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: | $[43,43,-w^{4} + 6w^{2} + w - 9]$ |
| Dimension: | $31$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $62$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{31} + 20x^{30} + 69x^{29} - 1216x^{28} - 10617x^{27} + 7869x^{26} + 398250x^{25} + 1084682x^{24} - 5793196x^{23} - 35541733x^{22} + 1773116x^{21} + 460064153x^{20} + 967138181x^{19} - 2188114357x^{18} - 11509514693x^{17} - 7277793170x^{16} + 47680408001x^{15} + 111724956848x^{14} + 11683329910x^{13} - 299188943319x^{12} - 468478057847x^{11} - 153985724083x^{10} + 351290286991x^{9} + 493195737757x^{8} + 268031585322x^{7} + 53753234632x^{6} - 7606439294x^{5} - 5129188237x^{4} - 731136344x^{3} - 21950976x^{2} + 2063488x + 103808\) |
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 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $...$ |
| 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 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $\phantom{-}1$ |
| 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 |
|---|---|---|
| $43$ | $[43,43,-w^{4} + 6w^{2} + w - 9]$ | $-1$ |