# Properties

 Base field $$\Q(\zeta_{7})^+$$ Weight [2, 2, 2] Level norm 83 Level $[83,83,-2w^{2} + w - 2]$ Label 3.3.49.1-83.3-a Dimension 2 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 $[83,83,-2w^{2} + w - 2]$ Label 3.3.49.1-83.3-a Dimension 2 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut 2x$$ $$\mathstrut -\mathstrut 7$$
Norm Prime Eigenvalue
7 $[7, 7, 2w^{2} - w - 3]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-\frac{3}{2}e + \frac{1}{2}$
13 $[13, 13, -w^{2} - w + 3]$ $-\frac{1}{2}e - \frac{5}{2}$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}2e - 2$
13 $[13, 13, -2w^{2} + w + 2]$ $-\frac{1}{2}e - \frac{5}{2}$
27 $[27, 3, 3]$ $-2e + 3$
29 $[29, 29, 3w^{2} - 2w - 4]$ $-2e + 5$
29 $[29, 29, 2w^{2} + w - 4]$ $-e - 3$
29 $[29, 29, -w^{2} + 3w + 1]$ $\phantom{-}\frac{3}{2}e - \frac{5}{2}$
41 $[41, 41, w^{2} - w - 5]$ $-e + 9$
41 $[41, 41, 2w^{2} - 3w - 4]$ $\phantom{-}e - 7$
41 $[41, 41, -3w^{2} + w + 3]$ $\phantom{-}e - 7$
43 $[43, 43, w^{2} + 2w - 5]$ $\phantom{-}e - 5$
43 $[43, 43, 2w^{2} + w - 5]$ $\phantom{-}\frac{7}{2}e - \frac{9}{2}$
43 $[43, 43, 3w^{2} - 2w - 3]$ $\phantom{-}3$
71 $[71, 71, 4w^{2} - 3w - 5]$ $-2e + 6$
71 $[71, 71, 3w^{2} - 4w - 5]$ $\phantom{-}\frac{1}{2}e + \frac{13}{2}$
71 $[71, 71, -4w^{2} + w + 5]$ $-e - 2$
83 $[83, 83, w^{2} + w - 7]$ $\phantom{-}2$
83 $[83, 83, w^{2} - 2w - 6]$ $-\frac{5}{2}e + \frac{3}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
83 $[83,83,-2w^{2} + w - 2]$ $-1$