# Properties

 Label 4.4.8789.1-17.1-b Base field 4.4.8789.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ Dimension: $7$ CM: no Base change: no Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{7} - x^{6} - 30x^{5} + 8x^{4} + 267x^{3} + 86x^{2} - 500x - 24$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{29}{458}e^{6} + \frac{15}{229}e^{5} - \frac{501}{458}e^{4} - \frac{366}{229}e^{3} + \frac{663}{458}e^{2} + \frac{1237}{458}e + \frac{827}{229}$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $-\frac{89}{916}e^{6} - \frac{21}{916}e^{5} + \frac{414}{229}e^{4} + \frac{151}{229}e^{3} - \frac{4151}{916}e^{2} + \frac{877}{229}e - \frac{507}{229}$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-\frac{25}{458}e^{6} + \frac{61}{458}e^{5} + \frac{212}{229}e^{4} - \frac{561}{229}e^{3} - \frac{919}{458}e^{2} + \frac{2811}{229}e - \frac{784}{229}$
16 $[16, 2, 2]$ $-\frac{53}{916}e^{6} + \frac{111}{916}e^{5} + \frac{298}{229}e^{4} - \frac{471}{229}e^{3} - \frac{6455}{916}e^{2} + \frac{1482}{229}e + \frac{488}{229}$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-1$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}\frac{49}{458}e^{6} + \frac{27}{458}e^{5} - \frac{443}{229}e^{4} - \frac{421}{229}e^{3} + \frac{2131}{458}e^{2} + \frac{591}{229}e + \frac{126}{229}$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{229}e^{6} - \frac{69}{458}e^{5} - \frac{153}{458}e^{4} + \frac{567}{229}e^{3} + \frac{1310}{229}e^{2} - \frac{807}{458}e - \frac{1467}{229}$
19 $[19, 19, w^{2} - w - 2]$ $-\frac{21}{229}e^{6} - \frac{77}{229}e^{5} + \frac{347}{229}e^{4} + \frac{1604}{229}e^{3} - \frac{30}{229}e^{2} - \frac{4007}{229}e + \frac{350}{229}$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-\frac{24}{229}e^{6} - \frac{405}{458}e^{5} + \frac{695}{458}e^{4} + \frac{3796}{229}e^{3} + \frac{1765}{229}e^{2} - \frac{17043}{458}e - \frac{1203}{229}$
29 $[29, 29, w^{2} - w - 3]$ $-\frac{59}{458}e^{6} - \frac{369}{458}e^{5} + \frac{482}{229}e^{4} + \frac{3540}{229}e^{3} + \frac{1257}{458}e^{2} - \frac{8077}{229}e + \frac{1026}{229}$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{115}{458}e^{6} + \frac{269}{458}e^{5} - \frac{1021}{229}e^{4} - \frac{2778}{229}e^{3} + \frac{2945}{458}e^{2} + \frac{5252}{229}e - \frac{424}{229}$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - 9e^{3} - 12e^{2} + \frac{37}{2}e + 11$
47 $[47, 47, w^{3} - 7w - 4]$ $\phantom{-}\frac{5}{458}e^{6} + \frac{171}{458}e^{5} + \frac{95}{229}e^{4} - \frac{1674}{229}e^{3} - \frac{5129}{458}e^{2} + \frac{3972}{229}e + \frac{2172}{229}$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $-\frac{211}{916}e^{6} - \frac{163}{916}e^{5} + \frac{1087}{229}e^{4} + \frac{1063}{229}e^{3} - \frac{16953}{916}e^{2} - \frac{2331}{229}e + \frac{2673}{229}$
61 $[61, 61, -w - 3]$ $\phantom{-}\frac{127}{458}e^{6} + \frac{313}{458}e^{5} - \frac{1022}{229}e^{4} - \frac{3269}{229}e^{3} - \frac{113}{458}e^{2} + \frac{5808}{229}e + \frac{1766}{229}$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}\frac{81}{229}e^{6} + \frac{68}{229}e^{5} - \frac{1502}{229}e^{4} - \frac{1705}{229}e^{3} + \frac{3747}{229}e^{2} + \frac{2010}{229}e + \frac{482}{229}$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $-\frac{101}{916}e^{6} - \frac{65}{916}e^{5} + \frac{529}{229}e^{4} + \frac{511}{229}e^{3} - \frac{8879}{916}e^{2} - \frac{1920}{229}e + \frac{917}{229}$
81 $[81, 3, -3]$ $-\frac{50}{229}e^{6} - \frac{107}{229}e^{5} + \frac{848}{229}e^{4} + \frac{2107}{229}e^{3} - \frac{464}{229}e^{2} - \frac{2038}{229}e - \frac{1304}{229}$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}\frac{66}{229}e^{6} + \frac{255}{458}e^{5} - \frac{2541}{458}e^{4} - \frac{2653}{229}e^{3} + \frac{3333}{229}e^{2} + \frac{10629}{458}e - \frac{1329}{229}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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