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:
\(x^{7} - x^{6} - 30x^{5} + 8x^{4} + 267x^{3} + 86x^{2} - 500x - 24\) |
Show full eigenvalues Hide large eigenvalues
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 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $\phantom{-}\frac{66}{229}e^{6} + \frac{255}{458}e^{5} - \frac{2541}{458}e^{4} - \frac{2653}{229}e^{3} + \frac{3333}{229}e^{2} + \frac{10629}{458}e - \frac{1329}{229}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $1$ |