# Properties

 Base field $$\Q(\zeta_{7})^+$$ Weight [2, 2, 2] Level norm 169 Level $[169,13,-2w^{2} + 5w + 3]$ Label 3.3.49.1-169.3-a Dimension 1 CM no Base change no

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## Base field $$\Q(\zeta_{7})^+$$

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

## Form

 Weight [2, 2, 2] Level $[169,13,-2w^{2} + 5w + 3]$ Label 3.3.49.1-169.3-a Dimension 1 Is CM no Is base change no Parent newspace dimension 1

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, 2w^{2} - w - 3]$ $\phantom{-}0$
8 $[8, 2, 2]$ $-1$
13 $[13, 13, -w^{2} - w + 3]$ $-1$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}2$
13 $[13, 13, -2w^{2} + w + 2]$ $\phantom{-}1$
27 $[27, 3, 3]$ $\phantom{-}4$
29 $[29, 29, 3w^{2} - 2w - 4]$ $\phantom{-}2$
29 $[29, 29, 2w^{2} + w - 4]$ $-6$
29 $[29, 29, -w^{2} + 3w + 1]$ $\phantom{-}2$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}2$
41 $[41, 41, 2w^{2} - 3w - 4]$ $\phantom{-}6$
41 $[41, 41, -3w^{2} + w + 3]$ $-6$
43 $[43, 43, w^{2} + 2w - 5]$ $-4$
43 $[43, 43, 2w^{2} + w - 5]$ $-8$
43 $[43, 43, 3w^{2} - 2w - 3]$ $\phantom{-}0$
71 $[71, 71, 4w^{2} - 3w - 5]$ $\phantom{-}4$
71 $[71, 71, 3w^{2} - 4w - 5]$ $-12$
71 $[71, 71, -4w^{2} + w + 5]$ $\phantom{-}8$
83 $[83, 83, w^{2} + w - 7]$ $-8$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13,13,2w^{2} - w - 2]$ $-1$
13 $[13,13,w^{2} + w - 3]$ $1$