# Properties

 Label 2.2.165.1-15.1-g Base field $$\Q(\sqrt{165})$$ Weight $[2, 2]$ Level norm $15$ Level $[15, 15, -w - 7]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{165})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 41$$; narrow class number $$4$$ and class number $$2$$.

## Form

 Weight: $[2, 2]$ Level: $[15, 15, -w - 7]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $60$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
4 $[4, 2, 2]$ $-3$
5 $[5, 5, w + 2]$ $\phantom{-}1$
7 $[7, 7, w + 2]$ $\phantom{-}0$
7 $[7, 7, w + 4]$ $\phantom{-}0$
11 $[11, 11, w + 5]$ $\phantom{-}4$
13 $[13, 13, w + 1]$ $\phantom{-}2$
13 $[13, 13, w + 11]$ $\phantom{-}2$
23 $[23, 23, w + 10]$ $\phantom{-}0$
23 $[23, 23, w + 12]$ $\phantom{-}0$
29 $[29, 29, -w - 3]$ $\phantom{-}2$
29 $[29, 29, w - 4]$ $\phantom{-}2$
31 $[31, 31, -w - 8]$ $\phantom{-}0$
31 $[31, 31, w - 9]$ $\phantom{-}0$
41 $[41, 41, -w]$ $-10$
41 $[41, 41, w - 1]$ $-10$
43 $[43, 43, w + 18]$ $-4$
43 $[43, 43, w + 24]$ $-4$
47 $[47, 47, w + 13]$ $\phantom{-}8$
47 $[47, 47, w + 33]$ $\phantom{-}8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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