Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[21, 21, w^{3} - w^{2} - 5w - 1]$ |
Dimension: | $9$ |
CM: | no |
Base change: | no |
Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{9} - 7x^{8} + 83x^{6} - 101x^{5} - 268x^{4} + 441x^{3} + 175x^{2} - 520x + 200\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 1]$ | $-1$ |
4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $-\frac{229}{470}e^{8} + \frac{1473}{470}e^{7} + \frac{75}{47}e^{6} - \frac{17867}{470}e^{5} + \frac{257}{10}e^{4} + \frac{31156}{235}e^{3} - \frac{50639}{470}e^{2} - \frac{12879}{94}e + \frac{5190}{47}$ |
7 | $[7, 7, w - 2]$ | $-1$ |
11 | $[11, 11, w^{2} - 2w - 4]$ | $-\frac{9}{235}e^{8} + \frac{23}{235}e^{7} + \frac{57}{47}e^{6} - \frac{812}{235}e^{5} - \frac{43}{5}e^{4} + \frac{5937}{235}e^{3} + \frac{2991}{235}e^{2} - \frac{1902}{47}e + \frac{504}{47}$ |
23 | $[23, 23, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{24}{47}e^{8} - \frac{171}{47}e^{7} + \frac{39}{47}e^{6} + \frac{1805}{47}e^{5} - 49e^{4} - \frac{4693}{47}e^{3} + \frac{6594}{47}e^{2} + \frac{2753}{47}e - \frac{3712}{47}$ |
23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}\frac{123}{235}e^{8} - \frac{706}{235}e^{7} - \frac{215}{47}e^{6} + \frac{10314}{235}e^{5} - \frac{19}{5}e^{4} - \frac{46594}{235}e^{3} + \frac{23278}{235}e^{2} + \frac{12505}{47}e - \frac{8768}{47}$ |
27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}\frac{24}{235}e^{8} - \frac{218}{235}e^{7} + \frac{83}{47}e^{6} + \frac{1382}{235}e^{5} - \frac{117}{5}e^{4} + \frac{2968}{235}e^{3} + \frac{9649}{235}e^{2} - \frac{2777}{47}e + \frac{724}{47}$ |
31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $-\frac{273}{235}e^{8} + \frac{1716}{235}e^{7} + \frac{225}{47}e^{6} - \frac{21184}{235}e^{5} + \frac{259}{5}e^{4} + \frac{75984}{235}e^{3} - \frac{56383}{235}e^{2} - \frac{16146}{47}e + \frac{12468}{47}$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{40}{47}e^{8} + \frac{238}{47}e^{7} + \frac{264}{47}e^{6} - \frac{3165}{47}e^{5} + 19e^{4} + \frac{12647}{47}e^{3} - \frac{7089}{47}e^{2} - \frac{14944}{47}e + \frac{10636}{47}$ |
37 | $[37, 37, w^{2} - 2w - 6]$ | $-\frac{142}{235}e^{8} + \frac{859}{235}e^{7} + \frac{163}{47}e^{6} - \frac{11036}{235}e^{5} + \frac{86}{5}e^{4} + \frac{41816}{235}e^{3} - \frac{24092}{235}e^{2} - \frac{9204}{47}e + \frac{6260}{47}$ |
37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{37}{94}e^{8} - \frac{199}{94}e^{7} - \frac{202}{47}e^{6} + \frac{3051}{94}e^{5} + \frac{13}{2}e^{4} - \frac{7214}{47}e^{3} + \frac{4655}{94}e^{2} + \frac{19529}{94}e - \frac{6026}{47}$ |
43 | $[43, 43, w^{2} - 3w - 2]$ | $\phantom{-}\frac{12}{235}e^{8} - \frac{109}{235}e^{7} + \frac{18}{47}e^{6} + \frac{1396}{235}e^{5} - \frac{51}{5}e^{4} - \frac{5566}{235}e^{3} + \frac{9407}{235}e^{2} + \frac{1455}{47}e - \frac{1800}{47}$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{470}e^{8} - \frac{107}{470}e^{7} + \frac{83}{47}e^{6} - \frac{1137}{470}e^{5} - \frac{133}{10}e^{4} + \frac{9031}{235}e^{3} - \frac{19}{470}e^{2} - \frac{7011}{94}e + \frac{2698}{47}$ |
73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $\phantom{-}\frac{103}{470}e^{8} - \frac{681}{470}e^{7} - \frac{5}{47}e^{6} + \frac{7439}{470}e^{5} - \frac{179}{10}e^{4} - \frac{10512}{235}e^{3} + \frac{29533}{470}e^{2} + \frac{3453}{94}e - \frac{2038}{47}$ |
83 | $[83, 83, -w - 3]$ | $\phantom{-}\frac{63}{47}e^{8} - \frac{396}{47}e^{7} - \frac{256}{47}e^{6} + \frac{4838}{47}e^{5} - 58e^{4} - \frac{17072}{47}e^{3} + \frac{12151}{47}e^{2} + \frac{17878}{47}e - \frac{13316}{47}$ |
89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{211}{470}e^{8} + \frac{957}{470}e^{7} + \frac{394}{47}e^{6} - \frac{20003}{470}e^{5} - \frac{357}{10}e^{4} + \frac{59999}{235}e^{3} - \frac{18081}{470}e^{2} - \frac{37557}{94}e + \frac{11078}{47}$ |
89 | $[89, 89, 2w - 1]$ | $-\frac{379}{470}e^{8} + \frac{2483}{470}e^{7} + \frac{80}{47}e^{6} - \frac{28737}{470}e^{5} + \frac{497}{10}e^{4} + \frac{46086}{235}e^{3} - \frac{84919}{470}e^{2} - \frac{17131}{94}e + \frac{7510}{47}$ |
101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $-\frac{14}{47}e^{8} + \frac{135}{47}e^{7} - \frac{293}{47}e^{6} - \frac{814}{47}e^{5} + 78e^{4} - \frac{2076}{47}e^{3} - \frac{6032}{47}e^{2} + \frac{8362}{47}e - \frac{3600}{47}$ |
101 | $[101, 101, 2w^{2} - 3w - 3]$ | $\phantom{-}\frac{79}{470}e^{8} - \frac{463}{470}e^{7} - \frac{70}{47}e^{6} + \frac{7467}{470}e^{5} - \frac{47}{10}e^{4} - \frac{19281}{235}e^{3} + \frac{30929}{470}e^{2} + \frac{12387}{94}e - \frac{5502}{47}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w - 1]$ | $1$ |
$7$ | $[7, 7, w - 2]$ | $1$ |