# Properties

 Label 2.2.13.1-1764.1-c Base field $$\Q(\sqrt{13})$$ Weight $[2, 2]$ Level norm $1764$ Level $[1764, 42, 42]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{13})$$

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

## Form

 Weight: $[2, 2]$ Level: $[1764, 42, 42]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $47$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w]$ $-1$
3 $[3, 3, -w + 1]$ $-1$
4 $[4, 2, 2]$ $-1$
13 $[13, 13, -2w + 1]$ $\phantom{-}6$
17 $[17, 17, w + 4]$ $\phantom{-}1$
17 $[17, 17, -w + 5]$ $\phantom{-}1$
23 $[23, 23, 3w + 1]$ $\phantom{-}3$
23 $[23, 23, -3w + 4]$ $\phantom{-}3$
25 $[25, 5, 5]$ $\phantom{-}9$
29 $[29, 29, 3w - 2]$ $\phantom{-}9$
29 $[29, 29, -3w + 1]$ $\phantom{-}9$
43 $[43, 43, -4w - 1]$ $\phantom{-}7$
43 $[43, 43, 4w - 5]$ $\phantom{-}7$
49 $[49, 7, -7]$ $-1$
53 $[53, 53, -w - 7]$ $-10$
53 $[53, 53, w - 8]$ $-10$
61 $[61, 61, -3w - 8]$ $\phantom{-}11$
61 $[61, 61, 3w - 11]$ $\phantom{-}11$
79 $[79, 79, 5w - 4]$ $-12$
79 $[79, 79, 5w - 1]$ $-12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w]$ $1$
$3$ $[3, 3, -w + 1]$ $1$
$4$ $[4, 2, 2]$ $1$
$49$ $[49, 7, -7]$ $1$