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 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $-1$ |
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 |
---|---|---|
$43$ | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $1$ |