Base field 6.6.300125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[181,181,3w^{5} + w^{4} - 23w^{3} - 22w^{2} + 15w + 10]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 8x^{4} - 86x^{3} - 542x^{2} + 1202x - 537\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
29 | $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ | $-\frac{4525}{186859}e^{4} - \frac{40811}{186859}e^{3} + \frac{367963}{186859}e^{2} + \frac{2825359}{186859}e - \frac{3855040}{186859}$ |
29 | $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ | $\phantom{-}\frac{7505}{186859}e^{4} + \frac{64797}{186859}e^{3} - \frac{570647}{186859}e^{2} - \frac{4379217}{186859}e + \frac{3942982}{186859}$ |
29 | $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ | $\phantom{-}e$ |
29 | $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ | $-\frac{3093}{186859}e^{4} - \frac{37311}{186859}e^{3} + \frac{252507}{186859}e^{2} + \frac{2658312}{186859}e - \frac{3527852}{186859}$ |
29 | $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ | $\phantom{-}\frac{6165}{186859}e^{4} + \frac{48995}{186859}e^{3} - \frac{490794}{186859}e^{2} - \frac{3388300}{186859}e + \frac{4081518}{186859}$ |
29 | $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ | $\phantom{-}\frac{315}{186859}e^{4} + \frac{10687}{186859}e^{3} - \frac{26441}{186859}e^{2} - \frac{896010}{186859}e + \frac{327207}{186859}$ |
41 | $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ | $-\frac{3702}{186859}e^{4} - \frac{33058}{186859}e^{3} + \frac{291169}{186859}e^{2} + \frac{2335149}{186859}e - \frac{3076670}{186859}$ |
41 | $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ | $\phantom{-}\frac{3610}{186859}e^{4} + \frac{45360}{186859}e^{3} - \frac{255566}{186859}e^{2} - \frac{3159019}{186859}e + \frac{1676651}{186859}$ |
41 | $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ | $-\frac{3552}{186859}e^{4} - \frac{36867}{186859}e^{3} + \frac{269680}{186859}e^{2} + \frac{2549137}{186859}e - \frac{3454740}{186859}$ |
41 | $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ | $-\frac{6789}{186859}e^{4} - \frac{63047}{186859}e^{3} + \frac{512919}{186859}e^{2} + \frac{4202264}{186859}e - \frac{4339965}{186859}$ |
41 | $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ | $\phantom{-}\frac{407}{186859}e^{4} - \frac{1615}{186859}e^{3} - \frac{62044}{186859}e^{2} + \frac{114719}{186859}e + \frac{606072}{186859}$ |
41 | $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ | $\phantom{-}\frac{7453}{186859}e^{4} + \frac{63626}{186859}e^{3} - \frac{615518}{186859}e^{2} - \frac{4373673}{186859}e + \frac{5556461}{186859}$ |
49 | $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ | $\phantom{-}\frac{774}{186859}e^{4} + \frac{10243}{186859}e^{3} - \frac{43614}{186859}e^{2} - \frac{786835}{186859}e - \frac{1240777}{186859}$ |
64 | $[64, 2, -2]$ | $-\frac{6924}{186859}e^{4} - \frac{40933}{186859}e^{3} + \frac{550945}{186859}e^{2} + \frac{2664290}{186859}e - \frac{4186561}{186859}$ |
71 | $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ | $-\frac{1646}{186859}e^{4} - \frac{15506}{186859}e^{3} + \frac{153588}{186859}e^{2} + \frac{1167279}{186859}e - \frac{2677894}{186859}$ |
71 | $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ | $\phantom{-}\frac{3237}{186859}e^{4} + \frac{26180}{186859}e^{3} - \frac{243239}{186859}e^{2} - \frac{2026845}{186859}e + \frac{698366}{186859}$ |
71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ | $-\frac{8701}{186859}e^{4} - \frac{91730}{186859}e^{3} + \frac{659768}{186859}e^{2} + \frac{6375319}{186859}e - \frac{6820791}{186859}$ |
71 | $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ | $-\frac{4262}{186859}e^{4} - \frac{31295}{186859}e^{3} + \frac{296651}{186859}e^{2} + \frac{2121752}{186859}e - \frac{606341}{186859}$ |
71 | $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ | $\phantom{-}\frac{896}{186859}e^{4} + \frac{34551}{186859}e^{3} - \frac{46143}{186859}e^{2} - \frac{2610937}{186859}e + \frac{270487}{186859}$ |
71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ | $\phantom{-}\frac{5657}{186859}e^{4} + \frac{51929}{186859}e^{3} - \frac{440441}{186859}e^{2} - \frac{3420382}{186859}e + \frac{3256637}{186859}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$181$ | $[181,181,3w^{5} + w^{4} - 23w^{3} - 22w^{2} + 15w + 10]$ | $-1$ |