Base field 4.4.14197.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[37, 37, w^{3} - 4w - 1]$ |
| 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:
| \(x^{27} + 15x^{26} + x^{25} - 1030x^{24} - 3852x^{23} + 25281x^{22} + 165367x^{21} - 207059x^{20} - 3172041x^{19} - 1819302x^{18} + 33115647x^{17} + 52638633x^{16} - 198589839x^{15} - 481359217x^{14} + 682780467x^{13} + 2400554805x^{12} - 1192078547x^{11} - 7252113837x^{10} + 224804689x^{9} + 13520560536x^{8} + 3211622752x^{7} - 14973232365x^{6} - 6257331647x^{5} + 8674904406x^{4} + 5107977920x^{3} - 1643369929x^{2} - 1624253462x - 287802481\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 5w - 2]$ | $...$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $...$ |
| 13 | $[13, 13, -w + 2]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, w^{3} - w^{2} - 5w]$ | $...$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 6w]$ | $...$ |
| 23 | $[23, 23, -w^{2} + w + 3]$ | $...$ |
| 29 | $[29, 29, w^{3} - 5w]$ | $...$ |
| 31 | $[31, 31, w^{3} - 6w - 1]$ | $...$ |
| 31 | $[31, 31, w^{2} - 2]$ | $...$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $\phantom{-}1$ |
| 37 | $[37, 37, w^{3} - 7w - 4]$ | $...$ |
| 37 | $[37, 37, w^{2} - 3]$ | $...$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $...$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w - 1]$ | $...$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 5w - 4]$ | $...$ |
| 53 | $[53, 53, w^{3} - 6w]$ | $...$ |
| 61 | $[61, 61, w^{3} - w^{2} - 7w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, w^{3} - 4w - 1]$ | $-1$ |