Base field 6.6.1997632.1
Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[41, 41, w^{3} - w^{2} - 3w + 4]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 38x^{8} + 449x^{6} - 2024x^{4} + 3504x^{2} - 1728\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
8 | $[8, 2, w^{4} - 5w^{2} - w + 4]$ | $\phantom{-}e$ |
13 | $[13, 13, w]$ | $\phantom{-}\frac{37}{4560}e^{8} - \frac{661}{2280}e^{6} + \frac{731}{240}e^{4} - \frac{634}{57}e^{2} + \frac{1116}{95}$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}\frac{5}{2736}e^{9} - \frac{77}{1368}e^{7} + \frac{49}{144}e^{5} + \frac{1609}{1368}e^{3} - \frac{355}{57}e$ |
13 | $[13, 13, w^{2} + w - 3]$ | $-\frac{17}{4560}e^{9} + \frac{37}{285}e^{7} - \frac{301}{240}e^{5} + \frac{185}{57}e^{3} + \frac{153}{190}e$ |
27 | $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ | $-\frac{1}{57}e^{8} + \frac{73}{114}e^{6} - \frac{83}{12}e^{4} + \frac{5645}{228}e^{2} - \frac{479}{19}$ |
27 | $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ | $\phantom{-}\frac{13}{456}e^{8} - \frac{223}{228}e^{6} + \frac{221}{24}e^{4} - \frac{5575}{228}e^{2} + \frac{244}{19}$ |
29 | $[29, 29, w^{4} - 6w^{2} + w + 8]$ | $\phantom{-}\frac{61}{13680}e^{9} - \frac{1213}{6840}e^{7} + \frac{1613}{720}e^{5} - \frac{14501}{1368}e^{3} + \frac{4048}{285}e$ |
29 | $[29, 29, -w^{4} + 6w^{2} + w - 8]$ | $\phantom{-}\frac{13}{6840}e^{9} - \frac{503}{6840}e^{7} + \frac{329}{360}e^{5} - \frac{6049}{1368}e^{3} + \frac{3091}{570}e$ |
41 | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $\phantom{-}1$ |
41 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $\phantom{-}\frac{31}{4560}e^{9} - \frac{523}{2280}e^{7} + \frac{503}{240}e^{5} - \frac{2387}{456}e^{3} + \frac{481}{190}e$ |
41 | $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ | $\phantom{-}\frac{3}{1520}e^{9} - \frac{69}{760}e^{7} + \frac{109}{80}e^{5} - \frac{543}{76}e^{3} + \frac{577}{95}e$ |
41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ | $-\frac{1}{95}e^{8} + \frac{273}{760}e^{6} - \frac{139}{40}e^{4} + \frac{939}{76}e^{2} - \frac{1779}{95}$ |
43 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $-\frac{421}{27360}e^{9} + \frac{7783}{13680}e^{7} - \frac{9083}{1440}e^{5} + \frac{32995}{1368}e^{3} - \frac{15253}{570}e$ |
43 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $\phantom{-}\frac{1}{1368}e^{9} - \frac{65}{1368}e^{7} + \frac{71}{72}e^{5} - \frac{10061}{1368}e^{3} + \frac{1597}{114}e$ |
49 | $[49, 7, w^{4} - 5w^{2} + 7]$ | $-\frac{13}{912}e^{8} + \frac{223}{456}e^{6} - \frac{215}{48}e^{4} + \frac{533}{57}e^{2} - \frac{65}{19}$ |
97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ | $-\frac{13}{1520}e^{9} + \frac{51}{190}e^{7} - \frac{159}{80}e^{5} + \frac{279}{152}e^{3} + \frac{161}{190}e$ |
97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ | $-\frac{217}{27360}e^{9} + \frac{4231}{13680}e^{7} - \frac{5471}{1440}e^{5} + \frac{24115}{1368}e^{3} - \frac{15031}{570}e$ |
97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-\frac{619}{27360}e^{9} + \frac{10627}{13680}e^{7} - \frac{10577}{1440}e^{5} + \frac{26767}{1368}e^{3} - \frac{2051}{285}e$ |
97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $\phantom{-}\frac{83}{5472}e^{9} - \frac{1415}{2736}e^{7} + \frac{1393}{288}e^{5} - \frac{17887}{1368}e^{3} + \frac{388}{57}e$ |
113 | $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ | $\phantom{-}\frac{119}{9120}e^{9} - \frac{2357}{4560}e^{7} + \frac{3097}{480}e^{5} - \frac{13217}{456}e^{3} + \frac{6067}{190}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$41$ | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $-1$ |