# Properties

 Label 6.6.1868969.1-34.1-o Base field 6.6.1868969.1 Weight $[2, 2, 2, 2, 2, 2]$ Level norm $34$ Level $[34, 34, -w^{5} + w^{4} + 4w^{3} - 3w^{2} - 2w + 2]$ Dimension $5$ CM no Base change no

# Related objects

• L-function not available

## Base field 6.6.1868969.1

Generator $$w$$, with minimal polynomial $$x^{6} - 6x^{4} - x^{3} + 8x^{2} + x - 2$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[34, 34, -w^{5} + w^{4} + 4w^{3} - 3w^{2} - 2w + 2]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $32$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{5} + 16x^{4} + 80x^{3} + 87x^{2} - 243x - 266$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}e$
17 $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ $-1$
23 $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $-\frac{1}{5}e^{4} - \frac{12}{5}e^{3} - \frac{32}{5}e^{2} + \frac{31}{5}e + \frac{54}{5}$
31 $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ $\phantom{-}\frac{29}{25}e^{4} + \frac{308}{25}e^{3} + \frac{658}{25}e^{2} - \frac{1089}{25}e - \frac{1426}{25}$
32 $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ $\phantom{-}\frac{4}{25}e^{4} + \frac{33}{25}e^{3} + \frac{33}{25}e^{2} - \frac{114}{25}e + \frac{49}{25}$
43 $[43, 43, w^{4} - 5w^{2} + 3]$ $\phantom{-}\frac{4}{25}e^{4} + \frac{58}{25}e^{3} + \frac{183}{25}e^{2} - \frac{189}{25}e - \frac{526}{25}$
47 $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ $-\frac{13}{25}e^{4} - \frac{126}{25}e^{3} - \frac{226}{25}e^{2} + \frac{433}{25}e + \frac{322}{25}$
49 $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ $-\frac{6}{25}e^{4} - \frac{62}{25}e^{3} - \frac{137}{25}e^{2} + \frac{171}{25}e + \frac{264}{25}$
53 $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ $\phantom{-}\frac{26}{25}e^{4} + \frac{277}{25}e^{3} + \frac{577}{25}e^{2} - \frac{1041}{25}e - \frac{1244}{25}$
59 $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ $\phantom{-}\frac{6}{25}e^{4} + \frac{62}{25}e^{3} + \frac{137}{25}e^{2} - \frac{196}{25}e - \frac{464}{25}$
71 $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ $-\frac{46}{25}e^{4} - \frac{492}{25}e^{3} - \frac{1067}{25}e^{2} + \frac{1736}{25}e + \frac{2324}{25}$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-\frac{32}{25}e^{4} - \frac{339}{25}e^{3} - \frac{714}{25}e^{2} + \frac{1212}{25}e + \frac{1408}{25}$
83 $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ $-\frac{26}{25}e^{4} - \frac{277}{25}e^{3} - \frac{577}{25}e^{2} + \frac{1041}{25}e + \frac{1094}{25}$
83 $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ $-\frac{21}{25}e^{4} - \frac{242}{25}e^{3} - \frac{617}{25}e^{2} + \frac{636}{25}e + \frac{1324}{25}$
89 $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ $\phantom{-}\frac{19}{25}e^{4} + \frac{213}{25}e^{3} + \frac{488}{25}e^{2} - \frac{779}{25}e - \frac{1036}{25}$
89 $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ $\phantom{-}\frac{4}{5}e^{4} + \frac{43}{5}e^{3} + \frac{98}{5}e^{2} - \frac{149}{5}e - \frac{296}{5}$
89 $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ $\phantom{-}\frac{16}{25}e^{4} + \frac{182}{25}e^{3} + \frac{407}{25}e^{2} - \frac{781}{25}e - \frac{1004}{25}$
89 $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ $-\frac{6}{25}e^{4} - \frac{62}{25}e^{3} - \frac{162}{25}e^{2} + \frac{71}{25}e + \frac{564}{25}$
101 $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ $-\frac{51}{25}e^{4} - \frac{527}{25}e^{3} - \frac{1052}{25}e^{2} + \frac{2016}{25}e + \frac{2294}{25}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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