $\phantom{-}0$
37 $[37, 37, w + 11]$ $\phantom{-}10$
37 $[37, 37, w + 26]$ $\phantom{-}10$
41 $[41, 41, 3w + 7]$ $\phantom{-}10$
41 $[41, 41, -3w + 7]$ $\phantom{-}10$
43 $[43, 43, w + 15]$ $-4$
43 $[43, 43, w + 28]$ $-4$
49 $[49, 7, -7]$ $-14$
53 $[53, 53, w + 13]$ $\phantom{-}10$
53 $[53, 53, w + 40]$ $\phantom{-}10$
67 $[67, 67, w + 12]$ $-12$
67 $[67, 67, w + 55]$ $-12$
71 $[71, 71, -w - 9]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $-1$
$3$ $[3, 3, w + 2]$ $-1$
$5$ $[5, 5, w]$ $1$