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: | $[31,31,w - 8]$ |
| Dimension: | $19$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $45$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{19} + 12x^{18} + 28x^{17} - 189x^{16} - 913x^{15} + 553x^{14} + 8544x^{13} + 5139x^{12} - 38283x^{11} - 41548x^{10} + 96455x^{9} + 123703x^{8} - 148607x^{7} - 183029x^{6} + 145431x^{5} + 131825x^{4} - 84703x^{3} - 35085x^{2} + 20853x - 270\) |
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 | $[31, 31, w - 8]$ | $\phantom{-}1$ |
| 37 | $[37, 37, 2w - 9]$ | $...$ |
| 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 |
|---|---|---|
| $31$ | $[31,31,w - 8]$ | $-1$ |