# Properties

 Base field $$\Q(\sqrt{53})$$ Weight [2, 2] Level norm 1369 Level $[1369, 37, 37]$ Label 2.2.53.1-1369.1-b Dimension 1 CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{53})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 13$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[1369, 37, 37]$ Label 2.2.53.1-1369.1-b Dimension 1 Is CM no Is base change yes Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-4$
7 $[7, 7, w + 2]$ $-1$
7 $[7, 7, w - 3]$ $-1$
9 $[9, 3, 3]$ $-5$
11 $[11, 11, w + 1]$ $\phantom{-}3$
11 $[11, 11, w - 2]$ $\phantom{-}3$
13 $[13, 13, w]$ $-4$
13 $[13, 13, w - 1]$ $-4$
17 $[17, 17, -w - 5]$ $\phantom{-}6$
17 $[17, 17, w - 6]$ $\phantom{-}6$
25 $[25, 5, -5]$ $-10$
29 $[29, 29, -w - 6]$ $-6$
29 $[29, 29, w - 7]$ $-6$
37 $[37, 37, 2w - 5]$ $\phantom{-}1$
37 $[37, 37, -2w - 3]$ $\phantom{-}1$
43 $[43, 43, -w - 7]$ $\phantom{-}8$
43 $[43, 43, w - 8]$ $\phantom{-}8$
47 $[47, 47, 3w + 7]$ $\phantom{-}3$
47 $[47, 47, 3w - 10]$ $\phantom{-}3$
53 $[53, 53, 2w - 1]$ $-3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
37 $[37, 37, 2w - 5]$ $-1$
37 $[37, 37, -2w - 3]$ $-1$