# Properties

 Label 2.2.136.1-18.1-e Base field $$\Q(\sqrt{34})$$ Weight $[2, 2]$ Level norm $18$ Level $[18, 6, 3w - 18]$ Dimension $1$ CM no Base change no

# Related objects

## Base field $$\Q(\sqrt{34})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 34$$; narrow class number $$4$$ and class number $$2$$.

## Form

 Weight: $[2, 2]$ Level: $[18, 6, 3w - 18]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $20$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $-1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}3$
5 $[5, 5, w + 3]$ $\phantom{-}2$
11 $[11, 11, w + 1]$ $\phantom{-}5$
11 $[11, 11, w + 10]$ $\phantom{-}0$
17 $[17, 17, -3w + 17]$ $-3$
29 $[29, 29, w + 11]$ $\phantom{-}9$
29 $[29, 29, w + 18]$ $-4$
37 $[37, 37, w + 16]$ $-8$
37 $[37, 37, w + 21]$ $\phantom{-}3$
47 $[47, 47, -w - 9]$ $-7$
47 $[47, 47, w - 9]$ $\phantom{-}8$
49 $[49, 7, -7]$ $-5$
61 $[61, 61, w + 20]$ $\phantom{-}0$
61 $[61, 61, w + 41]$ $-10$
89 $[89, 89, 2w - 15]$ $-15$
89 $[89, 89, -2w - 15]$ $\phantom{-}10$
103 $[103, 103, -14w + 81]$ $-4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w - 6]$ $-1$
$3$ $[3, 3, w + 1]$ $1$
$3$ $[3, 3, w + 2]$ $-1$