# Properties

 Label 6.6.703493.1-43.1-a Base field 6.6.703493.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $43$ Level $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.703493.1

Generator $$w$$, with minimal polynomial $$x^{6} - 2x^{5} - 5x^{4} + 11x^{3} + 2x^{2} - 9x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 8x^{3} + 11x^{2} - 42x - 89$$
Norm Prime Eigenvalue
13 $[13, 13, 3w^{5} - 2w^{4} - 17w^{3} + 10w^{2} + 16w - 3]$ $-2e^{3} - 9e^{2} + 9e + 50$
13 $[13, 13, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 3w - 3]$ $-\frac{1}{2}e^{3} - 3e^{2} + e + \frac{35}{2}$
13 $[13, 13, 2w^{5} - w^{4} - 12w^{3} + 4w^{2} + 13w]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{3}{2}e^{3} + 7e^{2} - 7e - \frac{91}{2}$
41 $[41, 41, -2w^{5} + w^{4} + 11w^{3} - 4w^{2} - 10w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{7}{2}e - 10$
41 $[41, 41, -4w^{5} + 3w^{4} + 23w^{3} - 14w^{2} - 22w + 4]$ $-2e^{3} - 11e^{2} + 5e + 64$
41 $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ $\phantom{-}\frac{5}{2}e^{3} + \frac{27}{2}e^{2} - \frac{19}{2}e - 85$
41 $[41, 41, -3w^{5} + w^{4} + 18w^{3} - 4w^{2} - 20w - 1]$ $-2e^{3} - \frac{17}{2}e^{2} + \frac{21}{2}e + \frac{95}{2}$
43 $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ $\phantom{-}1$
43 $[43, 43, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 14w + 5]$ $\phantom{-}\frac{5}{2}e^{3} + 14e^{2} - 8e - \frac{169}{2}$
49 $[49, 7, 2w^{5} - w^{4} - 12w^{3} + 5w^{2} + 13w - 4]$ $\phantom{-}3e^{3} + \frac{29}{2}e^{2} - \frac{21}{2}e - \frac{167}{2}$
64 $[64, 2, -2]$ $\phantom{-}2e^{3} + \frac{17}{2}e^{2} - \frac{21}{2}e - \frac{101}{2}$
71 $[71, 71, -2w^{5} + w^{4} + 12w^{3} - 4w^{2} - 12w - 1]$ $\phantom{-}e^{3} + 3e^{2} - 8e - 16$
71 $[71, 71, -3w^{5} + 2w^{4} + 17w^{3} - 9w^{2} - 15w]$ $-\frac{9}{2}e^{3} - 22e^{2} + 18e + \frac{265}{2}$
83 $[83, 83, 4w^{5} - 2w^{4} - 24w^{3} + 9w^{2} + 26w - 1]$ $-5e^{3} - \frac{45}{2}e^{2} + \frac{49}{2}e + \frac{259}{2}$
83 $[83, 83, -4w^{5} + 2w^{4} + 23w^{3} - 9w^{2} - 23w]$ $\phantom{-}\frac{3}{2}e^{3} + \frac{15}{2}e^{2} - \frac{7}{2}e - 44$
97 $[97, 97, -w^{5} + 7w^{3} + w^{2} - 11w - 3]$ $-\frac{11}{2}e^{3} - 26e^{2} + 21e + \frac{297}{2}$
97 $[97, 97, -2w^{5} + w^{4} + 11w^{3} - 6w^{2} - 9w + 3]$ $\phantom{-}\frac{9}{2}e^{3} + 22e^{2} - 19e - \frac{267}{2}$
113 $[113, 113, -4w^{5} + 2w^{4} + 24w^{3} - 9w^{2} - 27w + 2]$ $\phantom{-}\frac{15}{2}e^{3} + 34e^{2} - 31e - \frac{385}{2}$
113 $[113, 113, 3w^{5} - 2w^{4} - 18w^{3} + 10w^{2} + 20w - 6]$ $-e^{3} - \frac{5}{2}e^{2} + \frac{11}{2}e + \frac{5}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$43$ $[43, 43, 3w^{5} - 2w^{4} - 17w^{3} + 11w^{2} + 16w - 6]$ $-1$