Base field 4.4.14197.1
Generator \(w\), with minimal polynomial \(x^4 - 6 x^2 - 3 x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[37, 37, w^3 - 4 w - 1]$ |
| Dimension: | $27$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{27} - 15 x^{26} + x^{25} + 1030 x^{24} - 3852 x^{23} - 25281 x^{22} + 165367 x^{21} + 207059 x^{20} - 3172041 x^{19} + 1819302 x^{18} + 33115647 x^{17} - 52638633 x^{16} - 198589839 x^{15} + 481359217 x^{14} + 682780467 x^{13} - 2400554805 x^{12} - 1192078547 x^{11} + 7252113837 x^{10} + 224804689 x^9 - 13520560536 x^8 + 3211622752 x^7 + 14973232365 x^6 - 6257331647 x^5 - 8674904406 x^4 + 5107977920 x^3 + 1643369929 x^2 - 1624253462 x + 287802481\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^3 - 5 w - 2]$ | $...$ |
| 9 | $[9, 3, w^3 - w^2 - 4 w]$ | $...$ |
| 13 | $[13, 13, -w + 2]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, w^3 - w^2 - 5 w]$ | $...$ |
| 19 | $[19, 19, -w^3 + w^2 + 6 w]$ | $...$ |
| 23 | $[23, 23, -w^2 + w + 3]$ | $...$ |
| 29 | $[29, 29, w^3 - 5 w]$ | $...$ |
| 31 | $[31, 31, w^3 - 6 w - 1]$ | $...$ |
| 31 | $[31, 31, w^2 - 2]$ | $...$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w^3 - 4 w - 1]$ | $-1$ |
| 37 | $[37, 37, w^3 - 7 w - 4]$ | $...$ |
| 37 | $[37, 37, w^2 - 3]$ | $...$ |
| 43 | $[43, 43, w^2 + w - 3]$ | $...$ |
| 43 | $[43, 43, w^3 - w^2 - 5 w - 1]$ | $...$ |
| 47 | $[47, 47, -w^3 + w^2 + 5 w - 4]$ | $...$ |
| 53 | $[53, 53, w^3 - 6 w]$ | $...$ |
| 61 | $[61, 61, w^3 - w^2 - 7 w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, w^3 - 4 w - 1]$ | $1$ |