Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[13,13,-2w - 11]$ |
| Dimension: | $21$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{21} - 39x^{19} - 8x^{18} + 623x^{17} + 245x^{16} - 5224x^{15} - 2945x^{14} + 24469x^{13} + 17581x^{12} - 62802x^{11} - 54375x^{10} + 79882x^{9} + 83045x^{8} - 38167x^{7} - 55284x^{6} - 584x^{5} + 12950x^{4} + 3074x^{3} - 259x^{2} - 73x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $...$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 11 | $[11, 11, -3w - 17]$ | $...$ |
| 11 | $[11, 11, 3w - 20]$ | $...$ |
| 13 | $[13, 13, 2w - 13]$ | $...$ |
| 13 | $[13, 13, 2w + 11]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w + 7]$ | $...$ |
| 17 | $[17, 17, -w + 8]$ | $...$ |
| 19 | $[19, 19, -w - 4]$ | $...$ |
| 19 | $[19, 19, -w + 5]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 31 | $[31, 31, -6w - 35]$ | $...$ |
| 31 | $[31, 31, -6w + 41]$ | $...$ |
| 37 | $[37, 37, -w - 1]$ | $...$ |
| 37 | $[37, 37, w - 2]$ | $...$ |
| 47 | $[47, 47, 3w + 16]$ | $...$ |
| 47 | $[47, 47, -3w + 19]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 67 | $[67, 67, 3w - 22]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,-2w - 11]$ | $-1$ |