# Properties

 Label 2.2.21.1-147.1-b Base field $$\Q(\sqrt{21})$$ Weight $[2, 2]$ Level norm $147$ Level $[147, 21, 7w + 7]$ Dimension $1$ CM no Base change yes

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## Base field $$\Q(\sqrt{21})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 5$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[147, 21, 7w + 7]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}0$
5 $[5, 5, w]$ $\phantom{-}2$
5 $[5, 5, w - 1]$ $\phantom{-}2$
7 $[7, 7, -w - 3]$ $\phantom{-}0$
17 $[17, 17, -2w + 3]$ $\phantom{-}0$
17 $[17, 17, -2w - 1]$ $\phantom{-}0$
37 $[37, 37, w + 6]$ $\phantom{-}3$
37 $[37, 37, -w + 7]$ $\phantom{-}3$
41 $[41, 41, 3w + 1]$ $\phantom{-}10$
41 $[41, 41, -3w + 4]$ $\phantom{-}10$
43 $[43, 43, 3w + 8]$ $\phantom{-}5$
43 $[43, 43, 3w - 11]$ $\phantom{-}5$
47 $[47, 47, 3w - 2]$ $\phantom{-}6$
47 $[47, 47, 3w - 1]$ $\phantom{-}6$
59 $[59, 59, -5w - 6]$ $\phantom{-}12$
59 $[59, 59, -4w - 3]$ $\phantom{-}12$
67 $[67, 67, -w - 8]$ $-5$
67 $[67, 67, w - 9]$ $-5$
79 $[79, 79, 2w - 11]$ $-1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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