Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[19,19,-w + 6]$ |
| Dimension: | $33$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{33} + 14x^{32} + 19x^{31} - 602x^{30} - 2697x^{29} + 8646x^{28} + 74602x^{27} - 5947x^{26} - 1026307x^{25} - 1351051x^{24} + 8117420x^{23} + 19619818x^{22} - 36637524x^{21} - 146030461x^{20} + 70082299x^{19} + 673278148x^{18} + 163882435x^{17} - 2020460543x^{16} - 1458370712x^{15} + 3957086135x^{14} + 4418395775x^{13} - 4897863060x^{12} - 7587620519x^{11} + 3524241168x^{10} + 7923621173x^{9} - 1170611350x^{8} - 5016700788x^{7} - 13154880x^{6} + 1866514983x^{5} + 92029467x^{4} - 376004169x^{3} - 9448781x^{2} + 31622528x - 1348627\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $...$ |
| 7 | $[7, 7, w + 6]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 19 | $[19, 19, w + 5]$ | $...$ |
| 19 | $[19, 19, w - 6]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w + 8]$ | $...$ |
| 23 | $[23, 23, -w + 9]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 29 | $[29, 29, -w - 4]$ | $...$ |
| 29 | $[29, 29, w - 5]$ | $...$ |
| 37 | $[37, 37, -w - 3]$ | $...$ |
| 37 | $[37, 37, w - 4]$ | $...$ |
| 41 | $[41, 41, -w - 9]$ | $...$ |
| 41 | $[41, 41, w - 10]$ | $...$ |
| 43 | $[43, 43, -w - 2]$ | $...$ |
| 43 | $[43, 43, w - 3]$ | $...$ |
| 47 | $[47, 47, -w - 1]$ | $...$ |
| 47 | $[47, 47, w - 2]$ | $...$ |
| 53 | $[53, 53, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w + 6]$ | $-1$ |