# Properties

 Label 3.3.49.1-49.1-a Base field $$\Q(\zeta_{7})^+$$ Weight $[2, 2, 2]$ Level norm $49$ Level $[49, 7, -w^{2} + 3w + 3]$ Dimension $1$ CM yes Base change yes

# Related objects

## 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: $[49, 7, -w^{2} + 3w + 3]$ Dimension: $1$ CM: yes Base change: yes 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 $[8, 2, 2]$ $-5$
13 $[13, 13, -w^{2} - w + 3]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}0$
13 $[13, 13, -2w^{2} + w + 2]$ $\phantom{-}0$
27 $[27, 3, 3]$ $\phantom{-}0$
29 $[29, 29, 3w^{2} - 2w - 4]$ $\phantom{-}2$
29 $[29, 29, 2w^{2} + w - 4]$ $\phantom{-}2$
29 $[29, 29, -w^{2} + 3w + 1]$ $\phantom{-}2$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}0$
41 $[41, 41, 2w^{2} - 3w - 4]$ $\phantom{-}0$
41 $[41, 41, -3w^{2} + w + 3]$ $\phantom{-}0$
43 $[43, 43, w^{2} + 2w - 5]$ $-12$
43 $[43, 43, 2w^{2} + w - 5]$ $-12$
43 $[43, 43, 3w^{2} - 2w - 3]$ $-12$
71 $[71, 71, 4w^{2} - 3w - 5]$ $\phantom{-}16$
71 $[71, 71, 3w^{2} - 4w - 5]$ $\phantom{-}16$
71 $[71, 71, -4w^{2} + w + 5]$ $\phantom{-}16$
83 $[83, 83, w^{2} + w - 7]$ $\phantom{-}0$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, 2w^{2} - w - 3]$ $-1$