# Properties

 Label 2.2.76.1-171.1-e Base field $$\Q(\sqrt{19})$$ Weight $[2, 2]$ Level norm $171$ Level $[171, 57, 3w]$ Dimension $1$ CM no Base change yes

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## Base field $$\Q(\sqrt{19})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 19$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[171, 57, 3w]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $98$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -3w - 13]$ $-2$
3 $[3, 3, w + 4]$ $-1$
3 $[3, 3, w - 4]$ $-1$
5 $[5, 5, 2w + 9]$ $-3$
5 $[5, 5, -2w + 9]$ $-3$
17 $[17, 17, w + 6]$ $-1$
17 $[17, 17, -w + 6]$ $-1$
19 $[19, 19, w]$ $-1$
31 $[31, 31, 20w + 87]$ $-6$
31 $[31, 31, 7w + 30]$ $-6$
49 $[49, 7, -7]$ $\phantom{-}11$
59 $[59, 59, 6w + 25]$ $-8$
59 $[59, 59, -6w + 25]$ $-8$
61 $[61, 61, -9w - 40]$ $-1$
61 $[61, 61, 9w - 40]$ $-1$
67 $[67, 67, 2w - 3]$ $\phantom{-}8$
67 $[67, 67, -2w - 3]$ $\phantom{-}8$
71 $[71, 71, 3w + 10]$ $-12$
71 $[71, 71, 3w - 10]$ $-12$
73 $[73, 73, 27w + 118]$ $-11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 4]$ $1$
$3$ $[3, 3, w - 4]$ $1$
$19$ $[19, 19, w]$ $1$