Base field \(\Q(\sqrt{101}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[37, 37, 2w - 9]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} + 8x^{21} - 23x^{20} - 337x^{19} - 186x^{18} + 5416x^{17} + 10681x^{16} - 39146x^{15} - 131001x^{14} + 88789x^{13} + 720617x^{12} + 380550x^{11} - 1744637x^{10} - 2332349x^{9} + 1086381x^{8} + 3496605x^{7} + 939941x^{6} - 1774004x^{5} - 1081151x^{4} + 163337x^{3} + 217766x^{2} + 29961x + 648\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 5]$ | $...$ |
| 5 | $[5, 5, -w - 4]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 13 | $[13, 13, w + 3]$ | $...$ |
| 13 | $[13, 13, w - 4]$ | $...$ |
| 17 | $[17, 17, w + 6]$ | $...$ |
| 17 | $[17, 17, -w + 7]$ | $...$ |
| 19 | $[19, 19, w + 2]$ | $...$ |
| 19 | $[19, 19, w - 3]$ | $...$ |
| 23 | $[23, 23, w + 1]$ | $...$ |
| 23 | $[23, 23, -w + 2]$ | $...$ |
| 31 | $[31, 31, -w - 7]$ | $...$ |
| 31 | $[31, 31, w - 8]$ | $...$ |
| 37 | $[37, 37, 2w - 9]$ | $\phantom{-}1$ |
| 37 | $[37, 37, 2w + 7]$ | $...$ |
| 43 | $[43, 43, 4w + 17]$ | $...$ |
| 43 | $[43, 43, 4w - 21]$ | $...$ |
| 47 | $[47, 47, -w - 8]$ | $...$ |
| 47 | $[47, 47, w - 9]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37, 37, 2w - 9]$ | $-1$ |