# Properties

 Base field 6.6.300125.1 Weight [2, 2, 2, 2, 2, 2] Level norm 41 Level $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ Label 6.6.300125.1-41.1-a Dimension 3 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 $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ Label 6.6.300125.1-41.1-a Dimension 3 Is CM no Is base change no Parent newspace dimension 3

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} - 10x^{2} + 12x + 24$$
Norm Prime Eigenvalue
29 $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ $\phantom{-}\frac{1}{2}e^{2} - 5e + 4$
29 $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ $\phantom{-}\frac{3}{4}e^{2} - \frac{11}{2}e$
29 $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ $-\frac{1}{2}e^{2} + 2e + 8$
29 $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ $-\frac{1}{4}e^{2} + \frac{3}{2}e + 4$
29 $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}e$
29 $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ $\phantom{-}e$
41 $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ $-1$
41 $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ $\phantom{-}\frac{1}{4}e^{2} - \frac{3}{2}e - 6$
41 $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ $-\frac{1}{2}e^{2} + 5e - 6$
41 $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ $\phantom{-}\frac{1}{4}e^{2} - 3e + 7$
41 $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ $\phantom{-}\frac{1}{2}e^{2} - 2e - 10$
41 $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{4}e^{2} - 3e + 7$
49 $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ $-e + 6$
64 $[64, 2, -2]$ $-\frac{1}{4}e^{2} + 4e - 4$
71 $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ $-\frac{3}{4}e^{2} + \frac{13}{2}e - 2$
71 $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ $-e^{2} + 7e + 2$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ $\phantom{-}\frac{1}{4}e^{2} - 2e + 7$
71 $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ $-\frac{1}{4}e^{2} + \frac{1}{2}e + 2$
71 $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ $\phantom{-}\frac{3}{4}e^{2} - \frac{13}{2}e - 2$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ $-\frac{3}{4}e^{2} + \frac{13}{2}e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
41 $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ $1$