# Properties

 Label 6.6.300125.1-139.2-a Base field 6.6.300125.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $139$ Level $[139,139,-w^{5} + 7w^{3} + 5w^{2} - 3w]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.300125.1

Generator $$w$$, with minimal polynomial $$x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[139,139,-w^{5} + 7w^{3} + 5w^{2} - 3w]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 6x - 3$$
Norm Prime Eigenvalue
29 $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ $\phantom{-}2e + 5$
29 $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ $\phantom{-}e - 2$
29 $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ $-2e - 7$
29 $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ $\phantom{-}1$
29 $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ $-e - 2$
29 $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ $\phantom{-}e$
41 $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ $-2e - 7$
41 $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ $\phantom{-}2e + 9$
41 $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ $-\frac{1}{2}e - \frac{15}{2}$
41 $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ $\phantom{-}\frac{1}{2}e - \frac{1}{2}$
41 $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ $-\frac{1}{2}e - \frac{15}{2}$
41 $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ $-\frac{1}{2}e - \frac{23}{2}$
49 $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ $-e - 12$
64 $[64, 2, -2]$ $\phantom{-}1$
71 $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ $\phantom{-}\frac{1}{2}e - \frac{7}{2}$
71 $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ $-\frac{3}{2}e - \frac{15}{2}$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ $-6$
71 $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ $-\frac{7}{2}e - \frac{27}{2}$
71 $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ $\phantom{-}\frac{7}{2}e + \frac{15}{2}$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ $\phantom{-}e + 3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$139$ $[139,139,-w^{5} + 7w^{3} + 5w^{2} - 3w]$ $-1$