# Properties

 Base field $$\Q(\zeta_{7})^+$$ Weight [2, 2, 2] Level norm 125 Level $[125, 5, -5]$ Label 3.3.49.1-125.1-a Dimension 2 CM no Base change yes

# 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 $[125, 5, -5]$ Label 3.3.49.1-125.1-a Dimension 2 Is CM no Is base change yes Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut 2x$$ $$\mathstrut -\mathstrut 17$$
Norm Prime Eigenvalue
7 $[7, 7, 2w^{2} - w - 3]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-\frac{1}{3}e + \frac{4}{3}$
13 $[13, 13, -w^{2} - w + 3]$ $-\frac{2}{3}e - \frac{4}{3}$
13 $[13, 13, -w^{2} + 2w + 2]$ $-\frac{2}{3}e - \frac{4}{3}$
13 $[13, 13, -2w^{2} + w + 2]$ $-\frac{2}{3}e - \frac{4}{3}$
27 $[27, 3, 3]$ $\phantom{-}\frac{4}{3}e - \frac{10}{3}$
29 $[29, 29, 3w^{2} - 2w - 4]$ $-1$
29 $[29, 29, 2w^{2} + w - 4]$ $-1$
29 $[29, 29, -w^{2} + 3w + 1]$ $-1$
41 $[41, 41, w^{2} - w - 5]$ $-\frac{2}{3}e - \frac{13}{3}$
41 $[41, 41, 2w^{2} - 3w - 4]$ $-\frac{2}{3}e - \frac{13}{3}$
41 $[41, 41, -3w^{2} + w + 3]$ $-\frac{2}{3}e - \frac{13}{3}$
43 $[43, 43, w^{2} + 2w - 5]$ $-\frac{1}{3}e + \frac{16}{3}$
43 $[43, 43, 2w^{2} + w - 5]$ $-\frac{1}{3}e + \frac{16}{3}$
43 $[43, 43, 3w^{2} - 2w - 3]$ $-\frac{1}{3}e + \frac{16}{3}$
71 $[71, 71, 4w^{2} - 3w - 5]$ $\phantom{-}2e - 6$
71 $[71, 71, 3w^{2} - 4w - 5]$ $\phantom{-}2e - 6$
71 $[71, 71, -4w^{2} + w + 5]$ $\phantom{-}2e - 6$
83 $[83, 83, w^{2} + w - 7]$ $\phantom{-}3e - 2$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}3e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
125 $[125, 5, -5]$ $-1$