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: | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ |
| Dimension: | $30$ |
| 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:
| \(x^{30} + 20x^{29} + 72x^{28} - 1066x^{27} - 8530x^{26} + 13486x^{25} + 297621x^{24} + 303636x^{23} - 5379645x^{22} - 12608412x^{21} + 58139649x^{20} + 199042552x^{19} - 396518303x^{18} - 1857005136x^{17} + 1722855885x^{16} + 11386641702x^{15} - 4622292488x^{14} - 47686042304x^{13} + 6949072861x^{12} + 137370506974x^{11} - 4410295335x^{10} - 267650881216x^{9} + 173401904x^{8} + 338045019792x^{7} - 1399445904x^{6} - 256444994176x^{5} + 653026608x^{4} + 102373935904x^{3} + 3666397056x^{2} - 16138829888x - 1927380800\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{4} - 5w^{2} - w + 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w]$ | $...$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $...$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $...$ |
| 27 | $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ | $...$ |
| 27 | $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ | $...$ |
| 29 | $[29, 29, w^{4} - 6w^{2} + w + 8]$ | $...$ |
| 29 | $[29, 29, -w^{4} + 6w^{2} + w - 8]$ | $...$ |
| 41 | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $...$ |
| 41 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ | $...$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ | $...$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $...$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $...$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 7]$ | $...$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ | $...$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ | $...$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $...$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $...$ |
| 113 | $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $-1$ |