# Properties

 Label 3.3.49.1-167.2-a Base field $$\Q(\zeta_{7})^+$$ Weight $[2, 2, 2]$ Level norm $167$ Level $[167,167,w^{2} - 2w - 7]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## 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: $[167,167,w^{2} - 2w - 7]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $3$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{3} - x^{2} - 4x - 1$$
Norm Prime Eigenvalue
7 $[7, 7, 2w^{2} - w - 3]$ $\phantom{-}e$
8 $[8, 2, 2]$ $\phantom{-}2e^{2} - 4e - 4$
13 $[13, 13, -w^{2} - w + 3]$ $-3e^{2} + 4e + 8$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}2e - 2$
13 $[13, 13, -2w^{2} + w + 2]$ $-e^{2} - e + 3$
27 $[27, 3, 3]$ $-3e^{2} + 6e + 6$
29 $[29, 29, 3w^{2} - 2w - 4]$ $\phantom{-}4e - 2$
29 $[29, 29, 2w^{2} + w - 4]$ $\phantom{-}4e^{2} - 6e - 12$
29 $[29, 29, -w^{2} + 3w + 1]$ $-e^{2} + e + 3$
41 $[41, 41, w^{2} - w - 5]$ $-2e^{2} + 4$
41 $[41, 41, 2w^{2} - 3w - 4]$ $\phantom{-}3e^{2} - 7e - 11$
41 $[41, 41, -3w^{2} + w + 3]$ $\phantom{-}4e^{2} - 5e - 8$
43 $[43, 43, w^{2} + 2w - 5]$ $\phantom{-}4e^{2} - 4e - 14$
43 $[43, 43, 2w^{2} + w - 5]$ $-6e^{2} + 10e + 16$
43 $[43, 43, 3w^{2} - 2w - 3]$ $-2e^{2} + 6$
71 $[71, 71, 4w^{2} - 3w - 5]$ $-2e^{2} + 4e + 2$
71 $[71, 71, 3w^{2} - 4w - 5]$ $-5e^{2} + 6e + 12$
71 $[71, 71, -4w^{2} + w + 5]$ $\phantom{-}3e^{2} - 5e + 3$
83 $[83, 83, w^{2} + w - 7]$ $\phantom{-}6e^{2} - 15e - 14$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}2e^{2} - 4e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$167$ $[167,167,w^{2} - 2w - 7]$ $-1$